Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.6% → 82.5%

Time: 30.3s

Alternatives: 25

Speedup: 0.5×

• 57.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;t_1 + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;t_1 + j \cdot \mathsf{fma}\left(a, c, y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))))
   (if (<= (+ t_1 (* j (- (* a c) (* y i)))) INFINITY)
     (+ t_1 (* j (fma a c (* y (- i)))))
     (* a (- (* c j) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double tmp;
	if ((t_1 + (j * ((a * c) - (y * i)))) <= ((double) INFINITY)) {
		tmp = t_1 + (j * fma(a, c, (y * -i)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i)))) <= Inf)
		tmp = Float64(t_1 + Float64(j * fma(a, c, Float64(y * Float64(-i)))));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 + N[(j * N[(a * c + N[(y * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 91.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 91.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 91.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 91.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 91.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 91.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. fma-neg 91.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \color{blue}{\mathsf{fma}\left(a, c, -y \cdot i\right)} \]

      2. *-commutative 91.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \mathsf{fma}\left(a, c, -\color{blue}{i \cdot y}\right) \]

   5. Applied egg-rr 91.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \color{blue}{\mathsf{fma}\left(a, c, -i \cdot y\right)} \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 0.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 0.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 0.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 0.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 9.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 9.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 9.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 9.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 9.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 9.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 9.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 20.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 49.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 49.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 49.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 49.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \mathsf{fma}\left(a, c, y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 2: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* a (- (* c j) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 91.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 0.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 0.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 0.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 0.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 9.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 9.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 9.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 9.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 9.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 9.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 9.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 20.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 49.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 49.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 49.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 49.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 3: 57.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + t_1\\ t_4 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_5 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.2 \cdot 10^{+258}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{+128}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-200}:\\ \;\;\;\;t_4 + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-24}:\\ \;\;\;\;t_2 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+162}:\\ \;\;\;\;t_1 + t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j)))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 t_1))
        (t_4 (* b (- (* t i) (* z c))))
        (t_5 (* c (- (* a j) (* z b)))))
   (if (<= c -2.2e+258)
     t_5
     (if (<= c -4.4e+169)
       t_3
       (if (<= c -4.2e+128)
         t_5
         (if (<= c -1.5e+27)
           t_3
           (if (<= c -1.25e-200)
             (+ t_4 (* y (* x z)))
             (if (<= c 5.8e-290)
               (* t (- (* b i) (* x a)))
               (if (<= c 9.5e-24)
                 (- t_2 (* i (* y j)))
                 (if (<= c 1.6e+162) (+ t_1 t_4) t_5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + t_1;
	double t_4 = b * ((t * i) - (z * c));
	double t_5 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.2e+258) {
		tmp = t_5;
	} else if (c <= -4.4e+169) {
		tmp = t_3;
	} else if (c <= -4.2e+128) {
		tmp = t_5;
	} else if (c <= -1.5e+27) {
		tmp = t_3;
	} else if (c <= -1.25e-200) {
		tmp = t_4 + (y * (x * z));
	} else if (c <= 5.8e-290) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 9.5e-24) {
		tmp = t_2 - (i * (y * j));
	} else if (c <= 1.6e+162) {
		tmp = t_1 + t_4;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = c * (a * j)
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + t_1
    t_4 = b * ((t * i) - (z * c))
    t_5 = c * ((a * j) - (z * b))
    if (c <= (-2.2d+258)) then
        tmp = t_5
    else if (c <= (-4.4d+169)) then
        tmp = t_3
    else if (c <= (-4.2d+128)) then
        tmp = t_5
    else if (c <= (-1.5d+27)) then
        tmp = t_3
    else if (c <= (-1.25d-200)) then
        tmp = t_4 + (y * (x * z))
    else if (c <= 5.8d-290) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 9.5d-24) then
        tmp = t_2 - (i * (y * j))
    else if (c <= 1.6d+162) then
        tmp = t_1 + t_4
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + t_1;
	double t_4 = b * ((t * i) - (z * c));
	double t_5 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.2e+258) {
		tmp = t_5;
	} else if (c <= -4.4e+169) {
		tmp = t_3;
	} else if (c <= -4.2e+128) {
		tmp = t_5;
	} else if (c <= -1.5e+27) {
		tmp = t_3;
	} else if (c <= -1.25e-200) {
		tmp = t_4 + (y * (x * z));
	} else if (c <= 5.8e-290) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 9.5e-24) {
		tmp = t_2 - (i * (y * j));
	} else if (c <= 1.6e+162) {
		tmp = t_1 + t_4;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + t_1
	t_4 = b * ((t * i) - (z * c))
	t_5 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -2.2e+258:
		tmp = t_5
	elif c <= -4.4e+169:
		tmp = t_3
	elif c <= -4.2e+128:
		tmp = t_5
	elif c <= -1.5e+27:
		tmp = t_3
	elif c <= -1.25e-200:
		tmp = t_4 + (y * (x * z))
	elif c <= 5.8e-290:
		tmp = t * ((b * i) - (x * a))
	elif c <= 9.5e-24:
		tmp = t_2 - (i * (y * j))
	elif c <= 1.6e+162:
		tmp = t_1 + t_4
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(a * j))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + t_1)
	t_4 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_5 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.2e+258)
		tmp = t_5;
	elseif (c <= -4.4e+169)
		tmp = t_3;
	elseif (c <= -4.2e+128)
		tmp = t_5;
	elseif (c <= -1.5e+27)
		tmp = t_3;
	elseif (c <= -1.25e-200)
		tmp = Float64(t_4 + Float64(y * Float64(x * z)));
	elseif (c <= 5.8e-290)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 9.5e-24)
		tmp = Float64(t_2 - Float64(i * Float64(y * j)));
	elseif (c <= 1.6e+162)
		tmp = Float64(t_1 + t_4);
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (a * j);
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + t_1;
	t_4 = b * ((t * i) - (z * c));
	t_5 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.2e+258)
		tmp = t_5;
	elseif (c <= -4.4e+169)
		tmp = t_3;
	elseif (c <= -4.2e+128)
		tmp = t_5;
	elseif (c <= -1.5e+27)
		tmp = t_3;
	elseif (c <= -1.25e-200)
		tmp = t_4 + (y * (x * z));
	elseif (c <= 5.8e-290)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 9.5e-24)
		tmp = t_2 - (i * (y * j));
	elseif (c <= 1.6e+162)
		tmp = t_1 + t_4;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.2e+258], t$95$5, If[LessEqual[c, -4.4e+169], t$95$3, If[LessEqual[c, -4.2e+128], t$95$5, If[LessEqual[c, -1.5e+27], t$95$3, If[LessEqual[c, -1.25e-200], N[(t$95$4 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e-290], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e-24], N[(t$95$2 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e+162], N[(t$95$1 + t$95$4), $MachinePrecision], t$95$5]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -2.19999999999999983e258 or -4.4e169 < c < -4.1999999999999999e128 or 1.6000000000000001e162 < c

   1. Initial program 55.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 55.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 55.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 55.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 55.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 55.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 58.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 58.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 58.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 58.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 58.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 58.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 58.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 65.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around inf 82.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 74.9%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 74.9%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 74.9%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 74.9%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 74.9%

         \[\leadsto c \cdot \left(a \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      6. distribute-lft-out-- 82.1%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 82.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -2.19999999999999983e258 < c < -4.4e169 or -4.1999999999999999e128 < c < -1.49999999999999988e27

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 66.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in i around 0 79.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in b around 0 86.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)} \]

   if -1.49999999999999988e27 < c < -1.24999999999999998e-200

   1. Initial program 89.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 89.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 89.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 89.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 89.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 89.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 89.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 89.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 89.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 89.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 89.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 89.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 89.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 84.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 84.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      2. mul-1-neg 84.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      3. distribute-rgt-neg-in 84.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. mul-1-neg 84.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. distribute-lft-in 87.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. mul-1-neg 87.0%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. unsub-neg 87.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. *-commutative 87.0%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 87.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in j around 0 72.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

   if -1.24999999999999998e-200 < c < 5.79999999999999989e-290

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 84.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 84.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 84.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 84.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 84.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 84.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 84.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 84.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 74.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around 0 51.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 51.8%

         \[\leadsto i \cdot \left(t \cdot b\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      2. unsub-neg 51.8%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) - a \cdot \left(t \cdot x\right)} \]

      3. *-commutative 51.8%

         \[\leadsto i \cdot \left(t \cdot b\right) - a \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 61.7%

         \[\leadsto i \cdot \left(t \cdot b\right) - \color{blue}{\left(a \cdot x\right) \cdot t} \]

      5. cancel-sign-sub-inv 61.7%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(-a \cdot x\right) \cdot t} \]

      6. *-commutative 61.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} + \left(-a \cdot x\right) \cdot t \]

      7. associate-*l* 74.1%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} + \left(-a \cdot x\right) \cdot t \]

      8. distribute-rgt-in 74.1%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b + \left(-a \cdot x\right)\right)} \]

      9. unsub-neg 74.1%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   7. Simplified 74.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if 5.79999999999999989e-290 < c < 9.50000000000000029e-24

   1. Initial program 87.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 87.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 87.3%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 87.3%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 87.3%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 87.3%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 88.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 88.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 88.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 88.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 88.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 88.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around 0 81.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 81.0%

         \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + i \cdot \left(t \cdot b\right)} \]

      2. remove-double-neg 81.0%

         \[\leadsto \left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(-i \cdot \left(t \cdot b\right)\right)\right)} \]

      3. mul-1-neg 81.0%

         \[\leadsto \left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-\color{blue}{-1 \cdot \left(i \cdot \left(t \cdot b\right)\right)}\right) \]

      4. associate-+l+ 81.0%

         \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right)\right)} \]

      5. +-commutative 81.0%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \color{blue}{\left(\left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      6. mul-1-neg 81.0%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(\left(-\color{blue}{\left(-i \cdot \left(t \cdot b\right)\right)}\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]

      7. remove-double-neg 81.0%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(\color{blue}{i \cdot \left(t \cdot b\right)} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]

      8. mul-1-neg 81.0%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) \]

      9. associate-*r* 82.6%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \left(-\color{blue}{\left(y \cdot i\right) \cdot j}\right)\right) \]

      10. *-commutative 82.6%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \left(-\color{blue}{\left(i \cdot y\right)} \cdot j\right)\right) \]

      11. associate-*r* 81.1%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \left(-\color{blue}{i \cdot \left(y \cdot j\right)}\right)\right) \]

      12. distribute-rgt-neg-in 81.1%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \color{blue}{i \cdot \left(-y \cdot j\right)}\right) \]

      13. mul-1-neg 81.1%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right)}\right) \]

      14. distribute-lft-in 82.7%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      15. mul-1-neg 82.7%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      16. unsub-neg 82.7%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 82.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in b around 0 71.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 71.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right) \]

      2. mul-1-neg 71.8%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)} \]

      3. associate-*r* 73.4%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(-\color{blue}{\left(i \cdot y\right) \cdot j}\right) \]

      4. distribute-lft-neg-in 73.4%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(-i \cdot y\right) \cdot j} \]

      5. cancel-sign-sub-inv 73.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - \left(i \cdot y\right) \cdot j} \]

      6. associate-*r* 71.8%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - \color{blue}{i \cdot \left(y \cdot j\right)} \]

   9. Simplified 71.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - i \cdot \left(y \cdot j\right)} \]

   if 9.50000000000000029e-24 < c < 1.6000000000000001e162

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.2%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.2%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.2%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.2%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 76.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 76.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around 0 67.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.2%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(c \cdot \left(a \cdot j\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]

      2. associate-+r+ 67.2%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      3. +-commutative 67.2%

         \[\leadsto \color{blue}{\left(c \cdot \left(a \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. *-commutative 67.2%

         \[\leadsto \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. associate-*r* 67.2%

         \[\leadsto \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. *-commutative 67.2%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. associate-*r* 67.2%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. distribute-rgt-in 74.3%

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      9. mul-1-neg 74.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      10. unsub-neg 74.3%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      11. *-commutative 74.3%

          \[\leadsto a \cdot \left(c \cdot j - t \cdot x\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in x around 0 69.7%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+258}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{+128}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+162}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 4: 62.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 - i \cdot \left(y \cdot j\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right) + t_1\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+208}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+88}:\\ \;\;\;\;t_2 + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+44}:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq 520000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+148}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (- t_2 (* i (* y j))))
        (t_4 (+ (* a (- (* c j) (* x t))) t_1)))
   (if (<= x -7.5e+208)
     t_3
     (if (<= x -1.55e+88)
       (+ t_2 (* c (* a j)))
       (if (<= x -7e+44)
         (- t_1 (* j (* y i)))
         (if (<= x 520000000.0)
           t_4
           (if (<= x 1.02e+99)
             (* y (- (* x z) (* i j)))
             (if (<= x 7.8e+148) t_4 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 - (i * (y * j));
	double t_4 = (a * ((c * j) - (x * t))) + t_1;
	double tmp;
	if (x <= -7.5e+208) {
		tmp = t_3;
	} else if (x <= -1.55e+88) {
		tmp = t_2 + (c * (a * j));
	} else if (x <= -7e+44) {
		tmp = t_1 - (j * (y * i));
	} else if (x <= 520000000.0) {
		tmp = t_4;
	} else if (x <= 1.02e+99) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 7.8e+148) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 - (i * (y * j))
    t_4 = (a * ((c * j) - (x * t))) + t_1
    if (x <= (-7.5d+208)) then
        tmp = t_3
    else if (x <= (-1.55d+88)) then
        tmp = t_2 + (c * (a * j))
    else if (x <= (-7d+44)) then
        tmp = t_1 - (j * (y * i))
    else if (x <= 520000000.0d0) then
        tmp = t_4
    else if (x <= 1.02d+99) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 7.8d+148) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 - (i * (y * j));
	double t_4 = (a * ((c * j) - (x * t))) + t_1;
	double tmp;
	if (x <= -7.5e+208) {
		tmp = t_3;
	} else if (x <= -1.55e+88) {
		tmp = t_2 + (c * (a * j));
	} else if (x <= -7e+44) {
		tmp = t_1 - (j * (y * i));
	} else if (x <= 520000000.0) {
		tmp = t_4;
	} else if (x <= 1.02e+99) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 7.8e+148) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 - (i * (y * j))
	t_4 = (a * ((c * j) - (x * t))) + t_1
	tmp = 0
	if x <= -7.5e+208:
		tmp = t_3
	elif x <= -1.55e+88:
		tmp = t_2 + (c * (a * j))
	elif x <= -7e+44:
		tmp = t_1 - (j * (y * i))
	elif x <= 520000000.0:
		tmp = t_4
	elif x <= 1.02e+99:
		tmp = y * ((x * z) - (i * j))
	elif x <= 7.8e+148:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 - Float64(i * Float64(y * j)))
	t_4 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + t_1)
	tmp = 0.0
	if (x <= -7.5e+208)
		tmp = t_3;
	elseif (x <= -1.55e+88)
		tmp = Float64(t_2 + Float64(c * Float64(a * j)));
	elseif (x <= -7e+44)
		tmp = Float64(t_1 - Float64(j * Float64(y * i)));
	elseif (x <= 520000000.0)
		tmp = t_4;
	elseif (x <= 1.02e+99)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 7.8e+148)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 - (i * (y * j));
	t_4 = (a * ((c * j) - (x * t))) + t_1;
	tmp = 0.0;
	if (x <= -7.5e+208)
		tmp = t_3;
	elseif (x <= -1.55e+88)
		tmp = t_2 + (c * (a * j));
	elseif (x <= -7e+44)
		tmp = t_1 - (j * (y * i));
	elseif (x <= 520000000.0)
		tmp = t_4;
	elseif (x <= 1.02e+99)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 7.8e+148)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[x, -7.5e+208], t$95$3, If[LessEqual[x, -1.55e+88], N[(t$95$2 + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e+44], N[(t$95$1 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 520000000.0], t$95$4, If[LessEqual[x, 1.02e+99], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+148], t$95$4, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.49999999999999964e208 or 7.80000000000000004e148 < x

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around 0 78.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 78.3%

         \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + i \cdot \left(t \cdot b\right)} \]

      2. remove-double-neg 78.3%

         \[\leadsto \left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(-i \cdot \left(t \cdot b\right)\right)\right)} \]

      3. mul-1-neg 78.3%

         \[\leadsto \left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-\color{blue}{-1 \cdot \left(i \cdot \left(t \cdot b\right)\right)}\right) \]

      4. associate-+l+ 78.3%

         \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right)\right)} \]

      5. +-commutative 78.3%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \color{blue}{\left(\left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      6. mul-1-neg 78.3%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(\left(-\color{blue}{\left(-i \cdot \left(t \cdot b\right)\right)}\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]

      7. remove-double-neg 78.3%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(\color{blue}{i \cdot \left(t \cdot b\right)} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]

      8. mul-1-neg 78.3%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) \]

      9. associate-*r* 81.9%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \left(-\color{blue}{\left(y \cdot i\right) \cdot j}\right)\right) \]

      10. *-commutative 81.9%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \left(-\color{blue}{\left(i \cdot y\right)} \cdot j\right)\right) \]

      11. associate-*r* 83.5%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \left(-\color{blue}{i \cdot \left(y \cdot j\right)}\right)\right) \]

      12. distribute-rgt-neg-in 83.5%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \color{blue}{i \cdot \left(-y \cdot j\right)}\right) \]

      13. mul-1-neg 83.5%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right)}\right) \]

      14. distribute-lft-in 83.5%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      15. mul-1-neg 83.5%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      16. unsub-neg 83.5%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 83.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in b around 0 82.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 82.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right) \]

      2. mul-1-neg 82.5%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)} \]

      3. associate-*r* 81.9%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(-\color{blue}{\left(i \cdot y\right) \cdot j}\right) \]

      4. distribute-lft-neg-in 81.9%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(-i \cdot y\right) \cdot j} \]

      5. cancel-sign-sub-inv 81.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - \left(i \cdot y\right) \cdot j} \]

      6. associate-*r* 82.5%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - \color{blue}{i \cdot \left(y \cdot j\right)} \]

   9. Simplified 82.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - i \cdot \left(y \cdot j\right)} \]

   if -7.49999999999999964e208 < x < -1.5500000000000001e88

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 71.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in i around 0 64.9%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in b around 0 71.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)} \]

   if -1.5500000000000001e88 < x < -6.9999999999999998e44

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 77.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 77.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 77.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 77.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 67.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 67.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      2. mul-1-neg 67.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      3. distribute-rgt-neg-in 67.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. mul-1-neg 67.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. distribute-lft-in 67.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. mul-1-neg 67.9%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. unsub-neg 67.9%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. *-commutative 67.9%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 67.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]
   8. Step-by-step derivation

      1. +-commutative 79.0%

         \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]

      2. *-commutative 79.0%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right) \]

      3. mul-1-neg 79.0%

         \[\leadsto b \cdot \left(i \cdot t - c \cdot z\right) + \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)} \]

      4. unsub-neg 79.0%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right) - i \cdot \left(y \cdot j\right)} \]

      5. *-commutative 79.0%

         \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} - i \cdot \left(y \cdot j\right) \]

      6. associate-*r* 79.0%

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b - \color{blue}{\left(i \cdot y\right) \cdot j} \]

      7. *-commutative 79.0%

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b - \color{blue}{j \cdot \left(i \cdot y\right)} \]

   9. Simplified 79.0%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b - j \cdot \left(i \cdot y\right)} \]

   if -6.9999999999999998e44 < x < 5.2e8 or 1.01999999999999998e99 < x < 7.80000000000000004e148

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 78.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 78.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 78.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 78.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 78.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 78.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 78.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 78.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 78.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 78.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 78.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around 0 72.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 72.1%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(c \cdot \left(a \cdot j\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]

      2. associate-+r+ 72.1%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      3. +-commutative 72.1%

         \[\leadsto \color{blue}{\left(c \cdot \left(a \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. *-commutative 72.1%

         \[\leadsto \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. associate-*r* 70.6%

         \[\leadsto \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. *-commutative 70.6%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. associate-*r* 70.6%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. distribute-rgt-in 72.0%

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      9. mul-1-neg 72.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      10. unsub-neg 72.0%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      11. *-commutative 72.0%

          \[\leadsto a \cdot \left(c \cdot j - t \cdot x\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 72.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if 5.2e8 < x < 1.01999999999999998e99

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 63.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 63.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 63.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 63.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 63.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 74.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 74.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 74.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 74.2%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 74.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 74.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 74.2%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 74.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 74.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 74.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 74.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 74.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+208}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq 520000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+148}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]

Alternative 5: 55.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t_2 + y \cdot \left(x \cdot z\right)\\ t_4 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -8.2 \cdot 10^{+105}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{+160}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (+ t_2 (* y (* x z))))
        (t_4 (* c (- (* a j) (* z b)))))
   (if (<= c -8.2e+105)
     t_4
     (if (<= c -8.2e-199)
       t_3
       (if (<= c 1.3e-216)
         t_1
         (if (<= c 7.2e-111)
           t_3
           (if (<= c 6e-98)
             t_1
             (if (<= c 2.1e-25)
               (* x (- (* y z) (* t a)))
               (if (<= c 9.6e+160) (+ (* c (* a j)) t_2) t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_2 + (y * (x * z));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -8.2e+105) {
		tmp = t_4;
	} else if (c <= -8.2e-199) {
		tmp = t_3;
	} else if (c <= 1.3e-216) {
		tmp = t_1;
	} else if (c <= 7.2e-111) {
		tmp = t_3;
	} else if (c <= 6e-98) {
		tmp = t_1;
	} else if (c <= 2.1e-25) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 9.6e+160) {
		tmp = (c * (a * j)) + t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = b * ((t * i) - (z * c))
    t_3 = t_2 + (y * (x * z))
    t_4 = c * ((a * j) - (z * b))
    if (c <= (-8.2d+105)) then
        tmp = t_4
    else if (c <= (-8.2d-199)) then
        tmp = t_3
    else if (c <= 1.3d-216) then
        tmp = t_1
    else if (c <= 7.2d-111) then
        tmp = t_3
    else if (c <= 6d-98) then
        tmp = t_1
    else if (c <= 2.1d-25) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 9.6d+160) then
        tmp = (c * (a * j)) + t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_2 + (y * (x * z));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -8.2e+105) {
		tmp = t_4;
	} else if (c <= -8.2e-199) {
		tmp = t_3;
	} else if (c <= 1.3e-216) {
		tmp = t_1;
	} else if (c <= 7.2e-111) {
		tmp = t_3;
	} else if (c <= 6e-98) {
		tmp = t_1;
	} else if (c <= 2.1e-25) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 9.6e+160) {
		tmp = (c * (a * j)) + t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = b * ((t * i) - (z * c))
	t_3 = t_2 + (y * (x * z))
	t_4 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -8.2e+105:
		tmp = t_4
	elif c <= -8.2e-199:
		tmp = t_3
	elif c <= 1.3e-216:
		tmp = t_1
	elif c <= 7.2e-111:
		tmp = t_3
	elif c <= 6e-98:
		tmp = t_1
	elif c <= 2.1e-25:
		tmp = x * ((y * z) - (t * a))
	elif c <= 9.6e+160:
		tmp = (c * (a * j)) + t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(t_2 + Float64(y * Float64(x * z)))
	t_4 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -8.2e+105)
		tmp = t_4;
	elseif (c <= -8.2e-199)
		tmp = t_3;
	elseif (c <= 1.3e-216)
		tmp = t_1;
	elseif (c <= 7.2e-111)
		tmp = t_3;
	elseif (c <= 6e-98)
		tmp = t_1;
	elseif (c <= 2.1e-25)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 9.6e+160)
		tmp = Float64(Float64(c * Float64(a * j)) + t_2);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = b * ((t * i) - (z * c));
	t_3 = t_2 + (y * (x * z));
	t_4 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -8.2e+105)
		tmp = t_4;
	elseif (c <= -8.2e-199)
		tmp = t_3;
	elseif (c <= 1.3e-216)
		tmp = t_1;
	elseif (c <= 7.2e-111)
		tmp = t_3;
	elseif (c <= 6e-98)
		tmp = t_1;
	elseif (c <= 2.1e-25)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 9.6e+160)
		tmp = (c * (a * j)) + t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.2e+105], t$95$4, If[LessEqual[c, -8.2e-199], t$95$3, If[LessEqual[c, 1.3e-216], t$95$1, If[LessEqual[c, 7.2e-111], t$95$3, If[LessEqual[c, 6e-98], t$95$1, If[LessEqual[c, 2.1e-25], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.6e+160], N[(N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -8.2000000000000005e105 or 9.6000000000000006e160 < c

   1. Initial program 56.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 56.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 56.2%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 56.2%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 56.2%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 56.2%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 60.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 60.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 60.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 60.4%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 60.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 60.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 60.4%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 65.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around inf 74.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 69.2%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 69.2%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 69.2%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 69.2%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 69.2%

         \[\leadsto c \cdot \left(a \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      6. distribute-lft-out-- 74.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 74.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -8.2000000000000005e105 < c < -8.20000000000000043e-199 or 1.2999999999999999e-216 < c < 7.20000000000000019e-111

   1. Initial program 87.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 87.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 87.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 87.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 87.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 87.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 89.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 89.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 89.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 89.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 89.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 89.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 89.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 76.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 76.5%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      2. mul-1-neg 76.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      3. distribute-rgt-neg-in 76.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. mul-1-neg 76.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. distribute-lft-in 77.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. mul-1-neg 77.8%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. unsub-neg 77.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. *-commutative 77.8%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 77.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in j around 0 67.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

   if -8.20000000000000043e-199 < c < 1.2999999999999999e-216 or 7.20000000000000019e-111 < c < 6e-98

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 80.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 80.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 80.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 80.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 80.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 80.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 80.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 80.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 80.5%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 80.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 80.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 80.5%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 70.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around 0 50.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 50.7%

         \[\leadsto i \cdot \left(t \cdot b\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      2. unsub-neg 50.7%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) - a \cdot \left(t \cdot x\right)} \]

      3. *-commutative 50.7%

         \[\leadsto i \cdot \left(t \cdot b\right) - a \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 60.7%

         \[\leadsto i \cdot \left(t \cdot b\right) - \color{blue}{\left(a \cdot x\right) \cdot t} \]

      5. cancel-sign-sub-inv 60.7%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(-a \cdot x\right) \cdot t} \]

      6. *-commutative 60.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} + \left(-a \cdot x\right) \cdot t \]

      7. associate-*l* 68.3%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} + \left(-a \cdot x\right) \cdot t \]

      8. distribute-rgt-in 70.3%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b + \left(-a \cdot x\right)\right)} \]

      9. unsub-neg 70.3%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   7. Simplified 70.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if 6e-98 < c < 2.10000000000000002e-25

   1. Initial program 94.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 94.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 94.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 94.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 94.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 94.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 94.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 94.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 94.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 94.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 94.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 94.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 94.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in x around inf 76.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if 2.10000000000000002e-25 < c < 9.6000000000000006e160

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.2%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.2%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.2%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.2%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 76.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 76.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around 0 67.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.2%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(c \cdot \left(a \cdot j\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]

      2. associate-+r+ 67.2%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      3. +-commutative 67.2%

         \[\leadsto \color{blue}{\left(c \cdot \left(a \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. *-commutative 67.2%

         \[\leadsto \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. associate-*r* 67.2%

         \[\leadsto \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. *-commutative 67.2%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. associate-*r* 67.2%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. distribute-rgt-in 74.3%

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      9. mul-1-neg 74.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      10. unsub-neg 74.3%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      11. *-commutative 74.3%

          \[\leadsto a \cdot \left(c \cdot j - t \cdot x\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in x around 0 69.7%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-111}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{+160}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;c \leq -2.7 \cdot 10^{+27}:\\ \;\;\;\;\left(t_3 + c \cdot \left(a \cdot j\right)\right) - t_2\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t_1\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;t_3 + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - t_2\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* c (* z b)))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= c -2.7e+27)
     (- (+ t_3 (* c (* a j))) t_2)
     (if (<= c -1.75e-228)
       (+ (* y (- (* x z) (* i j))) t_1)
       (if (<= c 1.7e-7)
         (+ t_3 (* i (- (* t b) (* y j))))
         (if (<= c 3.8e+15)
           (- (* j (- (* a c) (* y i))) t_2)
           (if (<= c 8.6e+97)
             (+ (* a (- (* c j) (* x t))) t_1)
             (* c (- (* a j) (* z b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = c * (z * b);
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (c <= -2.7e+27) {
		tmp = (t_3 + (c * (a * j))) - t_2;
	} else if (c <= -1.75e-228) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else if (c <= 1.7e-7) {
		tmp = t_3 + (i * ((t * b) - (y * j)));
	} else if (c <= 3.8e+15) {
		tmp = (j * ((a * c) - (y * i))) - t_2;
	} else if (c <= 8.6e+97) {
		tmp = (a * ((c * j) - (x * t))) + t_1;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = c * (z * b)
    t_3 = x * ((y * z) - (t * a))
    if (c <= (-2.7d+27)) then
        tmp = (t_3 + (c * (a * j))) - t_2
    else if (c <= (-1.75d-228)) then
        tmp = (y * ((x * z) - (i * j))) + t_1
    else if (c <= 1.7d-7) then
        tmp = t_3 + (i * ((t * b) - (y * j)))
    else if (c <= 3.8d+15) then
        tmp = (j * ((a * c) - (y * i))) - t_2
    else if (c <= 8.6d+97) then
        tmp = (a * ((c * j) - (x * t))) + t_1
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = c * (z * b);
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (c <= -2.7e+27) {
		tmp = (t_3 + (c * (a * j))) - t_2;
	} else if (c <= -1.75e-228) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else if (c <= 1.7e-7) {
		tmp = t_3 + (i * ((t * b) - (y * j)));
	} else if (c <= 3.8e+15) {
		tmp = (j * ((a * c) - (y * i))) - t_2;
	} else if (c <= 8.6e+97) {
		tmp = (a * ((c * j) - (x * t))) + t_1;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = c * (z * b)
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if c <= -2.7e+27:
		tmp = (t_3 + (c * (a * j))) - t_2
	elif c <= -1.75e-228:
		tmp = (y * ((x * z) - (i * j))) + t_1
	elif c <= 1.7e-7:
		tmp = t_3 + (i * ((t * b) - (y * j)))
	elif c <= 3.8e+15:
		tmp = (j * ((a * c) - (y * i))) - t_2
	elif c <= 8.6e+97:
		tmp = (a * ((c * j) - (x * t))) + t_1
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(z * b))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (c <= -2.7e+27)
		tmp = Float64(Float64(t_3 + Float64(c * Float64(a * j))) - t_2);
	elseif (c <= -1.75e-228)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	elseif (c <= 1.7e-7)
		tmp = Float64(t_3 + Float64(i * Float64(Float64(t * b) - Float64(y * j))));
	elseif (c <= 3.8e+15)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - t_2);
	elseif (c <= 8.6e+97)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + t_1);
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = c * (z * b);
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (c <= -2.7e+27)
		tmp = (t_3 + (c * (a * j))) - t_2;
	elseif (c <= -1.75e-228)
		tmp = (y * ((x * z) - (i * j))) + t_1;
	elseif (c <= 1.7e-7)
		tmp = t_3 + (i * ((t * b) - (y * j)));
	elseif (c <= 3.8e+15)
		tmp = (j * ((a * c) - (y * i))) - t_2;
	elseif (c <= 8.6e+97)
		tmp = (a * ((c * j) - (x * t))) + t_1;
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.7e+27], N[(N[(t$95$3 + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[c, -1.75e-228], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, 1.7e-7], N[(t$95$3 + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.8e+15], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[c, 8.6e+97], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -2.6999999999999997e27

   1. Initial program 64.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 64.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 64.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 64.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 64.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in i around 0 74.4%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   if -2.6999999999999997e27 < c < -1.74999999999999987e-228

   1. Initial program 87.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 87.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 87.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 87.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 87.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 87.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 87.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 87.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 87.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 87.4%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 87.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 87.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 79.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 79.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      2. mul-1-neg 79.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      3. distribute-rgt-neg-in 79.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. mul-1-neg 79.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. distribute-lft-in 81.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. mul-1-neg 81.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. unsub-neg 81.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. *-commutative 81.3%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 81.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -1.74999999999999987e-228 < c < 1.69999999999999987e-7

   1. Initial program 87.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 87.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 87.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 87.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 87.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 87.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 88.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 88.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 88.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 88.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 88.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 88.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 88.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around 0 82.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 82.1%

         \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + i \cdot \left(t \cdot b\right)} \]

      2. remove-double-neg 82.1%

         \[\leadsto \left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(-i \cdot \left(t \cdot b\right)\right)\right)} \]

      3. mul-1-neg 82.1%

         \[\leadsto \left(\left(y \cdot z - a \cdot t\right) \cdot x + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-\color{blue}{-1 \cdot \left(i \cdot \left(t \cdot b\right)\right)}\right) \]

      4. associate-+l+ 82.1%

         \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right)\right)} \]

      5. +-commutative 82.1%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \color{blue}{\left(\left(--1 \cdot \left(i \cdot \left(t \cdot b\right)\right)\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      6. mul-1-neg 82.1%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(\left(-\color{blue}{\left(-i \cdot \left(t \cdot b\right)\right)}\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]

      7. remove-double-neg 82.1%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(\color{blue}{i \cdot \left(t \cdot b\right)} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) \]

      8. mul-1-neg 82.1%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) \]

      9. associate-*r* 83.3%

         \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \left(-\color{blue}{\left(y \cdot i\right) \cdot j}\right)\right) \]

      10. *-commutative 83.3%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \left(-\color{blue}{\left(i \cdot y\right)} \cdot j\right)\right) \]

      11. associate-*r* 82.2%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \left(-\color{blue}{i \cdot \left(y \cdot j\right)}\right)\right) \]

      12. distribute-rgt-neg-in 82.2%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + \color{blue}{i \cdot \left(-y \cdot j\right)}\right) \]

      13. mul-1-neg 82.2%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \left(i \cdot \left(t \cdot b\right) + i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right)}\right) \]

      14. distribute-lft-in 83.3%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      15. mul-1-neg 83.3%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      16. unsub-neg 83.3%

          \[\leadsto \left(y \cdot z - a \cdot t\right) \cdot x + i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 83.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if 1.69999999999999987e-7 < c < 3.8e15

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 99.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 99.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 99.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 99.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 99.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. associate-*r* 99.8%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. neg-mul-1 99.8%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(b \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 99.8%

         \[\leadsto \left(-c\right) \cdot \color{blue}{\left(z \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 99.8%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if 3.8e15 < c < 8.5999999999999996e97

   1. Initial program 57.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 57.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 57.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 57.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 57.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 57.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 57.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 57.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 57.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 57.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 57.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 57.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 57.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 57.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around 0 57.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 57.8%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(c \cdot \left(a \cdot j\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]

      2. associate-+r+ 57.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      3. +-commutative 57.8%

         \[\leadsto \color{blue}{\left(c \cdot \left(a \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. *-commutative 57.8%

         \[\leadsto \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. associate-*r* 57.8%

         \[\leadsto \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. *-commutative 57.8%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. associate-*r* 57.8%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. distribute-rgt-in 72.1%

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      9. mul-1-neg 72.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      10. unsub-neg 72.1%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      11. *-commutative 72.1%

          \[\leadsto a \cdot \left(c \cdot j - t \cdot x\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 72.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if 8.5999999999999996e97 < c

   1. Initial program 60.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 60.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 60.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 60.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 60.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 60.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 62.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 62.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 62.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 62.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 62.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 62.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 62.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around inf 81.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 77.7%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 77.7%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 77.7%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 77.7%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 77.7%

         \[\leadsto c \cdot \left(a \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      6. distribute-lft-out-- 81.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 81.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.7 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 7: 55.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.4 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* b (- (* t i) (* z c))) (* y (* x z))))
        (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -2.4e+97)
     t_2
     (if (<= c -3.8e-199)
       t_1
       (if (<= c 4.6e-219)
         (* t (- (* b i) (* x a)))
         (if (<= c 1.05e-149)
           t_1
           (if (<= c 3e-72)
             (* x (- (* y z) (* t a)))
             (if (<= c 2.9e+94) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) + (y * (x * z));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.4e+97) {
		tmp = t_2;
	} else if (c <= -3.8e-199) {
		tmp = t_1;
	} else if (c <= 4.6e-219) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 1.05e-149) {
		tmp = t_1;
	} else if (c <= 3e-72) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 2.9e+94) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * ((t * i) - (z * c))) + (y * (x * z))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-2.4d+97)) then
        tmp = t_2
    else if (c <= (-3.8d-199)) then
        tmp = t_1
    else if (c <= 4.6d-219) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 1.05d-149) then
        tmp = t_1
    else if (c <= 3d-72) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 2.9d+94) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) + (y * (x * z));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.4e+97) {
		tmp = t_2;
	} else if (c <= -3.8e-199) {
		tmp = t_1;
	} else if (c <= 4.6e-219) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 1.05e-149) {
		tmp = t_1;
	} else if (c <= 3e-72) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 2.9e+94) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((t * i) - (z * c))) + (y * (x * z))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -2.4e+97:
		tmp = t_2
	elif c <= -3.8e-199:
		tmp = t_1
	elif c <= 4.6e-219:
		tmp = t * ((b * i) - (x * a))
	elif c <= 1.05e-149:
		tmp = t_1
	elif c <= 3e-72:
		tmp = x * ((y * z) - (t * a))
	elif c <= 2.9e+94:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(y * Float64(x * z)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.4e+97)
		tmp = t_2;
	elseif (c <= -3.8e-199)
		tmp = t_1;
	elseif (c <= 4.6e-219)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 1.05e-149)
		tmp = t_1;
	elseif (c <= 3e-72)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 2.9e+94)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * ((t * i) - (z * c))) + (y * (x * z));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.4e+97)
		tmp = t_2;
	elseif (c <= -3.8e-199)
		tmp = t_1;
	elseif (c <= 4.6e-219)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 1.05e-149)
		tmp = t_1;
	elseif (c <= 3e-72)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 2.9e+94)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.4e+97], t$95$2, If[LessEqual[c, -3.8e-199], t$95$1, If[LessEqual[c, 4.6e-219], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e-149], t$95$1, If[LessEqual[c, 3e-72], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e+94], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.4e97 or 2.8999999999999998e94 < c

   1. Initial program 60.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 60.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 60.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 60.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 60.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 60.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 63.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 63.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 63.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 63.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 63.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 63.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 63.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around inf 73.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 69.2%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 69.2%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 69.2%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 69.2%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 69.2%

         \[\leadsto c \cdot \left(a \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      6. distribute-lft-out-- 73.4%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 73.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -2.4e97 < c < -3.7999999999999998e-199 or 4.59999999999999977e-219 < c < 1.05000000000000005e-149 or 3e-72 < c < 2.8999999999999998e94

   1. Initial program 87.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 87.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 87.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 87.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 87.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 87.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 87.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 87.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 87.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 87.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 87.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 87.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 87.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 73.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 73.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      2. mul-1-neg 73.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      3. distribute-rgt-neg-in 73.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. mul-1-neg 73.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. distribute-lft-in 74.2%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. mul-1-neg 74.2%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. unsub-neg 74.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. *-commutative 74.2%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 74.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in j around 0 67.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

   if -3.7999999999999998e-199 < c < 4.59999999999999977e-219

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 82.2%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 82.2%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 82.2%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 82.2%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 82.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 82.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 82.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 82.2%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 82.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 82.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 82.2%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 68.5%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around 0 50.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 50.5%

         \[\leadsto i \cdot \left(t \cdot b\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      2. unsub-neg 50.5%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) - a \cdot \left(t \cdot x\right)} \]

      3. *-commutative 50.5%

         \[\leadsto i \cdot \left(t \cdot b\right) - a \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 59.8%

         \[\leadsto i \cdot \left(t \cdot b\right) - \color{blue}{\left(a \cdot x\right) \cdot t} \]

      5. cancel-sign-sub-inv 59.8%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(-a \cdot x\right) \cdot t} \]

      6. *-commutative 59.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} + \left(-a \cdot x\right) \cdot t \]

      7. associate-*l* 68.5%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} + \left(-a \cdot x\right) \cdot t \]

      8. distribute-rgt-in 68.5%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b + \left(-a \cdot x\right)\right)} \]

      9. unsub-neg 68.5%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   7. Simplified 68.5%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if 1.05000000000000005e-149 < c < 3e-72

   1. Initial program 84.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 84.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 84.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 84.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 84.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 84.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 89.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 89.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 89.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 89.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 89.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 89.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 89.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in x around inf 64.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-149}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+94}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 8: 69.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+102} \lor \neg \left(a \leq -3.05 \cdot 10^{+63}\right) \land a \leq 8.2 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -7.2e+124)
     t_2
     (if (or (<= a -8e+102) (and (not (<= a -3.05e+63)) (<= a 8.2e-13)))
       (+ (* y (- (* x z) (* i j))) t_1)
       (+ t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7.2e+124) {
		tmp = t_2;
	} else if ((a <= -8e+102) || (!(a <= -3.05e+63) && (a <= 8.2e-13))) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-7.2d+124)) then
        tmp = t_2
    else if ((a <= (-8d+102)) .or. (.not. (a <= (-3.05d+63))) .and. (a <= 8.2d-13)) then
        tmp = (y * ((x * z) - (i * j))) + t_1
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7.2e+124) {
		tmp = t_2;
	} else if ((a <= -8e+102) || (!(a <= -3.05e+63) && (a <= 8.2e-13))) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -7.2e+124:
		tmp = t_2
	elif (a <= -8e+102) or (not (a <= -3.05e+63) and (a <= 8.2e-13)):
		tmp = (y * ((x * z) - (i * j))) + t_1
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7.2e+124)
		tmp = t_2;
	elseif ((a <= -8e+102) || (!(a <= -3.05e+63) && (a <= 8.2e-13)))
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -7.2e+124)
		tmp = t_2;
	elseif ((a <= -8e+102) || (~((a <= -3.05e+63)) && (a <= 8.2e-13)))
		tmp = (y * ((x * z) - (i * j))) + t_1;
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e+124], t$95$2, If[Or[LessEqual[a, -8e+102], And[N[Not[LessEqual[a, -3.05e+63]], $MachinePrecision], LessEqual[a, 8.2e-13]]], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.19999999999999972e124

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 66.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 66.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 66.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 66.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 66.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 66.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 66.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 66.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 66.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 66.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 66.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 69.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 84.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 84.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 84.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 84.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 84.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -7.19999999999999972e124 < a < -7.99999999999999982e102 or -3.04999999999999984e63 < a < 8.2000000000000004e-13

   1. Initial program 81.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 81.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 81.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 81.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 81.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 81.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 83.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 83.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 83.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 83.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 83.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 83.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 83.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 85.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 75.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 75.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      2. mul-1-neg 75.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      3. distribute-rgt-neg-in 75.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. mul-1-neg 75.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. distribute-lft-in 76.1%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. mul-1-neg 76.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. unsub-neg 76.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. *-commutative 76.1%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 76.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -7.99999999999999982e102 < a < -3.04999999999999984e63 or 8.2000000000000004e-13 < a

   1. Initial program 70.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 70.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 70.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 70.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 70.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 70.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 71.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 71.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 71.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 71.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 71.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 71.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 71.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around 0 68.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 68.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(c \cdot \left(a \cdot j\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]

      2. associate-+r+ 68.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      3. +-commutative 68.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(a \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. *-commutative 68.0%

         \[\leadsto \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. associate-*r* 69.3%

         \[\leadsto \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. *-commutative 69.3%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. associate-*r* 69.3%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. distribute-rgt-in 73.8%

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      9. mul-1-neg 73.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      10. unsub-neg 73.8%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      11. *-commutative 73.8%

          \[\leadsto a \cdot \left(c \cdot j - t \cdot x\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 73.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+102} \lor \neg \left(a \leq -3.05 \cdot 10^{+63}\right) \land a \leq 8.2 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 9: 50.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.45 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -0.42:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 0.095:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -1.45e+113)
     t_2
     (if (<= c -0.42)
       t_1
       (if (<= c -1.4e-139)
         (* b (- (* t i) (* z c)))
         (if (<= c -7.5e-181)
           (* y (- (* x z) (* i j)))
           (if (<= c -2.9e-210)
             (* i (- (* t b) (* y j)))
             (if (<= c 5.6e-150)
               (* t (- (* b i) (* x a)))
               (if (<= c 0.095) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.45e+113) {
		tmp = t_2;
	} else if (c <= -0.42) {
		tmp = t_1;
	} else if (c <= -1.4e-139) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -7.5e-181) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -2.9e-210) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 5.6e-150) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 0.095) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-1.45d+113)) then
        tmp = t_2
    else if (c <= (-0.42d0)) then
        tmp = t_1
    else if (c <= (-1.4d-139)) then
        tmp = b * ((t * i) - (z * c))
    else if (c <= (-7.5d-181)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= (-2.9d-210)) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 5.6d-150) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 0.095d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.45e+113) {
		tmp = t_2;
	} else if (c <= -0.42) {
		tmp = t_1;
	} else if (c <= -1.4e-139) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -7.5e-181) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -2.9e-210) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 5.6e-150) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 0.095) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.45e+113:
		tmp = t_2
	elif c <= -0.42:
		tmp = t_1
	elif c <= -1.4e-139:
		tmp = b * ((t * i) - (z * c))
	elif c <= -7.5e-181:
		tmp = y * ((x * z) - (i * j))
	elif c <= -2.9e-210:
		tmp = i * ((t * b) - (y * j))
	elif c <= 5.6e-150:
		tmp = t * ((b * i) - (x * a))
	elif c <= 0.095:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.45e+113)
		tmp = t_2;
	elseif (c <= -0.42)
		tmp = t_1;
	elseif (c <= -1.4e-139)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (c <= -7.5e-181)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= -2.9e-210)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 5.6e-150)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 0.095)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.45e+113)
		tmp = t_2;
	elseif (c <= -0.42)
		tmp = t_1;
	elseif (c <= -1.4e-139)
		tmp = b * ((t * i) - (z * c));
	elseif (c <= -7.5e-181)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= -2.9e-210)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 5.6e-150)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 0.095)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.45e+113], t$95$2, If[LessEqual[c, -0.42], t$95$1, If[LessEqual[c, -1.4e-139], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.5e-181], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.9e-210], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.6e-150], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 0.095], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.44999999999999992e113 or 0.095000000000000001 < c

   1. Initial program 62.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 62.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 62.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 62.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 62.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 62.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 65.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 65.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 65.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 65.5%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 65.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 65.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 65.5%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around inf 68.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 65.3%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 65.3%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 65.3%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 65.3%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 65.3%

         \[\leadsto c \cdot \left(a \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      6. distribute-lft-out-- 68.9%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 68.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -1.44999999999999992e113 < c < -0.419999999999999984 or 5.59999999999999993e-150 < c < 0.095000000000000001

   1. Initial program 84.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 84.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 84.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 84.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 84.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 84.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 85.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 85.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 85.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 85.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 85.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 85.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 85.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in x around inf 69.1%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -0.419999999999999984 < c < -1.3999999999999999e-139

   1. Initial program 95.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 95.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 95.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 95.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 95.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 95.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 95.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 95.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 95.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 95.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 95.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 95.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 95.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in b around inf 61.2%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   if -1.3999999999999999e-139 < c < -7.5000000000000002e-181

   1. Initial program 89.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 89.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 89.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 89.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 89.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 89.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 89.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 89.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 89.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 89.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 89.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 89.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 89.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 78.1%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 78.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 78.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 78.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -7.5000000000000002e-181 < c < -2.90000000000000006e-210

   1. Initial program 72.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 72.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 72.3%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 72.3%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 72.3%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 72.3%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 72.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 72.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 72.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 72.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 72.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 72.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 72.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in i around inf 73.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 73.3%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 73.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 73.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if -2.90000000000000006e-210 < c < 5.59999999999999993e-150

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 85.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 85.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 85.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 85.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 85.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 85.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 85.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 85.7%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 85.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 85.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 85.7%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 64.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around 0 49.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 49.7%

         \[\leadsto i \cdot \left(t \cdot b\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      2. unsub-neg 49.7%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) - a \cdot \left(t \cdot x\right)} \]

      3. *-commutative 49.7%

         \[\leadsto i \cdot \left(t \cdot b\right) - a \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 57.1%

         \[\leadsto i \cdot \left(t \cdot b\right) - \color{blue}{\left(a \cdot x\right) \cdot t} \]

      5. cancel-sign-sub-inv 57.1%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(-a \cdot x\right) \cdot t} \]

      6. *-commutative 57.1%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} + \left(-a \cdot x\right) \cdot t \]

      7. associate-*l* 62.4%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} + \left(-a \cdot x\right) \cdot t \]

      8. distribute-rgt-in 64.2%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b + \left(-a \cdot x\right)\right)} \]

      9. unsub-neg 64.2%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   7. Simplified 64.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{+113}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -0.42:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 0.095:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 10: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ t_3 := t_2 + t_1\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) + t_2\\ \mathbf{if}\;b \leq -3 \cdot 10^{+73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-98}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 110000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+76}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1 + y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* c (* a j)))
        (t_3 (+ t_2 t_1))
        (t_4 (+ (* x (- (* y z) (* t a))) t_2)))
   (if (<= b -3e+73)
     t_3
     (if (<= b 1.7e-98)
       t_4
       (if (<= b 110000000.0)
         t_3
         (if (<= b 9e+76) t_4 (+ t_1 (* y (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = c * (a * j);
	double t_3 = t_2 + t_1;
	double t_4 = (x * ((y * z) - (t * a))) + t_2;
	double tmp;
	if (b <= -3e+73) {
		tmp = t_3;
	} else if (b <= 1.7e-98) {
		tmp = t_4;
	} else if (b <= 110000000.0) {
		tmp = t_3;
	} else if (b <= 9e+76) {
		tmp = t_4;
	} else {
		tmp = t_1 + (y * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = c * (a * j)
    t_3 = t_2 + t_1
    t_4 = (x * ((y * z) - (t * a))) + t_2
    if (b <= (-3d+73)) then
        tmp = t_3
    else if (b <= 1.7d-98) then
        tmp = t_4
    else if (b <= 110000000.0d0) then
        tmp = t_3
    else if (b <= 9d+76) then
        tmp = t_4
    else
        tmp = t_1 + (y * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = c * (a * j);
	double t_3 = t_2 + t_1;
	double t_4 = (x * ((y * z) - (t * a))) + t_2;
	double tmp;
	if (b <= -3e+73) {
		tmp = t_3;
	} else if (b <= 1.7e-98) {
		tmp = t_4;
	} else if (b <= 110000000.0) {
		tmp = t_3;
	} else if (b <= 9e+76) {
		tmp = t_4;
	} else {
		tmp = t_1 + (y * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = c * (a * j)
	t_3 = t_2 + t_1
	t_4 = (x * ((y * z) - (t * a))) + t_2
	tmp = 0
	if b <= -3e+73:
		tmp = t_3
	elif b <= 1.7e-98:
		tmp = t_4
	elif b <= 110000000.0:
		tmp = t_3
	elif b <= 9e+76:
		tmp = t_4
	else:
		tmp = t_1 + (y * (x * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(a * j))
	t_3 = Float64(t_2 + t_1)
	t_4 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2)
	tmp = 0.0
	if (b <= -3e+73)
		tmp = t_3;
	elseif (b <= 1.7e-98)
		tmp = t_4;
	elseif (b <= 110000000.0)
		tmp = t_3;
	elseif (b <= 9e+76)
		tmp = t_4;
	else
		tmp = Float64(t_1 + Float64(y * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = c * (a * j);
	t_3 = t_2 + t_1;
	t_4 = (x * ((y * z) - (t * a))) + t_2;
	tmp = 0.0;
	if (b <= -3e+73)
		tmp = t_3;
	elseif (b <= 1.7e-98)
		tmp = t_4;
	elseif (b <= 110000000.0)
		tmp = t_3;
	elseif (b <= 9e+76)
		tmp = t_4;
	else
		tmp = t_1 + (y * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[b, -3e+73], t$95$3, If[LessEqual[b, 1.7e-98], t$95$4, If[LessEqual[b, 110000000.0], t$95$3, If[LessEqual[b, 9e+76], t$95$4, N[(t$95$1 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.00000000000000011e73 or 1.7000000000000001e-98 < b < 1.1e8

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 79.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 79.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 79.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 79.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 79.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 79.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 70.6%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(c \cdot \left(a \cdot j\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]

      2. associate-+r+ 70.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      3. +-commutative 70.6%

         \[\leadsto \color{blue}{\left(c \cdot \left(a \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. *-commutative 70.6%

         \[\leadsto \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. associate-*r* 64.2%

         \[\leadsto \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. *-commutative 64.2%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. associate-*r* 64.2%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. distribute-rgt-in 64.2%

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      9. mul-1-neg 64.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      10. unsub-neg 64.2%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      11. *-commutative 64.2%

          \[\leadsto a \cdot \left(c \cdot j - t \cdot x\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in x around 0 68.2%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)} \]

   if -3.00000000000000011e73 < b < 1.7000000000000001e-98 or 1.1e8 < b < 8.9999999999999995e76

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 77.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in i around 0 67.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in b around 0 66.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)} \]

   if 8.9999999999999995e76 < b

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 80.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 80.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 80.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 80.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 80.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 80.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 80.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 72.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 72.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      2. mul-1-neg 72.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      3. distribute-rgt-neg-in 72.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. mul-1-neg 72.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. distribute-lft-in 72.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. mul-1-neg 72.9%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. unsub-neg 72.9%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. *-commutative 72.9%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 72.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in j around 0 72.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 110000000:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 11: 59.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + t_2\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 88000000:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* c (* a j)))
        (t_3 (+ (* x (- (* y z) (* t a))) t_2)))
   (if (<= b -1.4e+74)
     (+ t_2 t_1)
     (if (<= b 2.25e-71)
       t_3
       (if (<= b 88000000.0)
         (- t_1 (* j (* y i)))
         (if (<= b 1.7e+77) t_3 (+ t_1 (* y (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = c * (a * j);
	double t_3 = (x * ((y * z) - (t * a))) + t_2;
	double tmp;
	if (b <= -1.4e+74) {
		tmp = t_2 + t_1;
	} else if (b <= 2.25e-71) {
		tmp = t_3;
	} else if (b <= 88000000.0) {
		tmp = t_1 - (j * (y * i));
	} else if (b <= 1.7e+77) {
		tmp = t_3;
	} else {
		tmp = t_1 + (y * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = c * (a * j)
    t_3 = (x * ((y * z) - (t * a))) + t_2
    if (b <= (-1.4d+74)) then
        tmp = t_2 + t_1
    else if (b <= 2.25d-71) then
        tmp = t_3
    else if (b <= 88000000.0d0) then
        tmp = t_1 - (j * (y * i))
    else if (b <= 1.7d+77) then
        tmp = t_3
    else
        tmp = t_1 + (y * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = c * (a * j);
	double t_3 = (x * ((y * z) - (t * a))) + t_2;
	double tmp;
	if (b <= -1.4e+74) {
		tmp = t_2 + t_1;
	} else if (b <= 2.25e-71) {
		tmp = t_3;
	} else if (b <= 88000000.0) {
		tmp = t_1 - (j * (y * i));
	} else if (b <= 1.7e+77) {
		tmp = t_3;
	} else {
		tmp = t_1 + (y * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = c * (a * j)
	t_3 = (x * ((y * z) - (t * a))) + t_2
	tmp = 0
	if b <= -1.4e+74:
		tmp = t_2 + t_1
	elif b <= 2.25e-71:
		tmp = t_3
	elif b <= 88000000.0:
		tmp = t_1 - (j * (y * i))
	elif b <= 1.7e+77:
		tmp = t_3
	else:
		tmp = t_1 + (y * (x * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(a * j))
	t_3 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2)
	tmp = 0.0
	if (b <= -1.4e+74)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 2.25e-71)
		tmp = t_3;
	elseif (b <= 88000000.0)
		tmp = Float64(t_1 - Float64(j * Float64(y * i)));
	elseif (b <= 1.7e+77)
		tmp = t_3;
	else
		tmp = Float64(t_1 + Float64(y * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = c * (a * j);
	t_3 = (x * ((y * z) - (t * a))) + t_2;
	tmp = 0.0;
	if (b <= -1.4e+74)
		tmp = t_2 + t_1;
	elseif (b <= 2.25e-71)
		tmp = t_3;
	elseif (b <= 88000000.0)
		tmp = t_1 - (j * (y * i));
	elseif (b <= 1.7e+77)
		tmp = t_3;
	else
		tmp = t_1 + (y * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[b, -1.4e+74], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 2.25e-71], t$95$3, If[LessEqual[b, 88000000.0], N[(t$95$1 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+77], t$95$3, N[(t$95$1 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.40000000000000001e74

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 72.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 72.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 72.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 72.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 72.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 76.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 76.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around 0 69.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(c \cdot \left(a \cdot j\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]

      2. associate-+r+ 69.2%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      3. +-commutative 69.2%

         \[\leadsto \color{blue}{\left(c \cdot \left(a \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. *-commutative 69.2%

         \[\leadsto \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. associate-*r* 61.8%

         \[\leadsto \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. *-commutative 61.8%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. associate-*r* 61.8%

         \[\leadsto \left(\left(c \cdot j\right) \cdot a + \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. distribute-rgt-in 61.8%

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      9. mul-1-neg 61.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      10. unsub-neg 61.8%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      11. *-commutative 61.8%

          \[\leadsto a \cdot \left(c \cdot j - t \cdot x\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 61.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b + c \cdot \left(a \cdot j\right)} \]

   if -1.40000000000000001e74 < b < 2.2500000000000001e-71 or 8.8e7 < b < 1.69999999999999998e77

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 77.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in i around 0 68.0%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in b around 0 66.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)} \]

   if 2.2500000000000001e-71 < b < 8.8e7

   1. Initial program 84.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 84.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 84.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 84.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 84.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 84.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 84.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 84.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 84.7%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 84.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 84.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 84.7%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 59.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 59.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      2. mul-1-neg 59.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      3. distribute-rgt-neg-in 59.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. mul-1-neg 59.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. distribute-lft-in 59.2%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. mul-1-neg 59.2%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. unsub-neg 59.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. *-commutative 59.2%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 59.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in x around 0 74.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]
   8. Step-by-step derivation

      1. +-commutative 74.3%

         \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]

      2. *-commutative 74.3%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right) \]

      3. mul-1-neg 74.3%

         \[\leadsto b \cdot \left(i \cdot t - c \cdot z\right) + \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)} \]

      4. unsub-neg 74.3%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right) - i \cdot \left(y \cdot j\right)} \]

      5. *-commutative 74.3%

         \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} - i \cdot \left(y \cdot j\right) \]

      6. associate-*r* 74.3%

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b - \color{blue}{\left(i \cdot y\right) \cdot j} \]

      7. *-commutative 74.3%

         \[\leadsto \left(i \cdot t - c \cdot z\right) \cdot b - \color{blue}{j \cdot \left(i \cdot y\right)} \]

   9. Simplified 74.3%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b - j \cdot \left(i \cdot y\right)} \]

   if 1.69999999999999998e77 < b

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 80.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 80.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 80.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 80.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 80.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 80.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 80.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 72.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 72.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]

      2. mul-1-neg 72.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      3. distribute-rgt-neg-in 72.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      4. mul-1-neg 72.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      5. distribute-lft-in 72.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      6. mul-1-neg 72.9%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) + \left(i \cdot t - c \cdot z\right) \cdot b \]

      7. unsub-neg 72.9%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} + \left(i \cdot t - c \cdot z\right) \cdot b \]

      8. *-commutative 72.9%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Simplified 72.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in j around 0 72.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right) + \left(i \cdot t - c \cdot z\right) \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 88000000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 12: 49.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -7.4 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.46 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -7.4e-22)
     t_2
     (if (<= c -6.6e-230)
       t_1
       (if (<= c 4e-295)
         (* t (* x (- a)))
         (if (<= c 4.1e-75)
           t_1
           (if (<= c 1.46e-34) (* x (* y z)) (if (<= c 5.9e-9) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7.4e-22) {
		tmp = t_2;
	} else if (c <= -6.6e-230) {
		tmp = t_1;
	} else if (c <= 4e-295) {
		tmp = t * (x * -a);
	} else if (c <= 4.1e-75) {
		tmp = t_1;
	} else if (c <= 1.46e-34) {
		tmp = x * (y * z);
	} else if (c <= 5.9e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-7.4d-22)) then
        tmp = t_2
    else if (c <= (-6.6d-230)) then
        tmp = t_1
    else if (c <= 4d-295) then
        tmp = t * (x * -a)
    else if (c <= 4.1d-75) then
        tmp = t_1
    else if (c <= 1.46d-34) then
        tmp = x * (y * z)
    else if (c <= 5.9d-9) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7.4e-22) {
		tmp = t_2;
	} else if (c <= -6.6e-230) {
		tmp = t_1;
	} else if (c <= 4e-295) {
		tmp = t * (x * -a);
	} else if (c <= 4.1e-75) {
		tmp = t_1;
	} else if (c <= 1.46e-34) {
		tmp = x * (y * z);
	} else if (c <= 5.9e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -7.4e-22:
		tmp = t_2
	elif c <= -6.6e-230:
		tmp = t_1
	elif c <= 4e-295:
		tmp = t * (x * -a)
	elif c <= 4.1e-75:
		tmp = t_1
	elif c <= 1.46e-34:
		tmp = x * (y * z)
	elif c <= 5.9e-9:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -7.4e-22)
		tmp = t_2;
	elseif (c <= -6.6e-230)
		tmp = t_1;
	elseif (c <= 4e-295)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 4.1e-75)
		tmp = t_1;
	elseif (c <= 1.46e-34)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 5.9e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -7.4e-22)
		tmp = t_2;
	elseif (c <= -6.6e-230)
		tmp = t_1;
	elseif (c <= 4e-295)
		tmp = t * (x * -a);
	elseif (c <= 4.1e-75)
		tmp = t_1;
	elseif (c <= 1.46e-34)
		tmp = x * (y * z);
	elseif (c <= 5.9e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.4e-22], t$95$2, If[LessEqual[c, -6.6e-230], t$95$1, If[LessEqual[c, 4e-295], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.1e-75], t$95$1, If[LessEqual[c, 1.46e-34], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.9e-9], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.4e-22 or 5.8999999999999999e-9 < c

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 65.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 65.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 65.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 65.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 65.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 68.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 68.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 68.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 68.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 68.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 68.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 68.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around inf 63.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 60.8%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 60.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 60.8%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 60.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 60.8%

         \[\leadsto c \cdot \left(a \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      6. distribute-lft-out-- 63.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 63.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -7.4e-22 < c < -6.59999999999999987e-230 or 4.00000000000000024e-295 < c < 4.10000000000000002e-75 or 1.4599999999999999e-34 < c < 5.8999999999999999e-9

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 85.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 85.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 85.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 85.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 85.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 86.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 86.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 86.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 86.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 86.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 86.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 86.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in i around inf 55.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 55.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 55.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if -6.59999999999999987e-230 < c < 4.00000000000000024e-295

   1. Initial program 85.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 85.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 85.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 85.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 85.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 85.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 85.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 85.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 85.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 85.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 85.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 59.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 59.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 59.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 59.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 59.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 59.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 59.2%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 59.7%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-rgt-neg-in 59.7%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(-x\right)} \]

      4. *-commutative 59.7%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot \left(-x\right) \]

      5. associate-*r* 64.1%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(-x\right)\right)} \]

   9. Simplified 64.1%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(-x\right)\right)} \]

   if 4.10000000000000002e-75 < c < 1.4599999999999999e-34

   1. Initial program 99.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 99.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 99.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 99.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 99.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 99.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 99.7%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 50.5%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 50.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 50.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 50.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 50.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 51.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 57.5%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 57.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   9. Simplified 57.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.4 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{-230}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.46 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-9}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 13: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -3.2e+44)
     t_3
     (if (<= t -1.4e-73)
       t_2
       (if (<= t 5.5e-306)
         t_1
         (if (<= t 5.5e-267)
           t_2
           (if (<= t 5.5e+35) t_1 (if (<= t 3.1e+120) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -3.2e+44) {
		tmp = t_3;
	} else if (t <= -1.4e-73) {
		tmp = t_2;
	} else if (t <= 5.5e-306) {
		tmp = t_1;
	} else if (t <= 5.5e-267) {
		tmp = t_2;
	} else if (t <= 5.5e+35) {
		tmp = t_1;
	} else if (t <= 3.1e+120) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-3.2d+44)) then
        tmp = t_3
    else if (t <= (-1.4d-73)) then
        tmp = t_2
    else if (t <= 5.5d-306) then
        tmp = t_1
    else if (t <= 5.5d-267) then
        tmp = t_2
    else if (t <= 5.5d+35) then
        tmp = t_1
    else if (t <= 3.1d+120) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -3.2e+44) {
		tmp = t_3;
	} else if (t <= -1.4e-73) {
		tmp = t_2;
	} else if (t <= 5.5e-306) {
		tmp = t_1;
	} else if (t <= 5.5e-267) {
		tmp = t_2;
	} else if (t <= 5.5e+35) {
		tmp = t_1;
	} else if (t <= 3.1e+120) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = j * ((a * c) - (y * i))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -3.2e+44:
		tmp = t_3
	elif t <= -1.4e-73:
		tmp = t_2
	elif t <= 5.5e-306:
		tmp = t_1
	elif t <= 5.5e-267:
		tmp = t_2
	elif t <= 5.5e+35:
		tmp = t_1
	elif t <= 3.1e+120:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.2e+44)
		tmp = t_3;
	elseif (t <= -1.4e-73)
		tmp = t_2;
	elseif (t <= 5.5e-306)
		tmp = t_1;
	elseif (t <= 5.5e-267)
		tmp = t_2;
	elseif (t <= 5.5e+35)
		tmp = t_1;
	elseif (t <= 3.1e+120)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = j * ((a * c) - (y * i));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -3.2e+44)
		tmp = t_3;
	elseif (t <= -1.4e-73)
		tmp = t_2;
	elseif (t <= 5.5e-306)
		tmp = t_1;
	elseif (t <= 5.5e-267)
		tmp = t_2;
	elseif (t <= 5.5e+35)
		tmp = t_1;
	elseif (t <= 3.1e+120)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+44], t$95$3, If[LessEqual[t, -1.4e-73], t$95$2, If[LessEqual[t, 5.5e-306], t$95$1, If[LessEqual[t, 5.5e-267], t$95$2, If[LessEqual[t, 5.5e+35], t$95$1, If[LessEqual[t, 3.1e+120], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000004e44 or 3.09999999999999974e120 < t

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 63.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 63.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 63.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 63.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 63.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 65.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 65.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 65.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 65.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 65.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 65.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 65.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 68.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 75.5%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around 0 60.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 60.4%

         \[\leadsto i \cdot \left(t \cdot b\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      2. unsub-neg 60.4%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) - a \cdot \left(t \cdot x\right)} \]

      3. *-commutative 60.4%

         \[\leadsto i \cdot \left(t \cdot b\right) - a \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 67.0%

         \[\leadsto i \cdot \left(t \cdot b\right) - \color{blue}{\left(a \cdot x\right) \cdot t} \]

      5. cancel-sign-sub-inv 67.0%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(-a \cdot x\right) \cdot t} \]

      6. *-commutative 67.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} + \left(-a \cdot x\right) \cdot t \]

      7. associate-*l* 72.0%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} + \left(-a \cdot x\right) \cdot t \]

      8. distribute-rgt-in 75.5%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b + \left(-a \cdot x\right)\right)} \]

      9. unsub-neg 75.5%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   7. Simplified 75.5%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -3.20000000000000004e44 < t < -1.40000000000000006e-73 or 5.49999999999999992e-306 < t < 5.4999999999999999e-267 or 5.50000000000000001e35 < t < 3.09999999999999974e120

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 73.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 73.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 73.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 73.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 73.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 75.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 75.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 75.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 75.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 75.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 75.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 75.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 61.6%

      \[\leadsto \color{blue}{\left(c \cdot a + -1 \cdot \left(i \cdot y\right)\right) \cdot j} \]
   5. Step-by-step derivation

      1. *-commutative 61.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. neg-mul-1 61.6%

         \[\leadsto j \cdot \left(c \cdot a + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 61.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} \]

   6. Simplified 61.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right)} \]

   if -1.40000000000000006e-73 < t < 5.49999999999999992e-306 or 5.4999999999999999e-267 < t < 5.50000000000000001e35

   1. Initial program 86.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 86.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 86.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 86.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 86.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 86.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 87.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 87.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 87.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 87.7%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 87.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 87.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 87.7%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in z around inf 59.2%

      \[\leadsto \color{blue}{\left(y \cdot x + -1 \cdot \left(c \cdot b\right)\right) \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 59.2%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot x + -1 \cdot \left(c \cdot b\right)\right)} \]

      2. mul-1-neg 59.2%

         \[\leadsto z \cdot \left(y \cdot x + \color{blue}{\left(-c \cdot b\right)}\right) \]

      3. sub-neg 59.2%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x - c \cdot b\right)} \]

   6. Simplified 59.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-306}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-267}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 14: 51.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -9 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.46 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.7 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 0.00078:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -9e-21)
     t_2
     (if (<= c -1.46e-210)
       (* i (- (* t b) (* y j)))
       (if (<= c 7.7e-150)
         t_1
         (if (<= c 4.5e-110)
           (* y (- (* x z) (* i j)))
           (if (<= c 0.00078) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -9e-21) {
		tmp = t_2;
	} else if (c <= -1.46e-210) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 7.7e-150) {
		tmp = t_1;
	} else if (c <= 4.5e-110) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 0.00078) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-9d-21)) then
        tmp = t_2
    else if (c <= (-1.46d-210)) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 7.7d-150) then
        tmp = t_1
    else if (c <= 4.5d-110) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 0.00078d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -9e-21) {
		tmp = t_2;
	} else if (c <= -1.46e-210) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 7.7e-150) {
		tmp = t_1;
	} else if (c <= 4.5e-110) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 0.00078) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -9e-21:
		tmp = t_2
	elif c <= -1.46e-210:
		tmp = i * ((t * b) - (y * j))
	elif c <= 7.7e-150:
		tmp = t_1
	elif c <= 4.5e-110:
		tmp = y * ((x * z) - (i * j))
	elif c <= 0.00078:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -9e-21)
		tmp = t_2;
	elseif (c <= -1.46e-210)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 7.7e-150)
		tmp = t_1;
	elseif (c <= 4.5e-110)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 0.00078)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -9e-21)
		tmp = t_2;
	elseif (c <= -1.46e-210)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 7.7e-150)
		tmp = t_1;
	elseif (c <= 4.5e-110)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 0.00078)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9e-21], t$95$2, If[LessEqual[c, -1.46e-210], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.7e-150], t$95$1, If[LessEqual[c, 4.5e-110], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 0.00078], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -8.99999999999999936e-21 or 7.79999999999999986e-4 < c

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 65.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 65.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 65.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 65.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 65.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 68.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 68.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 68.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 68.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 68.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 68.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 68.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around inf 63.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 60.8%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 60.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 60.8%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 60.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 60.8%

         \[\leadsto c \cdot \left(a \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      6. distribute-lft-out-- 63.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 63.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -8.99999999999999936e-21 < c < -1.45999999999999994e-210

   1. Initial program 88.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 88.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 88.3%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 88.3%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 88.3%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 88.3%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 88.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 88.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 88.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 88.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 88.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 88.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 88.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in i around inf 59.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.1%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 59.1%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 59.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if -1.45999999999999994e-210 < c < 7.70000000000000003e-150 or 4.5000000000000001e-110 < c < 7.79999999999999986e-4

   1. Initial program 86.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 86.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 86.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 86.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 86.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 86.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 86.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 86.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 86.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 86.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 86.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 86.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 86.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 61.9%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around 0 50.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 50.1%

         \[\leadsto i \cdot \left(t \cdot b\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      2. unsub-neg 50.1%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) - a \cdot \left(t \cdot x\right)} \]

      3. *-commutative 50.1%

         \[\leadsto i \cdot \left(t \cdot b\right) - a \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 56.0%

         \[\leadsto i \cdot \left(t \cdot b\right) - \color{blue}{\left(a \cdot x\right) \cdot t} \]

      5. cancel-sign-sub-inv 56.0%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(-a \cdot x\right) \cdot t} \]

      6. *-commutative 56.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} + \left(-a \cdot x\right) \cdot t \]

      7. associate-*l* 59.5%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} + \left(-a \cdot x\right) \cdot t \]

      8. distribute-rgt-in 61.9%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b + \left(-a \cdot x\right)\right)} \]

      9. unsub-neg 61.9%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if 7.70000000000000003e-150 < c < 4.5000000000000001e-110

   1. Initial program 87.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 87.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 87.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 87.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 87.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 87.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 74.8%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 74.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 74.8%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 74.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 74.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{-21}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.46 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.7 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 0.00078:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 15: 29.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+24}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))))
   (if (<= a -8.2e+217)
     t_1
     (if (<= a -6.2e+77)
       (* a (* c j))
       (if (<= a -5e+63)
         t_1
         (if (<= a 8.6e-178)
           (* x (* y z))
           (if (<= a 3.8e+24) (* i (* t b)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (a <= -8.2e+217) {
		tmp = t_1;
	} else if (a <= -6.2e+77) {
		tmp = a * (c * j);
	} else if (a <= -5e+63) {
		tmp = t_1;
	} else if (a <= 8.6e-178) {
		tmp = x * (y * z);
	} else if (a <= 3.8e+24) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * -x)
    if (a <= (-8.2d+217)) then
        tmp = t_1
    else if (a <= (-6.2d+77)) then
        tmp = a * (c * j)
    else if (a <= (-5d+63)) then
        tmp = t_1
    else if (a <= 8.6d-178) then
        tmp = x * (y * z)
    else if (a <= 3.8d+24) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (a <= -8.2e+217) {
		tmp = t_1;
	} else if (a <= -6.2e+77) {
		tmp = a * (c * j);
	} else if (a <= -5e+63) {
		tmp = t_1;
	} else if (a <= 8.6e-178) {
		tmp = x * (y * z);
	} else if (a <= 3.8e+24) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	tmp = 0
	if a <= -8.2e+217:
		tmp = t_1
	elif a <= -6.2e+77:
		tmp = a * (c * j)
	elif a <= -5e+63:
		tmp = t_1
	elif a <= 8.6e-178:
		tmp = x * (y * z)
	elif a <= 3.8e+24:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (a <= -8.2e+217)
		tmp = t_1;
	elseif (a <= -6.2e+77)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -5e+63)
		tmp = t_1;
	elseif (a <= 8.6e-178)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 3.8e+24)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * -x);
	tmp = 0.0;
	if (a <= -8.2e+217)
		tmp = t_1;
	elseif (a <= -6.2e+77)
		tmp = a * (c * j);
	elseif (a <= -5e+63)
		tmp = t_1;
	elseif (a <= 8.6e-178)
		tmp = x * (y * z);
	elseif (a <= 3.8e+24)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+217], t$95$1, If[LessEqual[a, -6.2e+77], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e+63], t$95$1, If[LessEqual[a, 8.6e-178], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+24], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.2000000000000005e217 or -6.19999999999999997e77 < a < -5.00000000000000011e63 or 3.80000000000000015e24 < a

   1. Initial program 68.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 68.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 68.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 68.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 68.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 68.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 69.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 69.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 69.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 69.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 69.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 69.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 73.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 63.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 63.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 63.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 63.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 63.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 44.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 44.3%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 44.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 44.3%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 44.3%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -8.2000000000000005e217 < a < -6.19999999999999997e77

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 79.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 79.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 79.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 79.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 79.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 79.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 79.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 79.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 79.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 79.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 61.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 61.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 61.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 44.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -5.00000000000000011e63 < a < 8.6e-178

   1. Initial program 85.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 85.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 85.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 85.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 85.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 85.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 87.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 87.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 87.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 87.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 87.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 87.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 87.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 52.0%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 52.0%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 52.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 52.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 37.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.3%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 38.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   9. Simplified 38.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 8.6e-178 < a < 3.80000000000000015e24

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 63.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 63.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 63.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 63.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 63.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 67.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 67.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 67.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 67.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 67.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 67.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 67.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 67.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 38.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 35.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+24}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 16: 29.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+159}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))))
   (if (<= a -1.1e+216)
     t_1
     (if (<= a -4.5e+76)
       (* a (* c j))
       (if (<= a -8e+64)
         t_1
         (if (<= a -3.35e-158)
           (* y (* x z))
           (if (<= a 4.5e+159) (* c (* z (- b))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (a <= -1.1e+216) {
		tmp = t_1;
	} else if (a <= -4.5e+76) {
		tmp = a * (c * j);
	} else if (a <= -8e+64) {
		tmp = t_1;
	} else if (a <= -3.35e-158) {
		tmp = y * (x * z);
	} else if (a <= 4.5e+159) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * -x)
    if (a <= (-1.1d+216)) then
        tmp = t_1
    else if (a <= (-4.5d+76)) then
        tmp = a * (c * j)
    else if (a <= (-8d+64)) then
        tmp = t_1
    else if (a <= (-3.35d-158)) then
        tmp = y * (x * z)
    else if (a <= 4.5d+159) then
        tmp = c * (z * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (a <= -1.1e+216) {
		tmp = t_1;
	} else if (a <= -4.5e+76) {
		tmp = a * (c * j);
	} else if (a <= -8e+64) {
		tmp = t_1;
	} else if (a <= -3.35e-158) {
		tmp = y * (x * z);
	} else if (a <= 4.5e+159) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	tmp = 0
	if a <= -1.1e+216:
		tmp = t_1
	elif a <= -4.5e+76:
		tmp = a * (c * j)
	elif a <= -8e+64:
		tmp = t_1
	elif a <= -3.35e-158:
		tmp = y * (x * z)
	elif a <= 4.5e+159:
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (a <= -1.1e+216)
		tmp = t_1;
	elseif (a <= -4.5e+76)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -8e+64)
		tmp = t_1;
	elseif (a <= -3.35e-158)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 4.5e+159)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * -x);
	tmp = 0.0;
	if (a <= -1.1e+216)
		tmp = t_1;
	elseif (a <= -4.5e+76)
		tmp = a * (c * j);
	elseif (a <= -8e+64)
		tmp = t_1;
	elseif (a <= -3.35e-158)
		tmp = y * (x * z);
	elseif (a <= 4.5e+159)
		tmp = c * (z * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+216], t$95$1, If[LessEqual[a, -4.5e+76], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8e+64], t$95$1, If[LessEqual[a, -3.35e-158], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+159], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.1e216 or -4.4999999999999997e76 < a < -8.00000000000000017e64 or 4.50000000000000026e159 < a

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 67.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 67.3%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 67.3%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 67.3%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 67.3%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 69.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 69.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 69.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 69.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 69.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 69.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 69.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 70.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 72.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 72.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 72.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 72.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 72.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 55.7%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 55.7%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 55.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 55.7%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 55.7%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -1.1e216 < a < -4.4999999999999997e76

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 79.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 79.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 79.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 79.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 79.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 79.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 79.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 79.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 79.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 79.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 61.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 61.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 61.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 44.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -8.00000000000000017e64 < a < -3.35e-158

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 83.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 83.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 83.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 83.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 83.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 87.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 87.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 87.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 87.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 87.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 87.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 87.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 57.8%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 57.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 57.8%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 57.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 45.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.35e-158 < a < 4.50000000000000026e159

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.7%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.7%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in b around inf 51.7%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around 0 36.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 36.7%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

      2. distribute-rgt-neg-in 36.7%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

      3. *-commutative 36.7%

         \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

      4. distribute-rgt-neg-in 36.7%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   7. Simplified 36.7%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+216}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+159}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 17: 30.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))))
   (if (<= a -8.5e+211)
     t_1
     (if (<= a -8e+76)
       (* a (* c j))
       (if (<= a -6.5e+63)
         (* a (* t (- x)))
         (if (<= a -1.1e-160)
           (* y (* x z))
           (if (<= a 9.5e+65) (* c (* z (- b))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (a <= -8.5e+211) {
		tmp = t_1;
	} else if (a <= -8e+76) {
		tmp = a * (c * j);
	} else if (a <= -6.5e+63) {
		tmp = a * (t * -x);
	} else if (a <= -1.1e-160) {
		tmp = y * (x * z);
	} else if (a <= 9.5e+65) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x * -a)
    if (a <= (-8.5d+211)) then
        tmp = t_1
    else if (a <= (-8d+76)) then
        tmp = a * (c * j)
    else if (a <= (-6.5d+63)) then
        tmp = a * (t * -x)
    else if (a <= (-1.1d-160)) then
        tmp = y * (x * z)
    else if (a <= 9.5d+65) then
        tmp = c * (z * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (a <= -8.5e+211) {
		tmp = t_1;
	} else if (a <= -8e+76) {
		tmp = a * (c * j);
	} else if (a <= -6.5e+63) {
		tmp = a * (t * -x);
	} else if (a <= -1.1e-160) {
		tmp = y * (x * z);
	} else if (a <= 9.5e+65) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	tmp = 0
	if a <= -8.5e+211:
		tmp = t_1
	elif a <= -8e+76:
		tmp = a * (c * j)
	elif a <= -6.5e+63:
		tmp = a * (t * -x)
	elif a <= -1.1e-160:
		tmp = y * (x * z)
	elif a <= 9.5e+65:
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (a <= -8.5e+211)
		tmp = t_1;
	elseif (a <= -8e+76)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -6.5e+63)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (a <= -1.1e-160)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 9.5e+65)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (x * -a);
	tmp = 0.0;
	if (a <= -8.5e+211)
		tmp = t_1;
	elseif (a <= -8e+76)
		tmp = a * (c * j);
	elseif (a <= -6.5e+63)
		tmp = a * (t * -x);
	elseif (a <= -1.1e-160)
		tmp = y * (x * z);
	elseif (a <= 9.5e+65)
		tmp = c * (z * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+211], t$95$1, If[LessEqual[a, -8e+76], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.5e+63], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.1e-160], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+65], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.50000000000000091e211 or 9.5000000000000005e65 < a

   1. Initial program 62.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 62.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 62.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 62.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 62.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 62.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 63.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 63.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 63.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 63.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 63.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 63.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 63.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 66.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 66.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 66.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 46.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 45.1%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-rgt-neg-in 45.1%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(-x\right)} \]

      4. *-commutative 45.1%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot \left(-x\right) \]

      5. associate-*r* 47.4%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(-x\right)\right)} \]

   9. Simplified 47.4%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(-x\right)\right)} \]

   if -8.50000000000000091e211 < a < -8.0000000000000004e76

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 79.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 79.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 79.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 79.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 79.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 79.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 79.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 79.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 79.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 79.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 61.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 61.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 61.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 44.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -8.0000000000000004e76 < a < -6.49999999999999992e63

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 100.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 58.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 58.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 57.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 57.6%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 57.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 57.6%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 57.6%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -6.49999999999999992e63 < a < -1.1e-160

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 83.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 83.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 83.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 83.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 83.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 87.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 87.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 87.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 87.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 87.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 87.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 87.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 57.8%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 57.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 57.8%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 57.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 45.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.1e-160 < a < 9.5000000000000005e65

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 80.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 80.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 80.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 80.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 80.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 81.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 81.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 81.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 81.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 81.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 81.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 81.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in b around inf 53.1%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around 0 38.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 38.2%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

      2. distribute-rgt-neg-in 38.2%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

      3. *-commutative 38.2%

         \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

      4. distribute-rgt-neg-in 38.2%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+211}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 18: 30.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+66}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.3e+217)
   (* x (* t (- a)))
   (if (<= a -6.8e+75)
     (* a (* c j))
     (if (<= a -1.7e+64)
       (* a (* t (- x)))
       (if (<= a -3e-161)
         (* y (* x z))
         (if (<= a 7.5e+66) (* c (* z (- b))) (* t (* x (- a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.3e+217) {
		tmp = x * (t * -a);
	} else if (a <= -6.8e+75) {
		tmp = a * (c * j);
	} else if (a <= -1.7e+64) {
		tmp = a * (t * -x);
	} else if (a <= -3e-161) {
		tmp = y * (x * z);
	} else if (a <= 7.5e+66) {
		tmp = c * (z * -b);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.3d+217)) then
        tmp = x * (t * -a)
    else if (a <= (-6.8d+75)) then
        tmp = a * (c * j)
    else if (a <= (-1.7d+64)) then
        tmp = a * (t * -x)
    else if (a <= (-3d-161)) then
        tmp = y * (x * z)
    else if (a <= 7.5d+66) then
        tmp = c * (z * -b)
    else
        tmp = t * (x * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.3e+217) {
		tmp = x * (t * -a);
	} else if (a <= -6.8e+75) {
		tmp = a * (c * j);
	} else if (a <= -1.7e+64) {
		tmp = a * (t * -x);
	} else if (a <= -3e-161) {
		tmp = y * (x * z);
	} else if (a <= 7.5e+66) {
		tmp = c * (z * -b);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.3e+217:
		tmp = x * (t * -a)
	elif a <= -6.8e+75:
		tmp = a * (c * j)
	elif a <= -1.7e+64:
		tmp = a * (t * -x)
	elif a <= -3e-161:
		tmp = y * (x * z)
	elif a <= 7.5e+66:
		tmp = c * (z * -b)
	else:
		tmp = t * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.3e+217)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (a <= -6.8e+75)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -1.7e+64)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (a <= -3e-161)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 7.5e+66)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = Float64(t * Float64(x * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.3e+217)
		tmp = x * (t * -a);
	elseif (a <= -6.8e+75)
		tmp = a * (c * j);
	elseif (a <= -1.7e+64)
		tmp = a * (t * -x);
	elseif (a <= -3e-161)
		tmp = y * (x * z);
	elseif (a <= 7.5e+66)
		tmp = c * (z * -b);
	else
		tmp = t * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.3e+217], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.8e+75], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.7e+64], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-161], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e+66], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.30000000000000006e217

   1. Initial program 65.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 65.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 65.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 65.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 65.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 65.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 65.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 65.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 65.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 65.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 65.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 65.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 65.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 82.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 82.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 82.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 82.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 82.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 57.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 57.4%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 68.5%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-rgt-neg-in 68.5%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(-x\right)} \]

      4. *-commutative 68.5%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot \left(-x\right) \]

      5. associate-*r* 57.6%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(-x\right)\right)} \]

   9. Simplified 57.6%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(-x\right)\right)} \]

   10. Taylor expanded in t around 0 57.4%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 57.4%

          \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

       2. *-commutative 57.4%

          \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot a} \]

       3. *-commutative 57.4%

          \[\leadsto -\color{blue}{\left(x \cdot t\right)} \cdot a \]

       4. associate-*l* 68.5%

          \[\leadsto -\color{blue}{x \cdot \left(t \cdot a\right)} \]

       5. distribute-rgt-neg-in 68.5%

          \[\leadsto \color{blue}{x \cdot \left(-t \cdot a\right)} \]

       6. *-commutative 68.5%

          \[\leadsto x \cdot \left(-\color{blue}{a \cdot t}\right) \]

   12. Simplified 68.5%

       \[\leadsto \color{blue}{x \cdot \left(-a \cdot t\right)} \]

   if -1.30000000000000006e217 < a < -6.80000000000000022e75

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 79.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 79.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 79.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 79.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 79.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 79.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 79.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 79.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 79.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 79.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 61.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 61.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 61.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 44.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -6.80000000000000022e75 < a < -1.7000000000000001e64

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 100.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 100.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 58.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 58.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 57.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 57.6%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 57.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 57.6%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 57.6%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -1.7000000000000001e64 < a < -2.99999999999999989e-161

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 83.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 83.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 83.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 83.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 83.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 87.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 87.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 87.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 87.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 87.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 87.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 87.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 57.8%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 57.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 57.8%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 57.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 45.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -2.99999999999999989e-161 < a < 7.50000000000000024e66

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 80.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 80.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 80.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 80.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 80.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 81.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 81.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 81.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 81.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 81.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 81.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 81.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in b around inf 53.1%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around 0 38.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 38.2%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

      2. distribute-rgt-neg-in 38.2%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

      3. *-commutative 38.2%

         \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

      4. distribute-rgt-neg-in 38.2%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} \]

   if 7.50000000000000024e66 < a

   1. Initial program 61.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 61.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 61.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 61.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 61.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 61.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 63.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 63.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 63.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 63.4%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 63.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 63.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 63.4%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 65.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 61.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 61.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 61.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 42.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 42.6%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 38.0%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-rgt-neg-in 38.0%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(-x\right)} \]

      4. *-commutative 38.0%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot \left(-x\right) \]

      5. associate-*r* 44.3%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(-x\right)\right)} \]

   9. Simplified 44.3%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(-x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+66}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 19: 41.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -4.5e+46)
     t_1
     (if (<= a -1.9e-158)
       (* y (* x z))
       (if (<= a 9.5e+27) (* c (* z (- b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.5e+46) {
		tmp = t_1;
	} else if (a <= -1.9e-158) {
		tmp = y * (x * z);
	} else if (a <= 9.5e+27) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-4.5d+46)) then
        tmp = t_1
    else if (a <= (-1.9d-158)) then
        tmp = y * (x * z)
    else if (a <= 9.5d+27) then
        tmp = c * (z * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.5e+46) {
		tmp = t_1;
	} else if (a <= -1.9e-158) {
		tmp = y * (x * z);
	} else if (a <= 9.5e+27) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.5e+46:
		tmp = t_1
	elif a <= -1.9e-158:
		tmp = y * (x * z)
	elif a <= 9.5e+27:
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.5e+46)
		tmp = t_1;
	elseif (a <= -1.9e-158)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 9.5e+27)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.5e+46)
		tmp = t_1;
	elseif (a <= -1.9e-158)
		tmp = y * (x * z);
	elseif (a <= 9.5e+27)
		tmp = c * (z * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+46], t$95$1, If[LessEqual[a, -1.9e-158], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+27], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5000000000000001e46 or 9.4999999999999997e27 < a

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 70.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 70.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 70.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 70.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 70.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 72.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 72.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 72.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 72.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 72.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 72.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 62.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 62.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 62.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 62.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -4.5000000000000001e46 < a < -1.8999999999999999e-158

   1. Initial program 86.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 86.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 86.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 86.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 86.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 86.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 88.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 88.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 88.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 88.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 88.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 88.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 88.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 59.4%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 59.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 45.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.8999999999999999e-158 < a < 9.4999999999999997e27

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 79.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 79.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 79.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 79.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 80.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 80.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 80.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 80.2%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 80.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 80.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 80.2%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 82.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in b around inf 56.7%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around 0 40.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 40.1%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

      2. distribute-rgt-neg-in 40.1%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

      3. *-commutative 40.1%

         \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

      4. distribute-rgt-neg-in 40.1%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   7. Simplified 40.1%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 20: 44.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -3.8e+46)
     t_1
     (if (<= a -1.2e-158)
       (* y (* x z))
       (if (<= a 8.8e+58) (* c (- (* a j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.8e+46) {
		tmp = t_1;
	} else if (a <= -1.2e-158) {
		tmp = y * (x * z);
	} else if (a <= 8.8e+58) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-3.8d+46)) then
        tmp = t_1
    else if (a <= (-1.2d-158)) then
        tmp = y * (x * z)
    else if (a <= 8.8d+58) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.8e+46) {
		tmp = t_1;
	} else if (a <= -1.2e-158) {
		tmp = y * (x * z);
	} else if (a <= 8.8e+58) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.8e+46:
		tmp = t_1
	elif a <= -1.2e-158:
		tmp = y * (x * z)
	elif a <= 8.8e+58:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.8e+46)
		tmp = t_1;
	elseif (a <= -1.2e-158)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 8.8e+58)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.8e+46)
		tmp = t_1;
	elseif (a <= -1.2e-158)
		tmp = y * (x * z);
	elseif (a <= 8.8e+58)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+46], t$95$1, If[LessEqual[a, -1.2e-158], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+58], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7999999999999999e46 or 8.8000000000000003e58 < a

   1. Initial program 69.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 69.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 69.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 69.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 69.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 69.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 70.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 70.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 70.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 70.7%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 70.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 70.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 70.7%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 64.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 64.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 64.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 64.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 64.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -3.7999999999999999e46 < a < -1.20000000000000004e-158

   1. Initial program 86.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 86.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 86.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 86.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 86.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 86.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 88.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 88.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 88.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 88.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 88.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 88.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 88.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 59.4%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 59.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 45.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.20000000000000004e-158 < a < 8.8000000000000003e58

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 79.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 79.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 79.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 79.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 80.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 80.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 80.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 80.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 80.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 80.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 80.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around inf 41.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 40.7%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 40.7%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 40.7%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 40.7%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 40.7%

         \[\leadsto c \cdot \left(a \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      6. distribute-lft-out-- 41.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 41.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 21: 51.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.15 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-208}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -3.15e-21)
     t_1
     (if (<= c -2.3e-208)
       (* i (- (* t b) (* y j)))
       (if (<= c 6.5e-8) (* t (- (* b i) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.15e-21) {
		tmp = t_1;
	} else if (c <= -2.3e-208) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 6.5e-8) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-3.15d-21)) then
        tmp = t_1
    else if (c <= (-2.3d-208)) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 6.5d-8) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.15e-21) {
		tmp = t_1;
	} else if (c <= -2.3e-208) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 6.5e-8) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -3.15e-21:
		tmp = t_1
	elif c <= -2.3e-208:
		tmp = i * ((t * b) - (y * j))
	elif c <= 6.5e-8:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.15e-21)
		tmp = t_1;
	elseif (c <= -2.3e-208)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 6.5e-8)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.15e-21)
		tmp = t_1;
	elseif (c <= -2.3e-208)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 6.5e-8)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.15e-21], t$95$1, If[LessEqual[c, -2.3e-208], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e-8], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.15e-21 or 6.49999999999999997e-8 < c

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 65.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 65.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 65.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 65.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 65.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 68.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 68.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 68.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 68.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 68.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 68.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 68.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around inf 63.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 60.8%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 60.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 60.8%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 60.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 60.8%

         \[\leadsto c \cdot \left(a \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      6. distribute-lft-out-- 63.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 63.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -3.15e-21 < c < -2.29999999999999997e-208

   1. Initial program 88.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 88.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 88.3%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 88.3%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 88.3%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 88.3%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 88.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 88.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 88.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 88.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 88.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 88.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 88.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in i around inf 59.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.1%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 59.1%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 59.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if -2.29999999999999997e-208 < c < 6.49999999999999997e-8

   1. Initial program 87.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 87.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 87.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 87.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 87.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 87.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 88.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 88.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 88.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 88.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 88.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 88.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 88.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 57.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around 0 47.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 47.0%

         \[\leadsto i \cdot \left(t \cdot b\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      2. unsub-neg 47.0%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) - a \cdot \left(t \cdot x\right)} \]

      3. *-commutative 47.0%

         \[\leadsto i \cdot \left(t \cdot b\right) - a \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 52.4%

         \[\leadsto i \cdot \left(t \cdot b\right) - \color{blue}{\left(a \cdot x\right) \cdot t} \]

      5. cancel-sign-sub-inv 52.4%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(-a \cdot x\right) \cdot t} \]

      6. *-commutative 52.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} + \left(-a \cdot x\right) \cdot t \]

      7. associate-*l* 55.5%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} + \left(-a \cdot x\right) \cdot t \]

      8. distribute-rgt-in 57.7%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b + \left(-a \cdot x\right)\right)} \]

      9. unsub-neg 57.7%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   7. Simplified 57.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.15 \cdot 10^{-21}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-208}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 22: 28.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+65} \lor \neg \left(b \leq 3.5 \cdot 10^{-61}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.7e+65) (not (<= b 3.5e-61))) (* i (* t b)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.7e+65) || !(b <= 3.5e-61)) {
		tmp = i * (t * b);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-2.7d+65)) .or. (.not. (b <= 3.5d-61))) then
        tmp = i * (t * b)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.7e+65) || !(b <= 3.5e-61)) {
		tmp = i * (t * b);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.7e+65) or not (b <= 3.5e-61):
		tmp = i * (t * b)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.7e+65) || !(b <= 3.5e-61))
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.7e+65) || ~((b <= 3.5e-61)))
		tmp = i * (t * b);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.7e+65], N[Not[LessEqual[b, 3.5e-61]], $MachinePrecision]], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.70000000000000019e65 or 3.5000000000000003e-61 < b

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 77.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 77.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 77.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 77.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 80.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 80.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 80.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 80.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 80.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 80.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 80.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 44.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 33.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -2.70000000000000019e65 < b < 3.5000000000000003e-61

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 75.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 75.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 75.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 75.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 75.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 75.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 75.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 75.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 46.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 46.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 29.6%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+65} \lor \neg \left(b \leq 3.5 \cdot 10^{-61}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 23: 29.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4500:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4500.0)
   (* t (* b i))
   (if (<= t 3.4e+46) (* x (* y z)) (* i (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4500.0) {
		tmp = t * (b * i);
	} else if (t <= 3.4e+46) {
		tmp = x * (y * z);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-4500.0d0)) then
        tmp = t * (b * i)
    else if (t <= 3.4d+46) then
        tmp = x * (y * z)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4500.0) {
		tmp = t * (b * i);
	} else if (t <= 3.4e+46) {
		tmp = x * (y * z);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4500.0:
		tmp = t * (b * i)
	elif t <= 3.4e+46:
		tmp = x * (y * z)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4500.0)
		tmp = Float64(t * Float64(b * i));
	elseif (t <= 3.4e+46)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4500.0)
		tmp = t * (b * i);
	elseif (t <= 3.4e+46)
		tmp = x * (y * z);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4500.0], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+46], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4500

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 72.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 72.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 72.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 72.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 72.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 74.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 74.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 74.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 74.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 74.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 74.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 67.4%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 30.6%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot b\right)} \]

   if -4500 < t < 3.3999999999999998e46

   1. Initial program 85.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 85.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 85.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 85.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 85.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 85.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 86.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 86.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 86.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 86.2%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 86.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 86.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 86.2%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 41.1%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 41.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 41.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 41.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 29.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 32.8%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 32.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   9. Simplified 32.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 3.3999999999999998e46 < t

   1. Initial program 55.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 55.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 55.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 55.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 55.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 55.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 58.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 58.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 58.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 58.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 58.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 58.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 58.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 62.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 64.9%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 45.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4500:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 24: 29.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -105000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -105000.0)
   (* b (* t i))
   (if (<= t 1.15e+47) (* x (* y z)) (* i (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -105000.0) {
		tmp = b * (t * i);
	} else if (t <= 1.15e+47) {
		tmp = x * (y * z);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-105000.0d0)) then
        tmp = b * (t * i)
    else if (t <= 1.15d+47) then
        tmp = x * (y * z)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -105000.0) {
		tmp = b * (t * i);
	} else if (t <= 1.15e+47) {
		tmp = x * (y * z);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -105000.0:
		tmp = b * (t * i)
	elif t <= 1.15e+47:
		tmp = x * (y * z)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -105000.0)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 1.15e+47)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -105000.0)
		tmp = b * (t * i);
	elseif (t <= 1.15e+47)
		tmp = x * (y * z);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -105000.0], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+47], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -105000

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 72.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 72.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 72.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 72.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 72.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 74.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 74.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 74.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 74.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 74.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 74.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 67.4%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 28.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 35.3%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 35.3%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   7. Simplified 35.3%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot b} \]

   if -105000 < t < 1.1499999999999999e47

   1. Initial program 85.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 85.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 85.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 85.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 85.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 85.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 86.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 86.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 86.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 86.2%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 86.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 86.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 86.2%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 41.1%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 41.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 41.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 41.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 29.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 32.8%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 32.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   9. Simplified 32.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 1.1499999999999999e47 < t

   1. Initial program 55.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 55.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 55.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 55.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 55.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 55.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 58.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 58.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 58.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 58.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 58.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 58.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 58.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 62.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around inf 64.9%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 45.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -105000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 25: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. sub-neg 76.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. +-commutative 76.1%

      \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. associate-+l+ 76.1%

      \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   4. distribute-rgt-neg-in 76.1%

      \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   5. +-commutative 76.1%

      \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

   6. fma-def 77.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

   7. sub-neg 77.7%

      \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   8. +-commutative 77.7%

      \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   9. distribute-neg-in 77.7%

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   10. unsub-neg 77.7%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   11. remove-double-neg 77.7%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   12. *-commutative 77.7%

       \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

3. Simplified 79.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

4. Taylor expanded in a around inf 37.8%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 37.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 37.8%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 37.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

6. Simplified 37.8%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

7. Taylor expanded in c around inf 18.8%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

8. Final simplification 18.8%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))