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

Percentage Accurate: 73.3% → 81.7%

Time: 27.3s

Alternatives: 24

Speedup: 0.5×

• 57.0% 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: 73.3% 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: 81.7% accurate, 0.2× speedup

Math

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

FPCore

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

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $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 94.1%

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

      1. sub-neg 94.1%

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

      2. +-commutative 94.1%

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

      3. associate-+l+ 94.1%

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

      4. distribute-rgt-neg-in 94.1%

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

      5. +-commutative 94.1%

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

      6. fma-def 94.1%

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

      7. sub-neg 94.1%

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

      8. +-commutative 94.1%

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

      9. distribute-neg-in 94.1%

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

      10. unsub-neg 94.1%

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

      11. remove-double-neg 94.1%

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

      12. *-commutative 94.1%

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

   3. Simplified 94.1%

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

      1. fma-udef 94.1%

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

      2. *-commutative 94.1%

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

   5. Applied egg-rr 94.1%

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

   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. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. remove-double-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 52.5%

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

4. Final simplification 85.0%

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

Alternative 2: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $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 94.1%

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

   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. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. remove-double-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 52.5%

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

4. Final simplification 85.0%

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

Alternative 3: 52.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -18500000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-171}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (* c j)) (* b (- (* t i) (* z c)))))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -3.3e+112)
     t_3
     (if (<= z -18500000000000.0)
       t_2
       (if (<= z -1.2e-130)
         t_1
         (if (<= z -9e-216)
           (* a (- (* c j) (* x t)))
           (if (<= z 3.4e-269)
             t_1
             (if (<= z 6.2e-171)
               (* i (- (* t b) (* y j)))
               (if (<= z 3.4e-39)
                 (* j (- (* a c) (* y i)))
                 (if (<= z 3.65e-9) t_2 (if (<= z 4.3e+186) t_1 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 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.3e+112) {
		tmp = t_3;
	} else if (z <= -18500000000000.0) {
		tmp = t_2;
	} else if (z <= -1.2e-130) {
		tmp = t_1;
	} else if (z <= -9e-216) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 3.4e-269) {
		tmp = t_1;
	} else if (z <= 6.2e-171) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 3.4e-39) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 3.65e-9) {
		tmp = t_2;
	} else if (z <= 4.3e+186) {
		tmp = t_1;
	} 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 = (a * (c * j)) + (b * ((t * i) - (z * c)))
    t_2 = t * ((b * i) - (x * a))
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-3.3d+112)) then
        tmp = t_3
    else if (z <= (-18500000000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.2d-130)) then
        tmp = t_1
    else if (z <= (-9d-216)) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= 3.4d-269) then
        tmp = t_1
    else if (z <= 6.2d-171) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 3.4d-39) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 3.65d-9) then
        tmp = t_2
    else if (z <= 4.3d+186) then
        tmp = t_1
    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 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.3e+112) {
		tmp = t_3;
	} else if (z <= -18500000000000.0) {
		tmp = t_2;
	} else if (z <= -1.2e-130) {
		tmp = t_1;
	} else if (z <= -9e-216) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 3.4e-269) {
		tmp = t_1;
	} else if (z <= 6.2e-171) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 3.4e-39) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 3.65e-9) {
		tmp = t_2;
	} else if (z <= 4.3e+186) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)))
	t_2 = t * ((b * i) - (x * a))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -3.3e+112:
		tmp = t_3
	elif z <= -18500000000000.0:
		tmp = t_2
	elif z <= -1.2e-130:
		tmp = t_1
	elif z <= -9e-216:
		tmp = a * ((c * j) - (x * t))
	elif z <= 3.4e-269:
		tmp = t_1
	elif z <= 6.2e-171:
		tmp = i * ((t * b) - (y * j))
	elif z <= 3.4e-39:
		tmp = j * ((a * c) - (y * i))
	elif z <= 3.65e-9:
		tmp = t_2
	elif z <= 4.3e+186:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -3.3e+112)
		tmp = t_3;
	elseif (z <= -18500000000000.0)
		tmp = t_2;
	elseif (z <= -1.2e-130)
		tmp = t_1;
	elseif (z <= -9e-216)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= 3.4e-269)
		tmp = t_1;
	elseif (z <= 6.2e-171)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 3.4e-39)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 3.65e-9)
		tmp = t_2;
	elseif (z <= 4.3e+186)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	t_2 = t * ((b * i) - (x * a));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -3.3e+112)
		tmp = t_3;
	elseif (z <= -18500000000000.0)
		tmp = t_2;
	elseif (z <= -1.2e-130)
		tmp = t_1;
	elseif (z <= -9e-216)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= 3.4e-269)
		tmp = t_1;
	elseif (z <= 6.2e-171)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 3.4e-39)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 3.65e-9)
		tmp = t_2;
	elseif (z <= 4.3e+186)
		tmp = t_1;
	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[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+112], t$95$3, If[LessEqual[z, -18500000000000.0], t$95$2, If[LessEqual[z, -1.2e-130], t$95$1, If[LessEqual[z, -9e-216], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-269], t$95$1, If[LessEqual[z, 6.2e-171], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-39], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.65e-9], t$95$2, If[LessEqual[z, 4.3e+186], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.2999999999999999e112 or 4.3e186 < z

   1. Initial program 60.2%

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

      1. cancel-sign-sub 60.2%

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

      2. cancel-sign-sub-inv 60.2%

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

      3. *-commutative 60.2%

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

      4. remove-double-neg 60.2%

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

      5. *-commutative 60.2%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in z around inf 79.0%

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

   if -3.2999999999999999e112 < z < -1.85e13 or 3.3999999999999999e-39 < z < 3.65000000000000001e-9

   1. Initial program 79.4%

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

      1. cancel-sign-sub 79.4%

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

      2. cancel-sign-sub-inv 79.4%

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

      3. *-commutative 79.4%

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

      4. remove-double-neg 79.4%

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

      5. *-commutative 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in t around inf 59.6%

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

      1. distribute-lft-out-- 59.6%

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

      2. associate-*r* 59.6%

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

      3. mul-1-neg 59.6%

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

      4. *-commutative 59.6%

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

   6. Simplified 59.6%

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

   if -1.85e13 < z < -1.19999999999999998e-130 or -8.9999999999999997e-216 < z < 3.3999999999999997e-269 or 3.65000000000000001e-9 < z < 4.3e186

   1. Initial program 82.4%

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

      1. cancel-sign-sub 82.4%

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

      2. cancel-sign-sub-inv 82.4%

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

      3. *-commutative 82.4%

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

      4. remove-double-neg 82.4%

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

      5. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around 0 68.6%

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

      1. sub-neg 68.6%

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

      2. +-commutative 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-*r* 74.9%

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

      5. *-commutative 74.9%

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

      6. mul-1-neg 74.9%

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

      7. distribute-rgt-neg-in 74.9%

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

      8. mul-1-neg 74.9%

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

      9. distribute-lft-in 74.9%

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

      10. mul-1-neg 74.9%

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

      11. unsub-neg 74.9%

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

      12. *-commutative 74.9%

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

      13. *-commutative 74.9%

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

      14. distribute-rgt-neg-in 74.9%

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

      15. neg-sub0 74.9%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      16. associate-+l- 74.9%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      17. neg-sub0 74.9%

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

      18. +-commutative 74.9%

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

      19. sub-neg 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in j around inf 70.5%

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

      1. *-commutative 37.0%

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

   9. Simplified 70.5%

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

   if -1.19999999999999998e-130 < z < -8.9999999999999997e-216

   1. Initial program 59.2%

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

      1. cancel-sign-sub 59.2%

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

      2. cancel-sign-sub-inv 59.2%

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

      3. *-commutative 59.2%

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

      4. remove-double-neg 59.2%

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

      5. *-commutative 59.2%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in a around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. unsub-neg 68.9%

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

      4. *-commutative 68.9%

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

   6. Simplified 68.9%

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

   if 3.3999999999999997e-269 < z < 6.2000000000000001e-171

   1. Initial program 77.5%

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

      1. sub-neg 77.5%

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

      2. +-commutative 77.5%

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

      3. associate-+l+ 77.5%

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

      4. distribute-rgt-neg-in 77.5%

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

      5. +-commutative 77.5%

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

      6. fma-def 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 77.6%

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

      1. fma-udef 77.6%

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

      2. *-commutative 77.6%

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

   5. Applied egg-rr 77.6%

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

   6. Taylor expanded in i around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

   8. Simplified 73.9%

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

   if 6.2000000000000001e-171 < z < 3.3999999999999999e-39

   1. Initial program 81.5%

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

      1. sub-neg 81.5%

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

      2. +-commutative 81.5%

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

      3. associate-+l+ 81.5%

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

      4. distribute-rgt-neg-in 81.5%

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

      5. +-commutative 81.5%

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

      6. fma-def 85.2%

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

      7. sub-neg 85.2%

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

      8. +-commutative 85.2%

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

      9. distribute-neg-in 85.2%

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

      10. unsub-neg 85.2%

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

      11. remove-double-neg 85.2%

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

      12. *-commutative 85.2%

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

   3. Simplified 85.2%

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

      1. fma-udef 85.2%

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

      2. *-commutative 85.2%

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

   5. Applied egg-rr 85.2%

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

   6. Taylor expanded in j around inf 59.8%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -18500000000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-130}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-171}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+186}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 4: 55.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -980000000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (* c j)) (* b (- (* t i) (* z c)))))
        (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -3.2e+112)
     t_2
     (if (<= z -980000000000.0)
       (* t (- (* b i) (* x a)))
       (if (<= z -7.2e-133)
         t_1
         (if (<= z -5.6e-216)
           (* a (- (* c j) (* x t)))
           (if (<= z -1.66e-239)
             t_1
             (if (<= z 1.05e-76)
               (+ (* j (- (* a c) (* y i))) (* i (* t b)))
               (if (<= z 3.8e+134)
                 t_1
                 (if (<= z 8e+233) (* x (- (* y z) (* t a))) 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 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.2e+112) {
		tmp = t_2;
	} else if (z <= -980000000000.0) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= -7.2e-133) {
		tmp = t_1;
	} else if (z <= -5.6e-216) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= -1.66e-239) {
		tmp = t_1;
	} else if (z <= 1.05e-76) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (z <= 3.8e+134) {
		tmp = t_1;
	} else if (z <= 8e+233) {
		tmp = x * ((y * z) - (t * a));
	} 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 = (a * (c * j)) + (b * ((t * i) - (z * c)))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-3.2d+112)) then
        tmp = t_2
    else if (z <= (-980000000000.0d0)) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= (-7.2d-133)) then
        tmp = t_1
    else if (z <= (-5.6d-216)) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= (-1.66d-239)) then
        tmp = t_1
    else if (z <= 1.05d-76) then
        tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
    else if (z <= 3.8d+134) then
        tmp = t_1
    else if (z <= 8d+233) then
        tmp = x * ((y * z) - (t * a))
    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 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.2e+112) {
		tmp = t_2;
	} else if (z <= -980000000000.0) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= -7.2e-133) {
		tmp = t_1;
	} else if (z <= -5.6e-216) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= -1.66e-239) {
		tmp = t_1;
	} else if (z <= 1.05e-76) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (z <= 3.8e+134) {
		tmp = t_1;
	} else if (z <= 8e+233) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -3.2e+112:
		tmp = t_2
	elif z <= -980000000000.0:
		tmp = t * ((b * i) - (x * a))
	elif z <= -7.2e-133:
		tmp = t_1
	elif z <= -5.6e-216:
		tmp = a * ((c * j) - (x * t))
	elif z <= -1.66e-239:
		tmp = t_1
	elif z <= 1.05e-76:
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
	elif z <= 3.8e+134:
		tmp = t_1
	elif z <= 8e+233:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -3.2e+112)
		tmp = t_2;
	elseif (z <= -980000000000.0)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= -7.2e-133)
		tmp = t_1;
	elseif (z <= -5.6e-216)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= -1.66e-239)
		tmp = t_1;
	elseif (z <= 1.05e-76)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(i * Float64(t * b)));
	elseif (z <= 3.8e+134)
		tmp = t_1;
	elseif (z <= 8e+233)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -3.2e+112)
		tmp = t_2;
	elseif (z <= -980000000000.0)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= -7.2e-133)
		tmp = t_1;
	elseif (z <= -5.6e-216)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= -1.66e-239)
		tmp = t_1;
	elseif (z <= 1.05e-76)
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	elseif (z <= 3.8e+134)
		tmp = t_1;
	elseif (z <= 8e+233)
		tmp = x * ((y * z) - (t * a));
	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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+112], t$95$2, If[LessEqual[z, -980000000000.0], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-133], t$95$1, If[LessEqual[z, -5.6e-216], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.66e-239], t$95$1, If[LessEqual[z, 1.05e-76], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+134], t$95$1, If[LessEqual[z, 8e+233], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.19999999999999986e112 or 7.99999999999999979e233 < z

   1. Initial program 60.8%

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

      1. cancel-sign-sub 60.8%

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

      2. cancel-sign-sub-inv 60.8%

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

      3. *-commutative 60.8%

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

      4. remove-double-neg 60.8%

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

      5. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in z around inf 82.4%

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

   if -3.19999999999999986e112 < z < -9.8e11

   1. Initial program 75.2%

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

      1. cancel-sign-sub 75.2%

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

      2. cancel-sign-sub-inv 75.2%

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

      3. *-commutative 75.2%

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

      4. remove-double-neg 75.2%

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

      5. *-commutative 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in t around inf 56.0%

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

      1. distribute-lft-out-- 56.0%

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

      2. associate-*r* 56.0%

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

      3. mul-1-neg 56.0%

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

      4. *-commutative 56.0%

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

   6. Simplified 56.0%

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

   if -9.8e11 < z < -7.2000000000000008e-133 or -5.6e-216 < z < -1.6599999999999999e-239 or 1.04999999999999996e-76 < z < 3.79999999999999998e134

   1. Initial program 86.2%

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

      1. cancel-sign-sub 86.2%

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

      2. cancel-sign-sub-inv 86.2%

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

      3. *-commutative 86.2%

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

      4. remove-double-neg 86.2%

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

      5. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in y around 0 75.9%

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

      1. sub-neg 75.9%

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

      2. +-commutative 75.9%

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

      3. *-commutative 75.9%

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

      4. associate-*r* 79.4%

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

      5. *-commutative 79.4%

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

      6. mul-1-neg 79.4%

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

      7. distribute-rgt-neg-in 79.4%

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

      8. mul-1-neg 79.4%

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

      9. distribute-lft-in 79.4%

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

      10. mul-1-neg 79.4%

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

      11. unsub-neg 79.4%

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

      12. *-commutative 79.4%

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

      13. *-commutative 79.4%

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

      14. distribute-rgt-neg-in 79.4%

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

      15. neg-sub0 79.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      16. associate-+l- 79.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      17. neg-sub0 79.4%

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

      18. +-commutative 79.4%

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

      19. sub-neg 79.4%

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

   6. Simplified 79.4%

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

   7. Taylor expanded in j around inf 70.8%

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

      1. *-commutative 32.4%

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

   9. Simplified 70.8%

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

   if -7.2000000000000008e-133 < z < -5.6e-216

   1. Initial program 59.2%

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

      1. cancel-sign-sub 59.2%

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

      2. cancel-sign-sub-inv 59.2%

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

      3. *-commutative 59.2%

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

      4. remove-double-neg 59.2%

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

      5. *-commutative 59.2%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in a around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. unsub-neg 68.9%

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

      4. *-commutative 68.9%

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

   6. Simplified 68.9%

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

   if -1.6599999999999999e-239 < z < 1.04999999999999996e-76

   1. Initial program 77.2%

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

      1. cancel-sign-sub 77.2%

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

      2. cancel-sign-sub-inv 77.2%

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

      3. *-commutative 77.2%

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

      4. remove-double-neg 77.2%

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

      5. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in i around inf 68.2%

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

   if 3.79999999999999998e134 < z < 7.99999999999999979e233

   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. cancel-sign-sub 62.8%

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

      2. cancel-sign-sub-inv 62.8%

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

      3. *-commutative 62.8%

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

      4. remove-double-neg 62.8%

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

      5. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in x around inf 67.0%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -980000000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-133}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-239}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+134}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 5: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.00025:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))
   (if (<= t -6.8e-23)
     t_1
     (if (<= t -1.3e-73)
       (* y (- (* x z) (* i j)))
       (if (<= t -4e-150)
         t_1
         (if (<= t 0.00025)
           (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))
           (if (<= t 2.4e+218) t_1 (* t (- (* b i) (* x a))))))))))

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))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (t <= -6.8e-23) {
		tmp = t_1;
	} else if (t <= -1.3e-73) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -4e-150) {
		tmp = t_1;
	} else if (t <= 0.00025) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else if (t <= 2.4e+218) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (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) :: t_1
    real(8) :: tmp
    t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    if (t <= (-6.8d-23)) then
        tmp = t_1
    else if (t <= (-1.3d-73)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= (-4d-150)) then
        tmp = t_1
    else if (t <= 0.00025d0) then
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else if (t <= 2.4d+218) then
        tmp = t_1
    else
        tmp = t * ((b * i) - (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 t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (t <= -6.8e-23) {
		tmp = t_1;
	} else if (t <= -1.3e-73) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -4e-150) {
		tmp = t_1;
	} else if (t <= 0.00025) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else if (t <= 2.4e+218) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	tmp = 0
	if t <= -6.8e-23:
		tmp = t_1
	elif t <= -1.3e-73:
		tmp = y * ((x * z) - (i * j))
	elif t <= -4e-150:
		tmp = t_1
	elif t <= 0.00025:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	elif t <= 2.4e+218:
		tmp = t_1
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (t <= -6.8e-23)
		tmp = t_1;
	elseif (t <= -1.3e-73)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= -4e-150)
		tmp = t_1;
	elseif (t <= 0.00025)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (t <= 2.4e+218)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	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))) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (t <= -6.8e-23)
		tmp = t_1;
	elseif (t <= -1.3e-73)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= -4e-150)
		tmp = t_1;
	elseif (t <= 0.00025)
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	elseif (t <= 2.4e+218)
		tmp = t_1;
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-23], t$95$1, If[LessEqual[t, -1.3e-73], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e-150], t$95$1, If[LessEqual[t, 0.00025], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+218], t$95$1, N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.8000000000000001e-23 or -1.3e-73 < t < -4.00000000000000003e-150 or 2.5000000000000001e-4 < t < 2.39999999999999981e218

   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. cancel-sign-sub 65.8%

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

      2. cancel-sign-sub-inv 65.8%

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

      3. *-commutative 65.8%

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

      4. remove-double-neg 65.8%

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

      5. *-commutative 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in y around 0 67.0%

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

      1. sub-neg 67.0%

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

      2. +-commutative 67.0%

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

      3. *-commutative 67.0%

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

      4. associate-*r* 67.7%

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

      5. *-commutative 67.7%

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

      6. mul-1-neg 67.7%

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

      7. distribute-rgt-neg-in 67.7%

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

      8. mul-1-neg 67.7%

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

      9. distribute-lft-in 71.5%

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

      10. mul-1-neg 71.5%

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

      11. unsub-neg 71.5%

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

      12. *-commutative 71.5%

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

      13. *-commutative 71.5%

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

      14. distribute-rgt-neg-in 71.5%

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

      15. neg-sub0 71.5%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      16. associate-+l- 71.5%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      17. neg-sub0 71.5%

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

      18. +-commutative 71.5%

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

      19. sub-neg 71.5%

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

   6. Simplified 71.5%

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

   if -6.8000000000000001e-23 < t < -1.3e-73

   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. cancel-sign-sub 69.0%

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

      2. cancel-sign-sub-inv 69.0%

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

      3. *-commutative 69.0%

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

      4. remove-double-neg 69.0%

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

      5. *-commutative 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in y around inf 69.5%

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

      1. *-commutative 69.5%

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

      2. mul-1-neg 69.5%

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

      3. unsub-neg 69.5%

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

      4. *-commutative 69.5%

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

   6. Simplified 69.5%

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

   if -4.00000000000000003e-150 < t < 2.5000000000000001e-4

   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. cancel-sign-sub 88.3%

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

      2. cancel-sign-sub-inv 88.3%

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

      3. *-commutative 88.3%

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

      4. remove-double-neg 88.3%

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

      5. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in t around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. associate--l+ 78.2%

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

      3. sub-neg 78.2%

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

      4. +-commutative 78.2%

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

      5. associate-*r* 82.3%

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

      6. distribute-lft-neg-in 82.3%

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

      7. mul-1-neg 82.3%

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

      8. *-commutative 82.3%

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

      9. associate-*r* 81.3%

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

      10. distribute-rgt-in 81.3%

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

      11. +-commutative 81.3%

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

      12. mul-1-neg 81.3%

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

      13. sub-neg 81.3%

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

   6. Simplified 81.3%

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

   if 2.39999999999999981e218 < t

   1. Initial program 55.5%

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

      1. cancel-sign-sub 55.5%

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

      2. cancel-sign-sub-inv 55.5%

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

      3. *-commutative 55.5%

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

      4. remove-double-neg 55.5%

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

      5. *-commutative 55.5%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in t around inf 80.8%

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

      1. distribute-lft-out-- 80.8%

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

      2. associate-*r* 80.8%

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

      3. mul-1-neg 80.8%

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

      4. *-commutative 80.8%

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

   6. Simplified 80.8%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 0.00025:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+218}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 6: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))
   (if (<= t -2.9e-14)
     t_1
     (if (<= t -4.2e-76)
       (+ (* x (- (* y z) (* t a))) (* i (- (* t b) (* y j))))
       (if (<= t -2e-150)
         t_1
         (if (<= t 3e-5)
           (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))
           (if (<= t 6.8e+217) t_1 (* t (- (* b i) (* x a))))))))))

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))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (t <= -2.9e-14) {
		tmp = t_1;
	} else if (t <= -4.2e-76) {
		tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)));
	} else if (t <= -2e-150) {
		tmp = t_1;
	} else if (t <= 3e-5) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else if (t <= 6.8e+217) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (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) :: t_1
    real(8) :: tmp
    t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    if (t <= (-2.9d-14)) then
        tmp = t_1
    else if (t <= (-4.2d-76)) then
        tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)))
    else if (t <= (-2d-150)) then
        tmp = t_1
    else if (t <= 3d-5) then
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else if (t <= 6.8d+217) then
        tmp = t_1
    else
        tmp = t * ((b * i) - (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 t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (t <= -2.9e-14) {
		tmp = t_1;
	} else if (t <= -4.2e-76) {
		tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)));
	} else if (t <= -2e-150) {
		tmp = t_1;
	} else if (t <= 3e-5) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else if (t <= 6.8e+217) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	tmp = 0
	if t <= -2.9e-14:
		tmp = t_1
	elif t <= -4.2e-76:
		tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)))
	elif t <= -2e-150:
		tmp = t_1
	elif t <= 3e-5:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	elif t <= 6.8e+217:
		tmp = t_1
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (t <= -2.9e-14)
		tmp = t_1;
	elseif (t <= -4.2e-76)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(i * Float64(Float64(t * b) - Float64(y * j))));
	elseif (t <= -2e-150)
		tmp = t_1;
	elseif (t <= 3e-5)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (t <= 6.8e+217)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	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))) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (t <= -2.9e-14)
		tmp = t_1;
	elseif (t <= -4.2e-76)
		tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)));
	elseif (t <= -2e-150)
		tmp = t_1;
	elseif (t <= 3e-5)
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	elseif (t <= 6.8e+217)
		tmp = t_1;
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e-14], t$95$1, If[LessEqual[t, -4.2e-76], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-150], t$95$1, If[LessEqual[t, 3e-5], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+217], t$95$1, N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9000000000000003e-14 or -4.19999999999999985e-76 < t < -2.00000000000000001e-150 or 3.00000000000000008e-5 < t < 6.7999999999999998e217

   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. cancel-sign-sub 65.8%

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

      2. cancel-sign-sub-inv 65.8%

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

      3. *-commutative 65.8%

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

      4. remove-double-neg 65.8%

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

      5. *-commutative 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in y around 0 67.0%

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

      1. sub-neg 67.0%

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

      2. +-commutative 67.0%

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

      3. *-commutative 67.0%

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

      4. associate-*r* 67.7%

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

      5. *-commutative 67.7%

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

      6. mul-1-neg 67.7%

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

      7. distribute-rgt-neg-in 67.7%

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

      8. mul-1-neg 67.7%

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

      9. distribute-lft-in 71.5%

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

      10. mul-1-neg 71.5%

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

      11. unsub-neg 71.5%

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

      12. *-commutative 71.5%

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

      13. *-commutative 71.5%

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

      14. distribute-rgt-neg-in 71.5%

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

      15. neg-sub0 71.5%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      16. associate-+l- 71.5%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      17. neg-sub0 71.5%

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

      18. +-commutative 71.5%

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

      19. sub-neg 71.5%

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

   6. Simplified 71.5%

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

   if -2.9000000000000003e-14 < t < -4.19999999999999985e-76

   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 76.7%

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

      7. sub-neg 76.7%

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

      8. +-commutative 76.7%

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

      9. distribute-neg-in 76.7%

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

      10. unsub-neg 76.7%

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

      11. remove-double-neg 76.7%

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

      12. *-commutative 76.7%

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

   3. Simplified 76.7%

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

      1. fma-udef 76.7%

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

      2. *-commutative 76.7%

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

   5. Applied egg-rr 76.7%

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

   6. Taylor expanded in c around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-+l+ 69.3%

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

      3. associate-*r* 69.3%

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

      4. *-commutative 69.3%

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

      5. associate-*r* 77.1%

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

      6. associate-*r* 77.1%

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

      7. *-commutative 77.1%

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

      8. distribute-lft-in 77.1%

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

      9. +-commutative 77.1%

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

      10. mul-1-neg 77.1%

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

      11. unsub-neg 77.1%

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

   8. Simplified 77.1%

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

   if -2.00000000000000001e-150 < t < 3.00000000000000008e-5

   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. cancel-sign-sub 88.3%

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

      2. cancel-sign-sub-inv 88.3%

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

      3. *-commutative 88.3%

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

      4. remove-double-neg 88.3%

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

      5. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in t around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. associate--l+ 78.2%

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

      3. sub-neg 78.2%

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

      4. +-commutative 78.2%

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

      5. associate-*r* 82.3%

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

      6. distribute-lft-neg-in 82.3%

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

      7. mul-1-neg 82.3%

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

      8. *-commutative 82.3%

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

      9. associate-*r* 81.3%

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

      10. distribute-rgt-in 81.3%

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

      11. +-commutative 81.3%

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

      12. mul-1-neg 81.3%

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

      13. sub-neg 81.3%

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

   6. Simplified 81.3%

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

   if 6.7999999999999998e217 < t

   1. Initial program 55.5%

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

      1. cancel-sign-sub 55.5%

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

      2. cancel-sign-sub-inv 55.5%

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

      3. *-commutative 55.5%

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

      4. remove-double-neg 55.5%

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

      5. *-commutative 55.5%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in t around inf 80.8%

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

      1. distribute-lft-out-- 80.8%

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

      2. associate-*r* 80.8%

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

      3. mul-1-neg 80.8%

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

      4. *-commutative 80.8%

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

   6. Simplified 80.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 7: 59.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+62} \lor \neg \left(b \leq 8.4 \cdot 10^{+165}\right) \land b \leq 2.25 \cdot 10^{+204}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (* c j)) (* b (- (* t i) (* z c)))))
        (t_2 (+ (* j (- (* a c) (* y i))) (* y (* x z)))))
   (if (<= b -3e+49)
     t_1
     (if (<= b -7.5e-142)
       t_2
       (if (<= b -2.65e-219)
         (* a (- (* c j) (* x t)))
         (if (or (<= b 1.6e+62) (and (not (<= b 8.4e+165)) (<= b 2.25e+204)))
           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 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double t_2 = (j * ((a * c) - (y * i))) + (y * (x * z));
	double tmp;
	if (b <= -3e+49) {
		tmp = t_1;
	} else if (b <= -7.5e-142) {
		tmp = t_2;
	} else if (b <= -2.65e-219) {
		tmp = a * ((c * j) - (x * t));
	} else if ((b <= 1.6e+62) || (!(b <= 8.4e+165) && (b <= 2.25e+204))) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)))
    t_2 = (j * ((a * c) - (y * i))) + (y * (x * z))
    if (b <= (-3d+49)) then
        tmp = t_1
    else if (b <= (-7.5d-142)) then
        tmp = t_2
    else if (b <= (-2.65d-219)) then
        tmp = a * ((c * j) - (x * t))
    else if ((b <= 1.6d+62) .or. (.not. (b <= 8.4d+165)) .and. (b <= 2.25d+204)) then
        tmp = t_2
    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)) + (b * ((t * i) - (z * c)));
	double t_2 = (j * ((a * c) - (y * i))) + (y * (x * z));
	double tmp;
	if (b <= -3e+49) {
		tmp = t_1;
	} else if (b <= -7.5e-142) {
		tmp = t_2;
	} else if (b <= -2.65e-219) {
		tmp = a * ((c * j) - (x * t));
	} else if ((b <= 1.6e+62) || (!(b <= 8.4e+165) && (b <= 2.25e+204))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)))
	t_2 = (j * ((a * c) - (y * i))) + (y * (x * z))
	tmp = 0
	if b <= -3e+49:
		tmp = t_1
	elif b <= -7.5e-142:
		tmp = t_2
	elif b <= -2.65e-219:
		tmp = a * ((c * j) - (x * t))
	elif (b <= 1.6e+62) or (not (b <= 8.4e+165) and (b <= 2.25e+204)):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(y * Float64(x * z)))
	tmp = 0.0
	if (b <= -3e+49)
		tmp = t_1;
	elseif (b <= -7.5e-142)
		tmp = t_2;
	elseif (b <= -2.65e-219)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif ((b <= 1.6e+62) || (!(b <= 8.4e+165) && (b <= 2.25e+204)))
		tmp = t_2;
	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)) + (b * ((t * i) - (z * c)));
	t_2 = (j * ((a * c) - (y * i))) + (y * (x * z));
	tmp = 0.0;
	if (b <= -3e+49)
		tmp = t_1;
	elseif (b <= -7.5e-142)
		tmp = t_2;
	elseif (b <= -2.65e-219)
		tmp = a * ((c * j) - (x * t));
	elseif ((b <= 1.6e+62) || (~((b <= 8.4e+165)) && (b <= 2.25e+204)))
		tmp = t_2;
	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[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+49], t$95$1, If[LessEqual[b, -7.5e-142], t$95$2, If[LessEqual[b, -2.65e-219], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.6e+62], And[N[Not[LessEqual[b, 8.4e+165]], $MachinePrecision], LessEqual[b, 2.25e+204]]], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.0000000000000002e49 or 1.59999999999999992e62 < b < 8.4000000000000002e165 or 2.25000000000000001e204 < b

   1. Initial program 67.0%

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

      1. cancel-sign-sub 67.0%

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

      2. cancel-sign-sub-inv 67.0%

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

      3. *-commutative 67.0%

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

      4. remove-double-neg 67.0%

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

      5. *-commutative 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in y around 0 76.5%

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

      1. sub-neg 76.5%

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

      2. +-commutative 76.5%

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

      3. *-commutative 76.5%

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

      4. associate-*r* 80.1%

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

      5. *-commutative 80.1%

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

      6. mul-1-neg 80.1%

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

      7. distribute-rgt-neg-in 80.1%

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

      8. mul-1-neg 80.1%

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

      9. distribute-lft-in 81.0%

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

      10. mul-1-neg 81.0%

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

      11. unsub-neg 81.0%

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

      12. *-commutative 81.0%

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

      13. *-commutative 81.0%

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

      14. distribute-rgt-neg-in 81.0%

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

      15. neg-sub0 81.0%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      16. associate-+l- 81.0%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      17. neg-sub0 81.0%

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

      18. +-commutative 81.0%

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

      19. sub-neg 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in j around inf 78.2%

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

      1. *-commutative 25.2%

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

   9. Simplified 78.2%

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

   if -3.0000000000000002e49 < b < -7.49999999999999958e-142 or -2.6500000000000001e-219 < b < 1.59999999999999992e62 or 8.4000000000000002e165 < b < 2.25000000000000001e204

   1. Initial program 81.4%

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

      1. cancel-sign-sub 81.4%

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

      2. cancel-sign-sub-inv 81.4%

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

      3. *-commutative 81.4%

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

      4. remove-double-neg 81.4%

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

      5. *-commutative 81.4%

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

   3. Simplified 81.4%

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

   4. Taylor expanded in t around 0 73.4%

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

      1. +-commutative 73.4%

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

      2. associate--l+ 73.4%

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

      3. sub-neg 73.4%

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

      4. +-commutative 73.4%

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

      5. associate-*r* 73.5%

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

      6. distribute-lft-neg-in 73.5%

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

      7. mul-1-neg 73.5%

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

      8. *-commutative 73.5%

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

      9. associate-*r* 72.0%

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

      10. distribute-rgt-in 72.0%

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

      11. +-commutative 72.0%

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

      12. mul-1-neg 72.0%

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

      13. sub-neg 72.0%

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

   6. Simplified 72.0%

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

   7. Taylor expanded in b around 0 71.1%

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

   if -7.49999999999999958e-142 < b < -2.6500000000000001e-219

   1. Initial program 58.4%

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

      1. cancel-sign-sub 58.4%

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

      2. cancel-sign-sub-inv 58.4%

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

      3. *-commutative 58.4%

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

      4. remove-double-neg 58.4%

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

      5. *-commutative 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in a around inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. *-commutative 59.5%

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

   6. Simplified 59.5%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-142}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+62} \lor \neg \left(b \leq 8.4 \cdot 10^{+165}\right) \land b \leq 2.25 \cdot 10^{+204}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 8: 63.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-150}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c)))))
        (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -3.6e+112)
     t_2
     (if (<= z -7.5e-243)
       t_1
       (if (<= z 1e-150)
         (+ (* j (- (* a c) (* y i))) (* i (* t b)))
         (if (<= z 1.4e+192) 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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.6e+112) {
		tmp = t_2;
	} else if (z <= -7.5e-243) {
		tmp = t_1;
	} else if (z <= 1e-150) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (z <= 1.4e+192) {
		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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-3.6d+112)) then
        tmp = t_2
    else if (z <= (-7.5d-243)) then
        tmp = t_1
    else if (z <= 1d-150) then
        tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
    else if (z <= 1.4d+192) 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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.6e+112) {
		tmp = t_2;
	} else if (z <= -7.5e-243) {
		tmp = t_1;
	} else if (z <= 1e-150) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (z <= 1.4e+192) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -3.6e+112:
		tmp = t_2
	elif z <= -7.5e-243:
		tmp = t_1
	elif z <= 1e-150:
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
	elif z <= 1.4e+192:
		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(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -3.6e+112)
		tmp = t_2;
	elseif (z <= -7.5e-243)
		tmp = t_1;
	elseif (z <= 1e-150)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(i * Float64(t * b)));
	elseif (z <= 1.4e+192)
		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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -3.6e+112)
		tmp = t_2;
	elseif (z <= -7.5e-243)
		tmp = t_1;
	elseif (z <= 1e-150)
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	elseif (z <= 1.4e+192)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+112], t$95$2, If[LessEqual[z, -7.5e-243], t$95$1, If[LessEqual[z, 1e-150], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+192], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e112 or 1.39999999999999988e192 < z

   1. Initial program 60.2%

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

      1. cancel-sign-sub 60.2%

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

      2. cancel-sign-sub-inv 60.2%

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

      3. *-commutative 60.2%

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

      4. remove-double-neg 60.2%

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

      5. *-commutative 60.2%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in z around inf 79.0%

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

   if -3.6e112 < z < -7.5e-243 or 1.00000000000000001e-150 < z < 1.39999999999999988e192

   1. Initial program 78.8%

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

      1. cancel-sign-sub 78.8%

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

      2. cancel-sign-sub-inv 78.8%

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

      3. *-commutative 78.8%

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

      4. remove-double-neg 78.8%

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

      5. *-commutative 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in y around 0 66.2%

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

      1. sub-neg 66.2%

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

      2. +-commutative 66.2%

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

      3. *-commutative 66.2%

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

      4. associate-*r* 69.5%

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

      5. *-commutative 69.5%

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

      6. mul-1-neg 69.5%

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

      7. distribute-rgt-neg-in 69.5%

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

      8. mul-1-neg 69.5%

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

      9. distribute-lft-in 71.6%

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

      10. mul-1-neg 71.6%

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

      11. unsub-neg 71.6%

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

      12. *-commutative 71.6%

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

      13. *-commutative 71.6%

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

      14. distribute-rgt-neg-in 71.6%

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

      15. neg-sub0 71.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      16. associate-+l- 71.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      17. neg-sub0 71.6%

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

      18. +-commutative 71.6%

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

      19. sub-neg 71.6%

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

   6. Simplified 71.6%

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

   if -7.5e-243 < z < 1.00000000000000001e-150

   1. Initial program 77.8%

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

      1. cancel-sign-sub 77.8%

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

      2. cancel-sign-sub-inv 77.8%

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

      3. *-commutative 77.8%

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

      4. remove-double-neg 77.8%

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

      5. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in i around inf 70.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-243}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 10^{-150}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+192}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 9: 49.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -8 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-228}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 7.8:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -8e+49)
     t_2
     (if (<= c -3.4e-292)
       t_1
       (if (<= c 4.9e-228)
         (* z (* x y))
         (if (<= c 7.8)
           t_1
           (if (<= c 9.5e+139) (* a (- (* c j) (* x t))) 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 <= -8e+49) {
		tmp = t_2;
	} else if (c <= -3.4e-292) {
		tmp = t_1;
	} else if (c <= 4.9e-228) {
		tmp = z * (x * y);
	} else if (c <= 7.8) {
		tmp = t_1;
	} else if (c <= 9.5e+139) {
		tmp = a * ((c * j) - (x * t));
	} 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 <= (-8d+49)) then
        tmp = t_2
    else if (c <= (-3.4d-292)) then
        tmp = t_1
    else if (c <= 4.9d-228) then
        tmp = z * (x * y)
    else if (c <= 7.8d0) then
        tmp = t_1
    else if (c <= 9.5d+139) then
        tmp = a * ((c * j) - (x * t))
    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 <= -8e+49) {
		tmp = t_2;
	} else if (c <= -3.4e-292) {
		tmp = t_1;
	} else if (c <= 4.9e-228) {
		tmp = z * (x * y);
	} else if (c <= 7.8) {
		tmp = t_1;
	} else if (c <= 9.5e+139) {
		tmp = a * ((c * j) - (x * t));
	} 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 <= -8e+49:
		tmp = t_2
	elif c <= -3.4e-292:
		tmp = t_1
	elif c <= 4.9e-228:
		tmp = z * (x * y)
	elif c <= 7.8:
		tmp = t_1
	elif c <= 9.5e+139:
		tmp = a * ((c * j) - (x * t))
	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 <= -8e+49)
		tmp = t_2;
	elseif (c <= -3.4e-292)
		tmp = t_1;
	elseif (c <= 4.9e-228)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 7.8)
		tmp = t_1;
	elseif (c <= 9.5e+139)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	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 <= -8e+49)
		tmp = t_2;
	elseif (c <= -3.4e-292)
		tmp = t_1;
	elseif (c <= 4.9e-228)
		tmp = z * (x * y);
	elseif (c <= 7.8)
		tmp = t_1;
	elseif (c <= 9.5e+139)
		tmp = a * ((c * j) - (x * t));
	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, -8e+49], t$95$2, If[LessEqual[c, -3.4e-292], t$95$1, If[LessEqual[c, 4.9e-228], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.8], t$95$1, If[LessEqual[c, 9.5e+139], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.99999999999999957e49 or 9.5000000000000002e139 < c

   1. Initial program 66.9%

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

      1. cancel-sign-sub 66.9%

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

      2. cancel-sign-sub-inv 66.9%

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

      3. *-commutative 66.9%

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

      4. remove-double-neg 66.9%

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

      5. *-commutative 66.9%

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

   3. Simplified 66.9%

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

   4. Taylor expanded in c around inf 72.2%

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

      1. *-commutative 72.2%

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

   6. Simplified 72.2%

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

   if -7.99999999999999957e49 < c < -3.40000000000000017e-292 or 4.89999999999999988e-228 < c < 7.79999999999999982

   1. Initial program 79.4%

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

      1. sub-neg 79.4%

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

      2. +-commutative 79.4%

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

      3. associate-+l+ 79.4%

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

      4. distribute-rgt-neg-in 79.4%

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

      5. +-commutative 79.4%

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

      6. fma-def 81.2%

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

      7. sub-neg 81.2%

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

      8. +-commutative 81.2%

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

      9. distribute-neg-in 81.2%

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

      10. unsub-neg 81.2%

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

      11. remove-double-neg 81.2%

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

      12. *-commutative 81.2%

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

   3. Simplified 81.2%

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

      1. fma-udef 81.2%

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

      2. *-commutative 81.2%

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

   5. Applied egg-rr 81.2%

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

   6. Taylor expanded in i around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

   8. Simplified 51.1%

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

   if -3.40000000000000017e-292 < c < 4.89999999999999988e-228

   1. Initial program 79.8%

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

      1. cancel-sign-sub 79.8%

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

      2. cancel-sign-sub-inv 79.8%

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

      3. *-commutative 79.8%

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

      4. remove-double-neg 79.8%

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

      5. *-commutative 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in a around 0 57.4%

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

      1. sub-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. +-commutative 57.4%

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

      4. mul-1-neg 57.4%

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

      5. distribute-rgt-neg-in 57.4%

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

      6. mul-1-neg 57.4%

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

      7. distribute-lft-in 57.4%

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

      8. fma-udef 60.7%

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

      9. mul-1-neg 60.7%

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

      10. unsub-neg 60.7%

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

      11. *-commutative 60.7%

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

      12. distribute-rgt-neg-in 60.7%

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

      13. neg-sub0 60.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 60.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in x around inf 44.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.9%

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

      2. associate-*l* 45.0%

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

      3. *-commutative 45.0%

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

   9. Simplified 45.0%

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

   if 7.79999999999999982 < c < 9.5000000000000002e139

   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. cancel-sign-sub 64.7%

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

      2. cancel-sign-sub-inv 64.7%

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

      3. *-commutative 64.7%

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

      4. remove-double-neg 64.7%

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

      5. *-commutative 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in a around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. unsub-neg 65.5%

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

      4. *-commutative 65.5%

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

   6. Simplified 65.5%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-292}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-228}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 7.8:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 10: 27.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-131}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+162}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+232}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= t -4.6e-25)
     (* b (* t i))
     (if (<= t -1.3e-213)
       t_1
       (if (<= t 2.9e-131)
         (* z (* x y))
         (if (<= t 4e+58)
           t_1
           (if (<= t 2.3e+162)
             (* (* z c) (- b))
             (if (<= t 4.8e+232) (* i (* j (- y))) (* 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 t_1 = a * (c * j);
	double tmp;
	if (t <= -4.6e-25) {
		tmp = b * (t * i);
	} else if (t <= -1.3e-213) {
		tmp = t_1;
	} else if (t <= 2.9e-131) {
		tmp = z * (x * y);
	} else if (t <= 4e+58) {
		tmp = t_1;
	} else if (t <= 2.3e+162) {
		tmp = (z * c) * -b;
	} else if (t <= 4.8e+232) {
		tmp = i * (j * -y);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (t <= (-4.6d-25)) then
        tmp = b * (t * i)
    else if (t <= (-1.3d-213)) then
        tmp = t_1
    else if (t <= 2.9d-131) then
        tmp = z * (x * y)
    else if (t <= 4d+58) then
        tmp = t_1
    else if (t <= 2.3d+162) then
        tmp = (z * c) * -b
    else if (t <= 4.8d+232) then
        tmp = i * (j * -y)
    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 t_1 = a * (c * j);
	double tmp;
	if (t <= -4.6e-25) {
		tmp = b * (t * i);
	} else if (t <= -1.3e-213) {
		tmp = t_1;
	} else if (t <= 2.9e-131) {
		tmp = z * (x * y);
	} else if (t <= 4e+58) {
		tmp = t_1;
	} else if (t <= 2.3e+162) {
		tmp = (z * c) * -b;
	} else if (t <= 4.8e+232) {
		tmp = i * (j * -y);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if t <= -4.6e-25:
		tmp = b * (t * i)
	elif t <= -1.3e-213:
		tmp = t_1
	elif t <= 2.9e-131:
		tmp = z * (x * y)
	elif t <= 4e+58:
		tmp = t_1
	elif t <= 2.3e+162:
		tmp = (z * c) * -b
	elif t <= 4.8e+232:
		tmp = i * (j * -y)
	else:
		tmp = t * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (t <= -4.6e-25)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -1.3e-213)
		tmp = t_1;
	elseif (t <= 2.9e-131)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 4e+58)
		tmp = t_1;
	elseif (t <= 2.3e+162)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (t <= 4.8e+232)
		tmp = Float64(i * Float64(j * Float64(-y)));
	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)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (t <= -4.6e-25)
		tmp = b * (t * i);
	elseif (t <= -1.3e-213)
		tmp = t_1;
	elseif (t <= 2.9e-131)
		tmp = z * (x * y);
	elseif (t <= 4e+58)
		tmp = t_1;
	elseif (t <= 2.3e+162)
		tmp = (z * c) * -b;
	elseif (t <= 4.8e+232)
		tmp = i * (j * -y);
	else
		tmp = t * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e-25], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e-213], t$95$1, If[LessEqual[t, 2.9e-131], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+58], t$95$1, If[LessEqual[t, 2.3e+162], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[t, 4.8e+232], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.5999999999999998e-25

   1. Initial program 66.7%

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

      1. cancel-sign-sub 66.7%

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

      2. cancel-sign-sub-inv 66.7%

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

      3. *-commutative 66.7%

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

      4. remove-double-neg 66.7%

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

      5. *-commutative 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in b around inf 55.8%

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

   5. Taylor expanded in i around inf 47.4%

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

      1. *-commutative 47.4%

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

   7. Simplified 47.4%

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

   if -4.5999999999999998e-25 < t < -1.3000000000000001e-213 or 2.9000000000000002e-131 < t < 3.99999999999999978e58

   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. cancel-sign-sub 81.6%

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

      2. cancel-sign-sub-inv 81.6%

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

      3. *-commutative 81.6%

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

      4. remove-double-neg 81.6%

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

      5. *-commutative 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in a around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   6. Simplified 49.5%

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

   7. Taylor expanded in j around inf 44.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.3%

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

   9. Simplified 44.3%

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

   if -1.3000000000000001e-213 < t < 2.9000000000000002e-131

   1. Initial program 88.2%

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

      1. cancel-sign-sub 88.2%

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

      2. cancel-sign-sub-inv 88.2%

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

      3. *-commutative 88.2%

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

      4. remove-double-neg 88.2%

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

      5. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in a around 0 72.7%

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

      1. sub-neg 72.7%

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

      2. *-commutative 72.7%

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

      3. +-commutative 72.7%

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

      4. mul-1-neg 72.7%

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

      5. distribute-rgt-neg-in 72.7%

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

      6. mul-1-neg 72.7%

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

      7. distribute-lft-in 72.7%

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

      8. fma-udef 72.7%

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

      9. mul-1-neg 72.7%

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

      10. unsub-neg 72.7%

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

      11. *-commutative 72.7%

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

      12. distribute-rgt-neg-in 72.7%

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

      13. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in x around inf 36.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.1%

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

      2. associate-*l* 38.0%

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

      3. *-commutative 38.0%

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

   9. Simplified 38.0%

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

   if 3.99999999999999978e58 < t < 2.29999999999999994e162

   1. Initial program 33.7%

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

      1. cancel-sign-sub 33.7%

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

      2. cancel-sign-sub-inv 33.7%

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

      3. *-commutative 33.7%

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

      4. remove-double-neg 33.7%

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

      5. *-commutative 33.7%

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

   3. Simplified 33.7%

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

   4. Taylor expanded in b around inf 67.7%

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

   5. Taylor expanded in i around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. distribute-lft-neg-out 54.5%

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

      3. *-commutative 54.5%

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

   7. Simplified 54.5%

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

   if 2.29999999999999994e162 < t < 4.8000000000000003e232

   1. Initial program 62.5%

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

      1. cancel-sign-sub 62.5%

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

      2. cancel-sign-sub-inv 62.5%

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

      3. *-commutative 62.5%

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

      4. remove-double-neg 62.5%

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

      5. *-commutative 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in a around 0 56.4%

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

      1. sub-neg 56.4%

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

      2. *-commutative 56.4%

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

      3. +-commutative 56.4%

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

      4. mul-1-neg 56.4%

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

      5. distribute-rgt-neg-in 56.4%

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

      6. mul-1-neg 56.4%

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

      7. distribute-lft-in 56.4%

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

      8. fma-udef 62.6%

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

      9. mul-1-neg 62.6%

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

      10. unsub-neg 62.6%

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

      11. *-commutative 62.6%

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

      12. distribute-rgt-neg-in 62.6%

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

      13. neg-sub0 62.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 62.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in j around inf 44.9%

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

      1. *-commutative 44.9%

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

      2. associate-*r* 44.9%

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

      3. associate-*r* 45.0%

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

      4. associate-*r* 45.0%

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

      5. *-commutative 45.0%

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

      6. mul-1-neg 45.0%

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

      7. distribute-rgt-neg-in 45.0%

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

   9. Simplified 45.0%

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

   if 4.8000000000000003e232 < t

   1. Initial program 57.0%

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

      1. cancel-sign-sub 57.0%

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

      2. cancel-sign-sub-inv 57.0%

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

      3. *-commutative 57.0%

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

      4. remove-double-neg 57.0%

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

      5. *-commutative 57.0%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in t around inf 89.3%

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

      1. distribute-lft-out-- 89.3%

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

      2. associate-*r* 89.3%

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

      3. mul-1-neg 89.3%

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

      4. *-commutative 89.3%

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

   6. Simplified 89.3%

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

   7. Taylor expanded in a around inf 65.0%

      \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-213}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-131}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+162}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+232}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 11: 29.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+211}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= t -5e-25)
     (* b (* t i))
     (if (<= t -5.2e-213)
       t_1
       (if (<= t 2.7e-130)
         (* z (* x y))
         (if (<= t 4.4e-9)
           t_1
           (if (<= t 4.2e+211) (* i (* t 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 t_1 = a * (c * j);
	double tmp;
	if (t <= -5e-25) {
		tmp = b * (t * i);
	} else if (t <= -5.2e-213) {
		tmp = t_1;
	} else if (t <= 2.7e-130) {
		tmp = z * (x * y);
	} else if (t <= 4.4e-9) {
		tmp = t_1;
	} else if (t <= 4.2e+211) {
		tmp = i * (t * 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) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (t <= (-5d-25)) then
        tmp = b * (t * i)
    else if (t <= (-5.2d-213)) then
        tmp = t_1
    else if (t <= 2.7d-130) then
        tmp = z * (x * y)
    else if (t <= 4.4d-9) then
        tmp = t_1
    else if (t <= 4.2d+211) then
        tmp = i * (t * 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 t_1 = a * (c * j);
	double tmp;
	if (t <= -5e-25) {
		tmp = b * (t * i);
	} else if (t <= -5.2e-213) {
		tmp = t_1;
	} else if (t <= 2.7e-130) {
		tmp = z * (x * y);
	} else if (t <= 4.4e-9) {
		tmp = t_1;
	} else if (t <= 4.2e+211) {
		tmp = i * (t * b);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if t <= -5e-25:
		tmp = b * (t * i)
	elif t <= -5.2e-213:
		tmp = t_1
	elif t <= 2.7e-130:
		tmp = z * (x * y)
	elif t <= 4.4e-9:
		tmp = t_1
	elif t <= 4.2e+211:
		tmp = i * (t * b)
	else:
		tmp = t * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (t <= -5e-25)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -5.2e-213)
		tmp = t_1;
	elseif (t <= 2.7e-130)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 4.4e-9)
		tmp = t_1;
	elseif (t <= 4.2e+211)
		tmp = Float64(i * Float64(t * 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)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (t <= -5e-25)
		tmp = b * (t * i);
	elseif (t <= -5.2e-213)
		tmp = t_1;
	elseif (t <= 2.7e-130)
		tmp = z * (x * y);
	elseif (t <= 4.4e-9)
		tmp = t_1;
	elseif (t <= 4.2e+211)
		tmp = i * (t * b);
	else
		tmp = t * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-25], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-213], t$95$1, If[LessEqual[t, 2.7e-130], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-9], t$95$1, If[LessEqual[t, 4.2e+211], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.99999999999999962e-25

   1. Initial program 66.7%

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

      1. cancel-sign-sub 66.7%

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

      2. cancel-sign-sub-inv 66.7%

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

      3. *-commutative 66.7%

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

      4. remove-double-neg 66.7%

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

      5. *-commutative 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in b around inf 55.8%

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

   5. Taylor expanded in i around inf 47.4%

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

      1. *-commutative 47.4%

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

   7. Simplified 47.4%

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

   if -4.99999999999999962e-25 < t < -5.2000000000000003e-213 or 2.69999999999999991e-130 < t < 4.3999999999999997e-9

   1. Initial program 83.9%

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

      1. cancel-sign-sub 83.9%

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

      2. cancel-sign-sub-inv 83.9%

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

      3. *-commutative 83.9%

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

      4. remove-double-neg 83.9%

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

      5. *-commutative 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in a around inf 51.7%

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

      1. +-commutative 51.7%

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

      2. mul-1-neg 51.7%

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

      3. unsub-neg 51.7%

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

      4. *-commutative 51.7%

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

   6. Simplified 51.7%

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

   7. Taylor expanded in j around inf 46.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.9%

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

   9. Simplified 46.9%

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

   if -5.2000000000000003e-213 < t < 2.69999999999999991e-130

   1. Initial program 88.2%

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

      1. cancel-sign-sub 88.2%

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

      2. cancel-sign-sub-inv 88.2%

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

      3. *-commutative 88.2%

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

      4. remove-double-neg 88.2%

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

      5. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in a around 0 72.7%

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

      1. sub-neg 72.7%

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

      2. *-commutative 72.7%

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

      3. +-commutative 72.7%

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

      4. mul-1-neg 72.7%

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

      5. distribute-rgt-neg-in 72.7%

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

      6. mul-1-neg 72.7%

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

      7. distribute-lft-in 72.7%

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

      8. fma-udef 72.7%

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

      9. mul-1-neg 72.7%

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

      10. unsub-neg 72.7%

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

      11. *-commutative 72.7%

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

      12. distribute-rgt-neg-in 72.7%

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

      13. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in x around inf 36.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.1%

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

      2. associate-*l* 38.0%

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

      3. *-commutative 38.0%

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

   9. Simplified 38.0%

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

   if 4.3999999999999997e-9 < t < 4.2e211

   1. Initial program 52.8%

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

      1. cancel-sign-sub 52.8%

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

      2. cancel-sign-sub-inv 52.8%

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

      3. *-commutative 52.8%

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

      4. remove-double-neg 52.8%

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

      5. *-commutative 52.8%

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

   3. Simplified 52.8%

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

   4. Taylor expanded in b around inf 59.4%

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

   5. Taylor expanded in i around inf 37.8%

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

   if 4.2e211 < t

   1. Initial program 57.1%

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

      1. cancel-sign-sub 57.1%

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

      2. cancel-sign-sub-inv 57.1%

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

      3. *-commutative 57.1%

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

      4. remove-double-neg 57.1%

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

      5. *-commutative 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in t around inf 74.3%

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

      1. distribute-lft-out-- 74.3%

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

      2. associate-*r* 74.3%

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

      3. mul-1-neg 74.3%

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

      4. *-commutative 74.3%

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

   6. Simplified 74.3%

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

   7. Taylor expanded in a around inf 58.3%

      \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-213}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+211}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 12: 29.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -3.75 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+204}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= t -3.75e-25)
     (* b (* t i))
     (if (<= t -3.4e-214)
       t_1
       (if (<= t 1.02e-129)
         (* z (* x y))
         (if (<= t 3.1e-9)
           t_1
           (if (<= t 1.12e+204) (* i (* t b)) (* a (* 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 = a * (c * j);
	double tmp;
	if (t <= -3.75e-25) {
		tmp = b * (t * i);
	} else if (t <= -3.4e-214) {
		tmp = t_1;
	} else if (t <= 1.02e-129) {
		tmp = z * (x * y);
	} else if (t <= 3.1e-9) {
		tmp = t_1;
	} else if (t <= 1.12e+204) {
		tmp = i * (t * b);
	} else {
		tmp = a * (x * -t);
	}
	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)
    if (t <= (-3.75d-25)) then
        tmp = b * (t * i)
    else if (t <= (-3.4d-214)) then
        tmp = t_1
    else if (t <= 1.02d-129) then
        tmp = z * (x * y)
    else if (t <= 3.1d-9) then
        tmp = t_1
    else if (t <= 1.12d+204) then
        tmp = i * (t * b)
    else
        tmp = a * (x * -t)
    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);
	double tmp;
	if (t <= -3.75e-25) {
		tmp = b * (t * i);
	} else if (t <= -3.4e-214) {
		tmp = t_1;
	} else if (t <= 1.02e-129) {
		tmp = z * (x * y);
	} else if (t <= 3.1e-9) {
		tmp = t_1;
	} else if (t <= 1.12e+204) {
		tmp = i * (t * b);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if t <= -3.75e-25:
		tmp = b * (t * i)
	elif t <= -3.4e-214:
		tmp = t_1
	elif t <= 1.02e-129:
		tmp = z * (x * y)
	elif t <= 3.1e-9:
		tmp = t_1
	elif t <= 1.12e+204:
		tmp = i * (t * b)
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (t <= -3.75e-25)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -3.4e-214)
		tmp = t_1;
	elseif (t <= 1.02e-129)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 3.1e-9)
		tmp = t_1;
	elseif (t <= 1.12e+204)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (t <= -3.75e-25)
		tmp = b * (t * i);
	elseif (t <= -3.4e-214)
		tmp = t_1;
	elseif (t <= 1.02e-129)
		tmp = z * (x * y);
	elseif (t <= 3.1e-9)
		tmp = t_1;
	elseif (t <= 1.12e+204)
		tmp = i * (t * b);
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.75e-25], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.4e-214], t$95$1, If[LessEqual[t, 1.02e-129], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-9], t$95$1, If[LessEqual[t, 1.12e+204], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.74999999999999994e-25

   1. Initial program 66.7%

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

      1. cancel-sign-sub 66.7%

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

      2. cancel-sign-sub-inv 66.7%

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

      3. *-commutative 66.7%

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

      4. remove-double-neg 66.7%

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

      5. *-commutative 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in b around inf 55.8%

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

   5. Taylor expanded in i around inf 47.4%

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

      1. *-commutative 47.4%

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

   7. Simplified 47.4%

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

   if -3.74999999999999994e-25 < t < -3.3999999999999999e-214 or 1.02e-129 < t < 3.10000000000000005e-9

   1. Initial program 83.9%

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

      1. cancel-sign-sub 83.9%

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

      2. cancel-sign-sub-inv 83.9%

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

      3. *-commutative 83.9%

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

      4. remove-double-neg 83.9%

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

      5. *-commutative 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in a around inf 51.7%

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

      1. +-commutative 51.7%

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

      2. mul-1-neg 51.7%

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

      3. unsub-neg 51.7%

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

      4. *-commutative 51.7%

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

   6. Simplified 51.7%

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

   7. Taylor expanded in j around inf 46.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.9%

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

   9. Simplified 46.9%

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

   if -3.3999999999999999e-214 < t < 1.02e-129

   1. Initial program 88.2%

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

      1. cancel-sign-sub 88.2%

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

      2. cancel-sign-sub-inv 88.2%

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

      3. *-commutative 88.2%

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

      4. remove-double-neg 88.2%

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

      5. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in a around 0 72.7%

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

      1. sub-neg 72.7%

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

      2. *-commutative 72.7%

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

      3. +-commutative 72.7%

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

      4. mul-1-neg 72.7%

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

      5. distribute-rgt-neg-in 72.7%

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

      6. mul-1-neg 72.7%

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

      7. distribute-lft-in 72.7%

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

      8. fma-udef 72.7%

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

      9. mul-1-neg 72.7%

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

      10. unsub-neg 72.7%

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

      11. *-commutative 72.7%

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

      12. distribute-rgt-neg-in 72.7%

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

      13. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in x around inf 36.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.1%

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

      2. associate-*l* 38.0%

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

      3. *-commutative 38.0%

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

   9. Simplified 38.0%

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

   if 3.10000000000000005e-9 < t < 1.11999999999999996e204

   1. Initial program 52.8%

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

      1. cancel-sign-sub 52.8%

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

      2. cancel-sign-sub-inv 52.8%

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

      3. *-commutative 52.8%

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

      4. remove-double-neg 52.8%

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

      5. *-commutative 52.8%

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

   3. Simplified 52.8%

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

   4. Taylor expanded in b around inf 59.4%

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

   5. Taylor expanded in i around inf 37.8%

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

   if 1.11999999999999996e204 < t

   1. Initial program 57.1%

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

      1. cancel-sign-sub 57.1%

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

      2. cancel-sign-sub-inv 57.1%

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

      3. *-commutative 57.1%

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

      4. remove-double-neg 57.1%

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

      5. *-commutative 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in a around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 58.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 58.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 58.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 58.3%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-rgt-neg-in 58.3%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   9. Simplified 58.3%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.75 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+204}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 13: 37.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-78} \lor \neg \left(i \leq 3.7 \cdot 10^{+63}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.6e+58)
   (* b (* t i))
   (if (or (<= i 7.2e-78) (not (<= i 3.7e+63)))
     (* a (- (* c j) (* x t)))
     (* 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 tmp;
	if (i <= -2.6e+58) {
		tmp = b * (t * i);
	} else if ((i <= 7.2e-78) || !(i <= 3.7e+63)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = 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) :: tmp
    if (i <= (-2.6d+58)) then
        tmp = b * (t * i)
    else if ((i <= 7.2d-78) .or. (.not. (i <= 3.7d+63))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = 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 tmp;
	if (i <= -2.6e+58) {
		tmp = b * (t * i);
	} else if ((i <= 7.2e-78) || !(i <= 3.7e+63)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -2.6e+58:
		tmp = b * (t * i)
	elif (i <= 7.2e-78) or not (i <= 3.7e+63):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.6e+58)
		tmp = Float64(b * Float64(t * i));
	elseif ((i <= 7.2e-78) || !(i <= 3.7e+63))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -2.6e+58)
		tmp = b * (t * i);
	elseif ((i <= 7.2e-78) || ~((i <= 3.7e+63)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.6e+58], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 7.2e-78], N[Not[LessEqual[i, 3.7e+63]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.59999999999999988e58

   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. cancel-sign-sub 63.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 65.9%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 52.7%

      \[\leadsto \color{blue}{\left(i \cdot t\right)} \cdot b \]
   6. Step-by-step derivation

      1. *-commutative 52.7%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   7. Simplified 52.7%

      \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   if -2.59999999999999988e58 < i < 7.2000000000000005e-78 or 3.69999999999999968e63 < i

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 76.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 48.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 48.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 48.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 7.2000000000000005e-78 < i < 3.69999999999999968e63

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around 0 76.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b} \]
   5. Step-by-step derivation

      1. sub-neg 76.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\left(c \cdot z - i \cdot t\right) \cdot b\right)} \]

      2. *-commutative 76.8%

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\color{blue}{b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]

      3. +-commutative 76.8%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. mul-1-neg 76.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. distribute-rgt-neg-in 76.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      6. mul-1-neg 76.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      7. distribute-lft-in 76.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      8. fma-udef 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x + -1 \cdot \left(i \cdot j\right), -b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      9. mul-1-neg 76.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x + \color{blue}{\left(-i \cdot j\right)}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      10. unsub-neg 76.9%

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot x - i \cdot j}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      11. *-commutative 76.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - \color{blue}{j \cdot i}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      12. distribute-rgt-neg-in 76.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right) \]

      13. neg-sub0 76.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 76.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 76.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right) \]

   6. Simplified 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(i \cdot t - c \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 46.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-78} \lor \neg \left(i \leq 3.7 \cdot 10^{+63}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 14: 50.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-113}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -2.15e+104)
     t_1
     (if (<= y -6.4e-113)
       (* b (- (* t i) (* z c)))
       (if (<= y 6.5e-7) (* a (- (* c j) (* x t))) 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.15e+104) {
		tmp = t_1;
	} else if (y <= -6.4e-113) {
		tmp = b * ((t * i) - (z * c));
	} else if (y <= 6.5e-7) {
		tmp = a * ((c * j) - (x * t));
	} 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 = y * ((x * z) - (i * j))
    if (y <= (-2.15d+104)) then
        tmp = t_1
    else if (y <= (-6.4d-113)) then
        tmp = b * ((t * i) - (z * c))
    else if (y <= 6.5d-7) then
        tmp = a * ((c * j) - (x * t))
    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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.15e+104) {
		tmp = t_1;
	} else if (y <= -6.4e-113) {
		tmp = b * ((t * i) - (z * c));
	} else if (y <= 6.5e-7) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.15e+104:
		tmp = t_1
	elif y <= -6.4e-113:
		tmp = b * ((t * i) - (z * c))
	elif y <= 6.5e-7:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.15e+104)
		tmp = t_1;
	elseif (y <= -6.4e-113)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (y <= 6.5e-7)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.15e+104)
		tmp = t_1;
	elseif (y <= -6.4e-113)
		tmp = b * ((t * i) - (z * c));
	elseif (y <= 6.5e-7)
		tmp = a * ((c * j) - (x * t));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e+104], t$95$1, If[LessEqual[y, -6.4e-113], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-7], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1500000000000001e104 or 6.50000000000000024e-7 < y

   1. Initial program 62.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 62.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 62.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 62.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 62.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 62.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 62.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 64.3%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 64.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 64.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 64.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

      4. *-commutative 64.3%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   if -2.1500000000000001e104 < y < -6.4000000000000003e-113

   1. Initial program 85.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 85.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 54.5%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   if -6.4000000000000003e-113 < y < 6.50000000000000024e-7

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 53.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 53.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 53.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-113}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 15: 51.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.85 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-241}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.85e+43)
     t_1
     (if (<= i 2.2e-241)
       (* a (- (* c j) (* x t)))
       (if (<= i 1.02e+89) (* z (- (* x y) (* b c))) 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.85e+43) {
		tmp = t_1;
	} else if (i <= 2.2e-241) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.02e+89) {
		tmp = z * ((x * y) - (b * c));
	} 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 = i * ((t * b) - (y * j))
    if (i <= (-1.85d+43)) then
        tmp = t_1
    else if (i <= 2.2d-241) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.02d+89) then
        tmp = z * ((x * y) - (b * c))
    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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.85e+43) {
		tmp = t_1;
	} else if (i <= 2.2e-241) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.02e+89) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.85e+43:
		tmp = t_1
	elif i <= 2.2e-241:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.02e+89:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (i <= -1.85e+43)
		tmp = t_1;
	elseif (i <= 2.2e-241)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.02e+89)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	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));
	tmp = 0.0;
	if (i <= -1.85e+43)
		tmp = t_1;
	elseif (i <= 2.2e-241)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.02e+89)
		tmp = z * ((x * y) - (b * c));
	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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.85e+43], t$95$1, If[LessEqual[i, 2.2e-241], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.02e+89], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.85e43 or 1.0199999999999999e89 < i

   1. Initial program 63.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 63.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 63.2%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 63.2%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 63.2%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 63.2%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 64.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 64.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 64.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 64.2%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 64.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 64.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 64.2%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 65.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]
   4. Step-by-step derivation

      1. fma-udef 64.2%

         \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)}\right) \]

      2. *-commutative 64.2%

         \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 64.2%

      \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(a \cdot c - y \cdot i\right)}\right) \]

   6. Taylor expanded in i around inf 68.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 68.3%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 68.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   8. Simplified 68.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if -1.85e43 < i < 2.1999999999999999e-241

   1. Initial program 84.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 84.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 48.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 48.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 2.1999999999999999e-241 < i < 1.0199999999999999e89

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 73.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 63.7%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.85 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-241}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 16: 29.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= t -5.1e-25)
     (* b (* t i))
     (if (<= t -5.5e-217)
       t_1
       (if (<= t 1.7e-126)
         (* z (* x y))
         (if (<= t 1e+83) t_1 (* x (* a (- 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 = a * (c * j);
	double tmp;
	if (t <= -5.1e-25) {
		tmp = b * (t * i);
	} else if (t <= -5.5e-217) {
		tmp = t_1;
	} else if (t <= 1.7e-126) {
		tmp = z * (x * y);
	} else if (t <= 1e+83) {
		tmp = t_1;
	} else {
		tmp = x * (a * -t);
	}
	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)
    if (t <= (-5.1d-25)) then
        tmp = b * (t * i)
    else if (t <= (-5.5d-217)) then
        tmp = t_1
    else if (t <= 1.7d-126) then
        tmp = z * (x * y)
    else if (t <= 1d+83) then
        tmp = t_1
    else
        tmp = x * (a * -t)
    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);
	double tmp;
	if (t <= -5.1e-25) {
		tmp = b * (t * i);
	} else if (t <= -5.5e-217) {
		tmp = t_1;
	} else if (t <= 1.7e-126) {
		tmp = z * (x * y);
	} else if (t <= 1e+83) {
		tmp = t_1;
	} else {
		tmp = x * (a * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if t <= -5.1e-25:
		tmp = b * (t * i)
	elif t <= -5.5e-217:
		tmp = t_1
	elif t <= 1.7e-126:
		tmp = z * (x * y)
	elif t <= 1e+83:
		tmp = t_1
	else:
		tmp = x * (a * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (t <= -5.1e-25)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -5.5e-217)
		tmp = t_1;
	elseif (t <= 1.7e-126)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 1e+83)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(a * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (t <= -5.1e-25)
		tmp = b * (t * i);
	elseif (t <= -5.5e-217)
		tmp = t_1;
	elseif (t <= 1.7e-126)
		tmp = z * (x * y);
	elseif (t <= 1e+83)
		tmp = t_1;
	else
		tmp = x * (a * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.1e-25], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-217], t$95$1, If[LessEqual[t, 1.7e-126], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+83], t$95$1, N[(x * N[(a * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.1000000000000003e-25

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 66.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 55.8%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 47.4%

      \[\leadsto \color{blue}{\left(i \cdot t\right)} \cdot b \]
   6. Step-by-step derivation

      1. *-commutative 47.4%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   7. Simplified 47.4%

      \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   if -5.1000000000000003e-25 < t < -5.49999999999999975e-217 or 1.7e-126 < t < 1.00000000000000003e83

   1. Initial program 81.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 81.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 81.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 81.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 81.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 47.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 47.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 47.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 47.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 42.5%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 42.5%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -5.49999999999999975e-217 < t < 1.7e-126

   1. Initial program 88.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 88.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 88.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around 0 72.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b} \]
   5. Step-by-step derivation

      1. sub-neg 72.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\left(c \cdot z - i \cdot t\right) \cdot b\right)} \]

      2. *-commutative 72.7%

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\color{blue}{b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]

      3. +-commutative 72.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. distribute-rgt-neg-in 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      6. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      7. distribute-lft-in 72.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      8. fma-udef 72.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x + -1 \cdot \left(i \cdot j\right), -b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      9. mul-1-neg 72.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x + \color{blue}{\left(-i \cdot j\right)}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      10. unsub-neg 72.7%

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot x - i \cdot j}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      11. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - \color{blue}{j \cdot i}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      12. distribute-rgt-neg-in 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right) \]

      13. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right) \]

   6. Simplified 72.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(i \cdot t - c \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 36.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.1%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 38.0%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

      3. *-commutative 38.0%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   9. Simplified 38.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if 1.00000000000000003e83 < t

   1. Initial program 48.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 48.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 48.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 48.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 48.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 48.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 48.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 47.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 47.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 47.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 47.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 43.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 43.5%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-rgt-neg-in 43.5%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   9. Simplified 43.5%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   10. Taylor expanded in a around 0 43.5%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 43.5%

          \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

       2. *-commutative 43.5%

          \[\leadsto -a \cdot \color{blue}{\left(x \cdot t\right)} \]

       3. *-commutative 43.5%

          \[\leadsto -\color{blue}{\left(x \cdot t\right) \cdot a} \]

       4. associate-*r* 47.8%

          \[\leadsto -\color{blue}{x \cdot \left(t \cdot a\right)} \]

       5. distribute-rgt-neg-in 47.8%

          \[\leadsto \color{blue}{x \cdot \left(-t \cdot a\right)} \]

       6. distribute-rgt-neg-in 47.8%

          \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   12. Simplified 47.8%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 10^{+83}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 17: 28.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* t (* b i))))
   (if (<= t -1.35e-8)
     t_2
     (if (<= t -2.6e-215)
       t_1
       (if (<= t 1.9e-127) (* y (* x z)) (if (<= t 3.7e-10) 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 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (t <= -1.35e-8) {
		tmp = t_2;
	} else if (t <= -2.6e-215) {
		tmp = t_1;
	} else if (t <= 1.9e-127) {
		tmp = y * (x * z);
	} else if (t <= 3.7e-10) {
		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 = a * (c * j)
    t_2 = t * (b * i)
    if (t <= (-1.35d-8)) then
        tmp = t_2
    else if (t <= (-2.6d-215)) then
        tmp = t_1
    else if (t <= 1.9d-127) then
        tmp = y * (x * z)
    else if (t <= 3.7d-10) 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 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (t <= -1.35e-8) {
		tmp = t_2;
	} else if (t <= -2.6e-215) {
		tmp = t_1;
	} else if (t <= 1.9e-127) {
		tmp = y * (x * z);
	} else if (t <= 3.7e-10) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = t * (b * i)
	tmp = 0
	if t <= -1.35e-8:
		tmp = t_2
	elif t <= -2.6e-215:
		tmp = t_1
	elif t <= 1.9e-127:
		tmp = y * (x * z)
	elif t <= 3.7e-10:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (t <= -1.35e-8)
		tmp = t_2;
	elseif (t <= -2.6e-215)
		tmp = t_1;
	elseif (t <= 1.9e-127)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 3.7e-10)
		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 = a * (c * j);
	t_2 = t * (b * i);
	tmp = 0.0;
	if (t <= -1.35e-8)
		tmp = t_2;
	elseif (t <= -2.6e-215)
		tmp = t_1;
	elseif (t <= 1.9e-127)
		tmp = y * (x * z);
	elseif (t <= 3.7e-10)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e-8], t$95$2, If[LessEqual[t, -2.6e-215], t$95$1, If[LessEqual[t, 1.9e-127], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-10], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000001e-8 or 3.70000000000000015e-10 < t

   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. cancel-sign-sub 61.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 61.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 61.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 61.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 61.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 61.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 52.4%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 35.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.9%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 40.9%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*r* 38.7%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   7. Simplified 38.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if -1.35000000000000001e-8 < t < -2.6e-215 or 1.90000000000000001e-127 < t < 3.70000000000000015e-10

   1. Initial program 82.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 82.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 51.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 46.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 46.3%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -2.6e-215 < t < 1.90000000000000001e-127

   1. Initial program 88.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 88.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 88.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around 0 72.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b} \]
   5. Step-by-step derivation

      1. sub-neg 72.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\left(c \cdot z - i \cdot t\right) \cdot b\right)} \]

      2. *-commutative 72.7%

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\color{blue}{b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]

      3. +-commutative 72.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. distribute-rgt-neg-in 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      6. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      7. distribute-lft-in 72.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      8. fma-udef 72.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x + -1 \cdot \left(i \cdot j\right), -b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      9. mul-1-neg 72.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x + \color{blue}{\left(-i \cdot j\right)}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      10. unsub-neg 72.7%

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot x - i \cdot j}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      11. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - \color{blue}{j \cdot i}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      12. distribute-rgt-neg-in 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right) \]

      13. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right) \]

   6. Simplified 72.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(i \cdot t - c \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 36.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 18: 28.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* t (* b i))))
   (if (<= t -3.3e-9)
     t_2
     (if (<= t -6.5e-215)
       t_1
       (if (<= t 7e-127) (* z (* x y)) (if (<= t 1.85e-7) 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 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (t <= -3.3e-9) {
		tmp = t_2;
	} else if (t <= -6.5e-215) {
		tmp = t_1;
	} else if (t <= 7e-127) {
		tmp = z * (x * y);
	} else if (t <= 1.85e-7) {
		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 = a * (c * j)
    t_2 = t * (b * i)
    if (t <= (-3.3d-9)) then
        tmp = t_2
    else if (t <= (-6.5d-215)) then
        tmp = t_1
    else if (t <= 7d-127) then
        tmp = z * (x * y)
    else if (t <= 1.85d-7) 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 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (t <= -3.3e-9) {
		tmp = t_2;
	} else if (t <= -6.5e-215) {
		tmp = t_1;
	} else if (t <= 7e-127) {
		tmp = z * (x * y);
	} else if (t <= 1.85e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = t * (b * i)
	tmp = 0
	if t <= -3.3e-9:
		tmp = t_2
	elif t <= -6.5e-215:
		tmp = t_1
	elif t <= 7e-127:
		tmp = z * (x * y)
	elif t <= 1.85e-7:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (t <= -3.3e-9)
		tmp = t_2;
	elseif (t <= -6.5e-215)
		tmp = t_1;
	elseif (t <= 7e-127)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 1.85e-7)
		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 = a * (c * j);
	t_2 = t * (b * i);
	tmp = 0.0;
	if (t <= -3.3e-9)
		tmp = t_2;
	elseif (t <= -6.5e-215)
		tmp = t_1;
	elseif (t <= 7e-127)
		tmp = z * (x * y);
	elseif (t <= 1.85e-7)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-9], t$95$2, If[LessEqual[t, -6.5e-215], t$95$1, If[LessEqual[t, 7e-127], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-7], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.30000000000000018e-9 or 1.85000000000000002e-7 < t

   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. cancel-sign-sub 61.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 61.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 61.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 61.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 61.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 61.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 52.4%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 35.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.9%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 40.9%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*r* 38.7%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   7. Simplified 38.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if -3.30000000000000018e-9 < t < -6.4999999999999999e-215 or 6.99999999999999979e-127 < t < 1.85000000000000002e-7

   1. Initial program 82.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 82.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 51.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 46.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 46.3%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -6.4999999999999999e-215 < t < 6.99999999999999979e-127

   1. Initial program 88.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 88.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 88.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around 0 72.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b} \]
   5. Step-by-step derivation

      1. sub-neg 72.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\left(c \cdot z - i \cdot t\right) \cdot b\right)} \]

      2. *-commutative 72.7%

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\color{blue}{b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]

      3. +-commutative 72.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. distribute-rgt-neg-in 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      6. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      7. distribute-lft-in 72.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      8. fma-udef 72.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x + -1 \cdot \left(i \cdot j\right), -b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      9. mul-1-neg 72.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x + \color{blue}{\left(-i \cdot j\right)}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      10. unsub-neg 72.7%

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot x - i \cdot j}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      11. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - \color{blue}{j \cdot i}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      12. distribute-rgt-neg-in 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right) \]

      13. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right) \]

   6. Simplified 72.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(i \cdot t - c \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 36.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.1%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 38.0%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

      3. *-commutative 38.0%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   9. Simplified 38.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 19: 28.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= t -3.4e-25)
     (* b (* t i))
     (if (<= t -2.6e-215)
       t_1
       (if (<= t 2.7e-128)
         (* z (* x y))
         (if (<= t 3.5e-9) t_1 (* t (* b i))))))))

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);
	double tmp;
	if (t <= -3.4e-25) {
		tmp = b * (t * i);
	} else if (t <= -2.6e-215) {
		tmp = t_1;
	} else if (t <= 2.7e-128) {
		tmp = z * (x * y);
	} else if (t <= 3.5e-9) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	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)
    if (t <= (-3.4d-25)) then
        tmp = b * (t * i)
    else if (t <= (-2.6d-215)) then
        tmp = t_1
    else if (t <= 2.7d-128) then
        tmp = z * (x * y)
    else if (t <= 3.5d-9) then
        tmp = t_1
    else
        tmp = t * (b * i)
    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);
	double tmp;
	if (t <= -3.4e-25) {
		tmp = b * (t * i);
	} else if (t <= -2.6e-215) {
		tmp = t_1;
	} else if (t <= 2.7e-128) {
		tmp = z * (x * y);
	} else if (t <= 3.5e-9) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if t <= -3.4e-25:
		tmp = b * (t * i)
	elif t <= -2.6e-215:
		tmp = t_1
	elif t <= 2.7e-128:
		tmp = z * (x * y)
	elif t <= 3.5e-9:
		tmp = t_1
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (t <= -3.4e-25)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -2.6e-215)
		tmp = t_1;
	elseif (t <= 2.7e-128)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 3.5e-9)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (t <= -3.4e-25)
		tmp = b * (t * i);
	elseif (t <= -2.6e-215)
		tmp = t_1;
	elseif (t <= 2.7e-128)
		tmp = z * (x * y);
	elseif (t <= 3.5e-9)
		tmp = t_1;
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-25], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-215], t$95$1, If[LessEqual[t, 2.7e-128], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-9], t$95$1, N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.40000000000000002e-25

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 66.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 55.8%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 47.4%

      \[\leadsto \color{blue}{\left(i \cdot t\right)} \cdot b \]
   6. Step-by-step derivation

      1. *-commutative 47.4%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   7. Simplified 47.4%

      \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   if -3.40000000000000002e-25 < t < -2.6e-215 or 2.70000000000000006e-128 < t < 3.4999999999999999e-9

   1. Initial program 83.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 51.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 51.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 46.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 46.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -2.6e-215 < t < 2.70000000000000006e-128

   1. Initial program 88.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 88.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 88.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 88.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around 0 72.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b} \]
   5. Step-by-step derivation

      1. sub-neg 72.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\left(c \cdot z - i \cdot t\right) \cdot b\right)} \]

      2. *-commutative 72.7%

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right) + \left(-\color{blue}{b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]

      3. +-commutative 72.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. distribute-rgt-neg-in 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      6. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      7. distribute-lft-in 72.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      8. fma-udef 72.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x + -1 \cdot \left(i \cdot j\right), -b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      9. mul-1-neg 72.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x + \color{blue}{\left(-i \cdot j\right)}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      10. unsub-neg 72.7%

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot x - i \cdot j}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      11. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - \color{blue}{j \cdot i}, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      12. distribute-rgt-neg-in 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right) \]

      13. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      14. associate-+l- 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right) \]

      15. neg-sub0 72.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right) \]

   6. Simplified 72.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x - j \cdot i, b \cdot \left(i \cdot t - c \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 36.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.1%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 38.0%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

      3. *-commutative 38.0%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   9. Simplified 38.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if 3.4999999999999999e-9 < t

   1. Initial program 54.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 54.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 54.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 54.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 54.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 54.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 54.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 49.2%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 32.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 32.3%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 32.3%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*r* 32.3%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   7. Simplified 32.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 20: 51.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3950000 \lor \neg \left(y \leq 1.6 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -3950000.0) (not (<= y 1.6e-7)))
   (* y (- (* x z) (* i j)))
   (* 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 tmp;
	if ((y <= -3950000.0) || !(y <= 1.6e-7)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	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 ((y <= (-3950000.0d0)) .or. (.not. (y <= 1.6d-7))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = a * ((c * j) - (x * t))
    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 ((y <= -3950000.0) || !(y <= 1.6e-7)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -3950000.0) or not (y <= 1.6e-7):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -3950000.0) || !(y <= 1.6e-7))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	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)
	tmp = 0.0;
	if ((y <= -3950000.0) || ~((y <= 1.6e-7)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -3950000.0], N[Not[LessEqual[y, 1.6e-7]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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 y < -3.95e6 or 1.6e-7 < y

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 66.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 61.5%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 61.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

      4. *-commutative 61.5%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   6. Simplified 61.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   if -3.95e6 < y < 1.6e-7

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 80.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 80.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 80.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 80.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 47.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 47.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 47.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 47.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3950000 \lor \neg \left(y \leq 1.6 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 21: 43.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.9 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.9e+59)
   (* c (- (* a j) (* z b)))
   (if (<= b 8.5e+113)
     (* a (- (* c j) (* x t)))
     (if (<= b 2.6e+161) (* b (* t i)) (* (* z c) (- 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 (b <= -5.9e+59) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 8.5e+113) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 2.6e+161) {
		tmp = b * (t * i);
	} else {
		tmp = (z * c) * -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 (b <= (-5.9d+59)) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 8.5d+113) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 2.6d+161) then
        tmp = b * (t * i)
    else
        tmp = (z * c) * -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 (b <= -5.9e+59) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 8.5e+113) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 2.6e+161) {
		tmp = b * (t * i);
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.9e+59:
		tmp = c * ((a * j) - (z * b))
	elif b <= 8.5e+113:
		tmp = a * ((c * j) - (x * t))
	elif b <= 2.6e+161:
		tmp = b * (t * i)
	else:
		tmp = (z * c) * -b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.9e+59)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 8.5e+113)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 2.6e+161)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(Float64(z * c) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.9e+59)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 8.5e+113)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 2.6e+161)
		tmp = b * (t * i);
	else
		tmp = (z * c) * -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.9e+59], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+113], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+161], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.90000000000000038e59

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 55.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 55.4%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 55.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   if -5.90000000000000038e59 < b < 8.5000000000000001e113

   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. cancel-sign-sub 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 49.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 49.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 49.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 49.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 49.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 8.5000000000000001e113 < b < 2.5999999999999998e161

   1. Initial program 59.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 59.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 59.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 71.0%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 65.4%

      \[\leadsto \color{blue}{\left(i \cdot t\right)} \cdot b \]
   6. Step-by-step derivation

      1. *-commutative 65.4%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   7. Simplified 65.4%

      \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   if 2.5999999999999998e161 < b

   1. Initial program 66.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 66.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 66.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 66.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 66.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 66.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 57.7%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around 0 55.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \cdot b \]
   6. Step-by-step derivation

      1. mul-1-neg 55.0%

         \[\leadsto \color{blue}{\left(-c \cdot z\right)} \cdot b \]

      2. distribute-lft-neg-out 55.0%

         \[\leadsto \color{blue}{\left(\left(-c\right) \cdot z\right)} \cdot b \]

      3. *-commutative 55.0%

         \[\leadsto \color{blue}{\left(z \cdot \left(-c\right)\right)} \cdot b \]

   7. Simplified 55.0%

      \[\leadsto \color{blue}{\left(z \cdot \left(-c\right)\right)} \cdot b \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.9 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]

Alternative 22: 29.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-25} \lor \neg \left(t \leq 3.4 \cdot 10^{-10}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -4.8e-25) (not (<= t 3.4e-10))) (* 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 ((t <= -4.8e-25) || !(t <= 3.4e-10)) {
		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 ((t <= (-4.8d-25)) .or. (.not. (t <= 3.4d-10))) 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 ((t <= -4.8e-25) || !(t <= 3.4e-10)) {
		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 (t <= -4.8e-25) or not (t <= 3.4e-10):
		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 ((t <= -4.8e-25) || !(t <= 3.4e-10))
		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 ((t <= -4.8e-25) || ~((t <= 3.4e-10)))
		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[t, -4.8e-25], N[Not[LessEqual[t, 3.4e-10]], $MachinePrecision]], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.80000000000000018e-25 or 3.40000000000000015e-10 < t

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 61.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 61.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 61.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 61.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 52.8%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 35.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -4.80000000000000018e-25 < t < 3.40000000000000015e-10

   1. Initial program 85.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 85.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 85.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 85.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 85.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 40.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 40.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 40.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 40.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 40.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 40.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 34.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.8%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 34.8%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-25} \lor \neg \left(t \leq 3.4 \cdot 10^{-10}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 23: 28.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-25} \lor \neg \left(t \leq 2.5 \cdot 10^{-7}\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -3.9e-25) (not (<= t 2.5e-7))) (* t (* b i)) (* 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 ((t <= -3.9e-25) || !(t <= 2.5e-7)) {
		tmp = t * (b * i);
	} 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 ((t <= (-3.9d-25)) .or. (.not. (t <= 2.5d-7))) then
        tmp = t * (b * i)
    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 ((t <= -3.9e-25) || !(t <= 2.5e-7)) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -3.9e-25) or not (t <= 2.5e-7):
		tmp = t * (b * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -3.9e-25) || !(t <= 2.5e-7))
		tmp = Float64(t * Float64(b * i));
	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 ((t <= -3.9e-25) || ~((t <= 2.5e-7)))
		tmp = t * (b * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -3.9e-25], N[Not[LessEqual[t, 2.5e-7]], $MachinePrecision]], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e-25 or 2.49999999999999989e-7 < t

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 61.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 61.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 61.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 61.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 52.8%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 35.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.6%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 40.6%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*r* 38.4%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   7. Simplified 38.4%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if -3.9e-25 < t < 2.49999999999999989e-7

   1. Initial program 85.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 85.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 85.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 85.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 85.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 40.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 40.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 40.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 40.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 40.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 40.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 34.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.8%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 34.8%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-25} \lor \neg \left(t \leq 2.5 \cdot 10^{-7}\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 24: 21.5% 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 73.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub 73.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   2. cancel-sign-sub-inv 73.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   3. *-commutative 73.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

   4. remove-double-neg 73.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

   5. *-commutative 73.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

3. Simplified 73.5%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

4. Taylor expanded in a around inf 40.6%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 40.6%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.6%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.6%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 40.6%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

6. Simplified 40.6%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

7. Taylor expanded in j around inf 24.8%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 24.8%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

9. Simplified 24.8%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

10. Final simplification 24.8%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.3% 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 2023196 
(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)))))