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

Percentage Accurate: 72.9% → 80.9%

Time: 26.4s

Alternatives: 26

Speedup: 0.5×

• 58.0% 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: 72.9% 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: 80.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := t_1 + j \cdot t_2\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(t \cdot \left(b \cdot i - x \cdot a\right) - \left(j \cdot \left(y \cdot i - a \cdot c\right) - y \cdot \left(x \cdot z\right)\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t_2, t_1\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_2 (- (* a c) (* y i)))
        (t_3 (+ t_1 (* j t_2))))
   (if (<= t_3 (- INFINITY))
     (-
      (- (* t (- (* b i) (* x a))) (- (* j (- (* y i) (* a c))) (* y (* x z))))
      (* c (* z b)))
     (if (<= t_3 INFINITY) (fma j t_2 t_1) (* a (- (* c j) (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = (a * c) - (y * i);
	double t_3 = t_1 + (j * t_2);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((t * ((b * i) - (x * a))) - ((j * ((y * i) - (a * c))) - (y * (x * z)))) - (c * (z * b));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	t_3 = Float64(t_1 + Float64(j * t_2))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) - Float64(Float64(j * Float64(Float64(y * i) - Float64(a * c))) - Float64(y * Float64(x * z)))) - Float64(c * Float64(z * b)));
	elseif (t_3 <= Inf)
		tmp = fma(j, t_2, t_1);
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 3 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 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. +-commutative 77.8%

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

      2. fma-def 77.8%

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

      3. *-commutative 77.8%

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

      4. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in t around -inf 84.2%

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

   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)))) < +inf.0

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. fma-def 93.4%

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

      3. *-commutative 93.4%

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

      4. *-commutative 93.4%

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

   3. Simplified 93.4%

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

   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. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in a around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

   6. Simplified 60.0%

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

4. Final simplification 85.0%

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

Alternative 2: 80.9% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 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 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. +-commutative 77.8%

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

      2. fma-def 77.8%

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

      3. *-commutative 77.8%

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

      4. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in t around -inf 84.2%

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

   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)))) < +inf.0

   1. Initial program 93.4%

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

   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. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in a around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

   6. Simplified 60.0%

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

4. Final simplification 85.0%

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

Alternative 3: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.7%

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

   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. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in a around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

   6. Simplified 60.0%

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

4. Final simplification 83.4%

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

Alternative 4: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot b\right)\\ t_2 := \left(y \cdot \left(x \cdot z\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - t_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) + t_3\\ \mathbf{if}\;j \leq -4.5 \cdot 10^{+195}:\\ \;\;\;\;t_3 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -6800000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+197}:\\ \;\;\;\;t_3 - t_1\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+275}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z b)))
        (t_2 (- (+ (* y (* x z)) (* t (- (* b i) (* x a)))) t_1))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (+ (* x (- (* y z) (* t a))) t_3)))
   (if (<= j -4.5e+195)
     (+ t_3 (* b (- (* t i) (* z c))))
     (if (<= j -6800000.0)
       t_4
       (if (<= j 6.8e-101)
         t_2
         (if (<= j 3.8e-7)
           t_4
           (if (<= j 8e+72)
             t_2
             (if (<= j 5.5e+197)
               (- t_3 t_1)
               (if (<= j 1.7e+275) t_4 (* y (- (* x z) (* i j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * b);
	double t_2 = ((y * (x * z)) + (t * ((b * i) - (x * a)))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = (x * ((y * z) - (t * a))) + t_3;
	double tmp;
	if (j <= -4.5e+195) {
		tmp = t_3 + (b * ((t * i) - (z * c)));
	} else if (j <= -6800000.0) {
		tmp = t_4;
	} else if (j <= 6.8e-101) {
		tmp = t_2;
	} else if (j <= 3.8e-7) {
		tmp = t_4;
	} else if (j <= 8e+72) {
		tmp = t_2;
	} else if (j <= 5.5e+197) {
		tmp = t_3 - t_1;
	} else if (j <= 1.7e+275) {
		tmp = t_4;
	} else {
		tmp = y * ((x * z) - (i * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = c * (z * b)
    t_2 = ((y * (x * z)) + (t * ((b * i) - (x * a)))) - t_1
    t_3 = j * ((a * c) - (y * i))
    t_4 = (x * ((y * z) - (t * a))) + t_3
    if (j <= (-4.5d+195)) then
        tmp = t_3 + (b * ((t * i) - (z * c)))
    else if (j <= (-6800000.0d0)) then
        tmp = t_4
    else if (j <= 6.8d-101) then
        tmp = t_2
    else if (j <= 3.8d-7) then
        tmp = t_4
    else if (j <= 8d+72) then
        tmp = t_2
    else if (j <= 5.5d+197) then
        tmp = t_3 - t_1
    else if (j <= 1.7d+275) then
        tmp = t_4
    else
        tmp = y * ((x * z) - (i * 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 t_1 = c * (z * b);
	double t_2 = ((y * (x * z)) + (t * ((b * i) - (x * a)))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = (x * ((y * z) - (t * a))) + t_3;
	double tmp;
	if (j <= -4.5e+195) {
		tmp = t_3 + (b * ((t * i) - (z * c)));
	} else if (j <= -6800000.0) {
		tmp = t_4;
	} else if (j <= 6.8e-101) {
		tmp = t_2;
	} else if (j <= 3.8e-7) {
		tmp = t_4;
	} else if (j <= 8e+72) {
		tmp = t_2;
	} else if (j <= 5.5e+197) {
		tmp = t_3 - t_1;
	} else if (j <= 1.7e+275) {
		tmp = t_4;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * b)
	t_2 = ((y * (x * z)) + (t * ((b * i) - (x * a)))) - t_1
	t_3 = j * ((a * c) - (y * i))
	t_4 = (x * ((y * z) - (t * a))) + t_3
	tmp = 0
	if j <= -4.5e+195:
		tmp = t_3 + (b * ((t * i) - (z * c)))
	elif j <= -6800000.0:
		tmp = t_4
	elif j <= 6.8e-101:
		tmp = t_2
	elif j <= 3.8e-7:
		tmp = t_4
	elif j <= 8e+72:
		tmp = t_2
	elif j <= 5.5e+197:
		tmp = t_3 - t_1
	elif j <= 1.7e+275:
		tmp = t_4
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * b))
	t_2 = Float64(Float64(Float64(y * Float64(x * z)) + Float64(t * Float64(Float64(b * i) - Float64(x * a)))) - t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_3)
	tmp = 0.0
	if (j <= -4.5e+195)
		tmp = Float64(t_3 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= -6800000.0)
		tmp = t_4;
	elseif (j <= 6.8e-101)
		tmp = t_2;
	elseif (j <= 3.8e-7)
		tmp = t_4;
	elseif (j <= 8e+72)
		tmp = t_2;
	elseif (j <= 5.5e+197)
		tmp = Float64(t_3 - t_1);
	elseif (j <= 1.7e+275)
		tmp = t_4;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * b);
	t_2 = ((y * (x * z)) + (t * ((b * i) - (x * a)))) - t_1;
	t_3 = j * ((a * c) - (y * i));
	t_4 = (x * ((y * z) - (t * a))) + t_3;
	tmp = 0.0;
	if (j <= -4.5e+195)
		tmp = t_3 + (b * ((t * i) - (z * c)));
	elseif (j <= -6800000.0)
		tmp = t_4;
	elseif (j <= 6.8e-101)
		tmp = t_2;
	elseif (j <= 3.8e-7)
		tmp = t_4;
	elseif (j <= 8e+72)
		tmp = t_2;
	elseif (j <= 5.5e+197)
		tmp = t_3 - t_1;
	elseif (j <= 1.7e+275)
		tmp = t_4;
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[j, -4.5e+195], N[(t$95$3 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6800000.0], t$95$4, If[LessEqual[j, 6.8e-101], t$95$2, If[LessEqual[j, 3.8e-7], t$95$4, If[LessEqual[j, 8e+72], t$95$2, If[LessEqual[j, 5.5e+197], N[(t$95$3 - t$95$1), $MachinePrecision], If[LessEqual[j, 1.7e+275], t$95$4, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -4.50000000000000009e195

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. fma-def 78.0%

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

      3. *-commutative 78.0%

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

      4. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in x around 0 78.3%

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

   if -4.50000000000000009e195 < j < -6.8e6 or 6.79999999999999978e-101 < j < 3.80000000000000015e-7 or 5.4999999999999999e197 < j < 1.7e275

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. fma-def 79.9%

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

      3. *-commutative 79.9%

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

      4. *-commutative 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in b around 0 80.1%

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

   if -6.8e6 < j < 6.79999999999999978e-101 or 3.80000000000000015e-7 < j < 7.99999999999999955e72

   1. Initial program 70.8%

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

      1. +-commutative 70.8%

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

      2. fma-def 71.6%

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

      3. *-commutative 71.6%

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

      4. *-commutative 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in t around -inf 77.6%

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

   5. Taylor expanded in j around 0 77.0%

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

   if 7.99999999999999955e72 < j < 5.4999999999999999e197

   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. +-commutative 62.5%

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

      2. fma-def 62.5%

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

      3. *-commutative 62.5%

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

      4. *-commutative 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in t around -inf 81.0%

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

   5. Taylor expanded in j around inf 76.9%

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

   if 1.7e275 < j

   1. Initial program 50.7%

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

      1. associate-+l- 50.7%

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

      2. *-commutative 50.7%

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

      3. sub-neg 50.7%

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

      4. sub-neg 50.7%

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

      5. *-commutative 50.7%

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

   3. Simplified 50.7%

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

   4. Taylor expanded in y around -inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. *-commutative 75.1%

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

      3. distribute-rgt-neg-in 75.1%

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

      4. mul-1-neg 75.1%

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

      5. unsub-neg 75.1%

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

   6. Simplified 75.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.5 \cdot 10^{+195}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -6800000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{-101}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+72}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+197}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+275}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 5: 71.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{-93} \lor \neg \left(b \leq 1.15 \cdot 10^{+23}\right):\\ \;\;\;\;t_1 + \left(b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (or (<= b -1.4e-93) (not (<= b 1.15e+23)))
     (+ t_1 (- (* b (- (* t i) (* z c))) (* i (* y j))))
     (+ t_1 (* j (- (* a c) (* y 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 = x * ((y * z) - (t * a));
	double tmp;
	if ((b <= -1.4e-93) || !(b <= 1.15e+23)) {
		tmp = t_1 + ((b * ((t * i) - (z * c))) - (i * (y * j)));
	} else {
		tmp = t_1 + (j * ((a * c) - (y * 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 = x * ((y * z) - (t * a))
    if ((b <= (-1.4d-93)) .or. (.not. (b <= 1.15d+23))) then
        tmp = t_1 + ((b * ((t * i) - (z * c))) - (i * (y * j)))
    else
        tmp = t_1 + (j * ((a * c) - (y * 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 = x * ((y * z) - (t * a));
	double tmp;
	if ((b <= -1.4e-93) || !(b <= 1.15e+23)) {
		tmp = t_1 + ((b * ((t * i) - (z * c))) - (i * (y * j)));
	} else {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if (b <= -1.4e-93) or not (b <= 1.15e+23):
		tmp = t_1 + ((b * ((t * i) - (z * c))) - (i * (y * j)))
	else:
		tmp = t_1 + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if ((b <= -1.4e-93) || !(b <= 1.15e+23))
		tmp = Float64(t_1 + Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(i * Float64(y * j))));
	else
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if ((b <= -1.4e-93) || ~((b <= 1.15e+23)))
		tmp = t_1 + ((b * ((t * i) - (z * c))) - (i * (y * j)));
	else
		tmp = t_1 + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.4e-93], N[Not[LessEqual[b, 1.15e+23]], $MachinePrecision]], N[(t$95$1 + N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.39999999999999999e-93 or 1.15e23 < b

   1. Initial program 77.3%

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

      1. associate-+l- 77.3%

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

      2. *-commutative 77.3%

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

      3. sub-neg 77.3%

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

      4. sub-neg 77.3%

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

      5. *-commutative 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in a around 0 80.1%

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

      1. mul-1-neg 80.1%

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

   6. Simplified 80.1%

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

   if -1.39999999999999999e-93 < b < 1.15e23

   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. +-commutative 66.6%

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

      2. fma-def 67.4%

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

      3. *-commutative 67.4%

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

      4. *-commutative 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in b around 0 71.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{-93} \lor \neg \left(b \leq 1.15 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + \left(b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 6: 52.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -17200000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* c (* a j))))
        (t_2 (* b (- (* t i) (* z c)))))
   (if (<= x -1.7e+53)
     t_1
     (if (<= x -8.6e+23)
       t_2
       (if (<= x -17200000000000.0)
         (* a (- (* c j) (* x t)))
         (if (<= x -7.8e-150)
           (- (* y (* i (- j))) (* c (* z b)))
           (if (<= x 5.8e-285)
             (* j (- (* a c) (* y i)))
             (if (<= x 7e-209) 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 = (x * ((y * z) - (t * a))) + (c * (a * j));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (x <= -1.7e+53) {
		tmp = t_1;
	} else if (x <= -8.6e+23) {
		tmp = t_2;
	} else if (x <= -17200000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else if (x <= -7.8e-150) {
		tmp = (y * (i * -j)) - (c * (z * b));
	} else if (x <= 5.8e-285) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 7e-209) {
		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 = (x * ((y * z) - (t * a))) + (c * (a * j))
    t_2 = b * ((t * i) - (z * c))
    if (x <= (-1.7d+53)) then
        tmp = t_1
    else if (x <= (-8.6d+23)) then
        tmp = t_2
    else if (x <= (-17200000000000.0d0)) then
        tmp = a * ((c * j) - (x * t))
    else if (x <= (-7.8d-150)) then
        tmp = (y * (i * -j)) - (c * (z * b))
    else if (x <= 5.8d-285) then
        tmp = j * ((a * c) - (y * i))
    else if (x <= 7d-209) 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 = (x * ((y * z) - (t * a))) + (c * (a * j));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (x <= -1.7e+53) {
		tmp = t_1;
	} else if (x <= -8.6e+23) {
		tmp = t_2;
	} else if (x <= -17200000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else if (x <= -7.8e-150) {
		tmp = (y * (i * -j)) - (c * (z * b));
	} else if (x <= 5.8e-285) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 7e-209) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (c * (a * j))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if x <= -1.7e+53:
		tmp = t_1
	elif x <= -8.6e+23:
		tmp = t_2
	elif x <= -17200000000000.0:
		tmp = a * ((c * j) - (x * t))
	elif x <= -7.8e-150:
		tmp = (y * (i * -j)) - (c * (z * b))
	elif x <= 5.8e-285:
		tmp = j * ((a * c) - (y * i))
	elif x <= 7e-209:
		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(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(c * Float64(a * j)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (x <= -1.7e+53)
		tmp = t_1;
	elseif (x <= -8.6e+23)
		tmp = t_2;
	elseif (x <= -17200000000000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (x <= -7.8e-150)
		tmp = Float64(Float64(y * Float64(i * Float64(-j))) - Float64(c * Float64(z * b)));
	elseif (x <= 5.8e-285)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (x <= 7e-209)
		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 = (x * ((y * z) - (t * a))) + (c * (a * j));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (x <= -1.7e+53)
		tmp = t_1;
	elseif (x <= -8.6e+23)
		tmp = t_2;
	elseif (x <= -17200000000000.0)
		tmp = a * ((c * j) - (x * t));
	elseif (x <= -7.8e-150)
		tmp = (y * (i * -j)) - (c * (z * b));
	elseif (x <= 5.8e-285)
		tmp = j * ((a * c) - (y * i));
	elseif (x <= 7e-209)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+53], t$95$1, If[LessEqual[x, -8.6e+23], t$95$2, If[LessEqual[x, -17200000000000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.8e-150], N[(N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-285], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-209], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.69999999999999999e53 or 7.00000000000000004e-209 < x

   1. Initial program 73.9%

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

      1. +-commutative 73.9%

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

      2. fma-def 74.6%

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

      3. *-commutative 74.6%

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

      4. *-commutative 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in b around 0 67.9%

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

   5. Taylor expanded in i around 0 64.2%

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

   if -1.69999999999999999e53 < x < -8.5999999999999997e23 or 5.7999999999999999e-285 < x < 7.00000000000000004e-209

   1. Initial program 78.1%

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

      1. associate-+l- 78.1%

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

      2. *-commutative 78.1%

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

      3. sub-neg 78.1%

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

      4. sub-neg 78.1%

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

      5. *-commutative 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in b around inf 81.7%

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

   if -8.5999999999999997e23 < x < -1.72e13

   1. Initial program 66.1%

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

      1. associate-+l- 66.1%

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

      2. *-commutative 66.1%

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

      3. sub-neg 66.1%

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

      4. sub-neg 66.1%

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

      5. *-commutative 66.1%

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

   3. Simplified 66.1%

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

   4. Taylor expanded in a around inf 99.5%

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

      1. +-commutative 99.5%

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

      2. mul-1-neg 99.5%

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

      3. unsub-neg 99.5%

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

   6. Simplified 99.5%

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

   if -1.72e13 < x < -7.8000000000000004e-150

   1. Initial program 66.0%

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

      1. associate-+l- 66.0%

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

      2. *-commutative 66.0%

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

      3. sub-neg 66.0%

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

      4. sub-neg 66.0%

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

      5. *-commutative 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in a around 0 63.2%

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

      1. mul-1-neg 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in t around 0 59.6%

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

      1. +-commutative 59.6%

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

      2. associate--r+ 59.6%

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

      3. unsub-neg 59.6%

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

      4. +-commutative 59.6%

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

      5. distribute-lft-neg-in 59.6%

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

      6. associate-*r* 56.9%

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

      7. distribute-lft-neg-out 56.9%

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

      8. mul-1-neg 56.9%

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

      9. *-commutative 56.9%

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

      10. associate-*r* 56.9%

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

      11. distribute-rgt-in 62.8%

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

      12. +-commutative 62.8%

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

      13. mul-1-neg 62.8%

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

      14. sub-neg 62.8%

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

      15. *-commutative 62.8%

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

   9. Simplified 62.8%

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

   10. Taylor expanded in x around 0 62.9%

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

       1. associate-*r* 62.9%

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

       2. neg-mul-1 62.9%

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

       3. *-commutative 62.9%

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

   12. Simplified 62.9%

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

   if -7.8000000000000004e-150 < x < 5.7999999999999999e-285

   1. Initial program 67.6%

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

      1. +-commutative 67.6%

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

      2. fma-def 70.7%

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

      3. *-commutative 70.7%

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

      4. *-commutative 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in i around 0 61.7%

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

   5. Taylor expanded in j around inf 60.2%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -17200000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-209}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 7: 65.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 - c \cdot \left(z \cdot b\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+191}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (- t_1 (* c (* z b))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -4.6e+191)
     t_3
     (if (<= b -1.85e+130)
       t_2
       (if (<= b -1.3e+54)
         (- (* z (- (* x y) (* b c))) (* i (* y j)))
         (if (<= b 1.6e+28)
           (+ (* x (- (* y z) (* t a))) t_1)
           (if (<= b 1.5e+52)
             (* t (- (* b i) (* x a)))
             (if (<= b 1.5e+138) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 - (c * (z * b));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.6e+191) {
		tmp = t_3;
	} else if (b <= -1.85e+130) {
		tmp = t_2;
	} else if (b <= -1.3e+54) {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	} else if (b <= 1.6e+28) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= 1.5e+52) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 1.5e+138) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 - (c * (z * b))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-4.6d+191)) then
        tmp = t_3
    else if (b <= (-1.85d+130)) then
        tmp = t_2
    else if (b <= (-1.3d+54)) then
        tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
    else if (b <= 1.6d+28) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else if (b <= 1.5d+52) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= 1.5d+138) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 - (c * (z * b));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.6e+191) {
		tmp = t_3;
	} else if (b <= -1.85e+130) {
		tmp = t_2;
	} else if (b <= -1.3e+54) {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	} else if (b <= 1.6e+28) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= 1.5e+52) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 1.5e+138) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 - (c * (z * b))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.6e+191:
		tmp = t_3
	elif b <= -1.85e+130:
		tmp = t_2
	elif b <= -1.3e+54:
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
	elif b <= 1.6e+28:
		tmp = (x * ((y * z) - (t * a))) + t_1
	elif b <= 1.5e+52:
		tmp = t * ((b * i) - (x * a))
	elif b <= 1.5e+138:
		tmp = t_2
	else:
		tmp = t_3
	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)))
	t_2 = Float64(t_1 - Float64(c * Float64(z * b)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.6e+191)
		tmp = t_3;
	elseif (b <= -1.85e+130)
		tmp = t_2;
	elseif (b <= -1.3e+54)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(i * Float64(y * j)));
	elseif (b <= 1.6e+28)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	elseif (b <= 1.5e+52)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= 1.5e+138)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 - (c * (z * b));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.6e+191)
		tmp = t_3;
	elseif (b <= -1.85e+130)
		tmp = t_2;
	elseif (b <= -1.3e+54)
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	elseif (b <= 1.6e+28)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	elseif (b <= 1.5e+52)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= 1.5e+138)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.6e+191], t$95$3, If[LessEqual[b, -1.85e+130], t$95$2, If[LessEqual[b, -1.3e+54], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+28], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 1.5e+52], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+138], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.5999999999999999e191 or 1.50000000000000005e138 < b

   1. Initial program 68.5%

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

      1. associate-+l- 68.5%

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

      2. *-commutative 68.5%

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

      3. sub-neg 68.5%

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

      4. sub-neg 68.5%

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

      5. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in b around inf 76.2%

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

   if -4.5999999999999999e191 < b < -1.8500000000000001e130 or 1.5e52 < b < 1.50000000000000005e138

   1. Initial program 81.1%

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

      1. +-commutative 81.1%

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

      2. fma-def 81.1%

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

      3. *-commutative 81.1%

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

      4. *-commutative 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in t around -inf 84.6%

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

   5. Taylor expanded in j around inf 81.5%

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

   if -1.8500000000000001e130 < b < -1.30000000000000003e54

   1. Initial program 73.0%

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

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. sub-neg 73.0%

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

      4. sub-neg 73.0%

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

      5. *-commutative 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in a around 0 86.4%

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

      1. mul-1-neg 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in t around 0 41.7%

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

      1. +-commutative 41.7%

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

      2. associate--r+ 41.7%

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

      3. unsub-neg 41.7%

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

      4. +-commutative 41.7%

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

      5. distribute-lft-neg-in 41.7%

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

      6. associate-*r* 67.2%

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

      7. distribute-lft-neg-out 67.2%

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

      8. mul-1-neg 67.2%

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

      9. *-commutative 67.2%

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

      10. associate-*r* 67.7%

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

      11. distribute-rgt-in 67.7%

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

      12. +-commutative 67.7%

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

      13. mul-1-neg 67.7%

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

      14. sub-neg 67.7%

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

      15. *-commutative 67.7%

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

   9. Simplified 67.7%

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

   if -1.30000000000000003e54 < b < 1.6e28

   1. Initial program 72.2%

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

      1. +-commutative 72.2%

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

      2. fma-def 72.9%

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

      3. *-commutative 72.9%

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

      4. *-commutative 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in b around 0 71.2%

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

   if 1.6e28 < b < 1.5e52

   1. Initial program 75.5%

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

      1. associate-+l- 75.5%

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

      2. *-commutative 75.5%

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

      3. sub-neg 75.5%

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

      4. sub-neg 75.5%

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

      5. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in y around 0 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in t around inf 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

      3. *-commutative 75.8%

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

   9. Simplified 75.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+191}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{+130}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+138}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 8: 69.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{+177}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+35} \lor \neg \left(b \leq 2.9 \cdot 10^{+27}\right):\\ \;\;\;\;t_1 + t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -3.7e+191)
     t_2
     (if (<= b -6.4e+177)
       (- t_1 (* c (* z b)))
       (if (or (<= b -2.5e+35) (not (<= b 2.9e+27)))
         (+ t_1 t_2)
         (+ (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e+191) {
		tmp = t_2;
	} else if (b <= -6.4e+177) {
		tmp = t_1 - (c * (z * b));
	} else if ((b <= -2.5e+35) || !(b <= 2.9e+27)) {
		tmp = t_1 + t_2;
	} else {
		tmp = (x * ((y * z) - (t * a))) + 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 = j * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-3.7d+191)) then
        tmp = t_2
    else if (b <= (-6.4d+177)) then
        tmp = t_1 - (c * (z * b))
    else if ((b <= (-2.5d+35)) .or. (.not. (b <= 2.9d+27))) then
        tmp = t_1 + t_2
    else
        tmp = (x * ((y * z) - (t * a))) + 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 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e+191) {
		tmp = t_2;
	} else if (b <= -6.4e+177) {
		tmp = t_1 - (c * (z * b));
	} else if ((b <= -2.5e+35) || !(b <= 2.9e+27)) {
		tmp = t_1 + t_2;
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.7e+191:
		tmp = t_2
	elif b <= -6.4e+177:
		tmp = t_1 - (c * (z * b))
	elif (b <= -2.5e+35) or not (b <= 2.9e+27):
		tmp = t_1 + t_2
	else:
		tmp = (x * ((y * z) - (t * a))) + t_1
	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)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.7e+191)
		tmp = t_2;
	elseif (b <= -6.4e+177)
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	elseif ((b <= -2.5e+35) || !(b <= 2.9e+27))
		tmp = Float64(t_1 + t_2);
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	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));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.7e+191)
		tmp = t_2;
	elseif (b <= -6.4e+177)
		tmp = t_1 - (c * (z * b));
	elseif ((b <= -2.5e+35) || ~((b <= 2.9e+27)))
		tmp = t_1 + t_2;
	else
		tmp = (x * ((y * z) - (t * a))) + t_1;
	end
	tmp_2 = 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]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e+191], t$95$2, If[LessEqual[b, -6.4e+177], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -2.5e+35], N[Not[LessEqual[b, 2.9e+27]], $MachinePrecision]], N[(t$95$1 + t$95$2), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.70000000000000019e191

   1. Initial program 62.1%

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

      1. associate-+l- 62.1%

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

      2. *-commutative 62.1%

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

      3. sub-neg 62.1%

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

      4. sub-neg 62.1%

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

      5. *-commutative 62.1%

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

   3. Simplified 62.1%

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

   4. Taylor expanded in b around inf 77.1%

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

   if -3.70000000000000019e191 < b < -6.4e177

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. *-commutative 99.7%

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

      4. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around -inf 99.7%

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

   5. Taylor expanded in j around inf 99.7%

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

   if -6.4e177 < b < -2.50000000000000011e35 or 2.9000000000000001e27 < b

   1. Initial program 74.2%

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

      1. +-commutative 74.2%

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

      2. fma-def 74.2%

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

      3. *-commutative 74.2%

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

      4. *-commutative 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in x around 0 72.2%

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

   if -2.50000000000000011e35 < b < 2.9000000000000001e27

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. fma-def 72.6%

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

      3. *-commutative 72.6%

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

      4. *-commutative 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in b around 0 71.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{+177}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+35} \lor \neg \left(b \leq 2.9 \cdot 10^{+27}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 9: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -0.000135:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -0.000135)
     t_3
     (if (<= t -6.3e-108)
       t_2
       (if (<= t -3.3e-122)
         t_3
         (if (<= t 6.2e-298)
           t_1
           (if (<= t 3.7e-238)
             t_2
             (if (<= t 1.05e-109)
               t_1
               (if (<= t 6.8e+38) (* x (- (* y z) (* t a))) 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 = c * ((a * j) - (z * b));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -0.000135) {
		tmp = t_3;
	} else if (t <= -6.3e-108) {
		tmp = t_2;
	} else if (t <= -3.3e-122) {
		tmp = t_3;
	} else if (t <= 6.2e-298) {
		tmp = t_1;
	} else if (t <= 3.7e-238) {
		tmp = t_2;
	} else if (t <= 1.05e-109) {
		tmp = t_1;
	} else if (t <= 6.8e+38) {
		tmp = x * ((y * z) - (t * a));
	} 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 = c * ((a * j) - (z * b))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-0.000135d0)) then
        tmp = t_3
    else if (t <= (-6.3d-108)) then
        tmp = t_2
    else if (t <= (-3.3d-122)) then
        tmp = t_3
    else if (t <= 6.2d-298) then
        tmp = t_1
    else if (t <= 3.7d-238) then
        tmp = t_2
    else if (t <= 1.05d-109) then
        tmp = t_1
    else if (t <= 6.8d+38) then
        tmp = x * ((y * z) - (t * a))
    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 = c * ((a * j) - (z * b));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -0.000135) {
		tmp = t_3;
	} else if (t <= -6.3e-108) {
		tmp = t_2;
	} else if (t <= -3.3e-122) {
		tmp = t_3;
	} else if (t <= 6.2e-298) {
		tmp = t_1;
	} else if (t <= 3.7e-238) {
		tmp = t_2;
	} else if (t <= 1.05e-109) {
		tmp = t_1;
	} else if (t <= 6.8e+38) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -0.000135:
		tmp = t_3
	elif t <= -6.3e-108:
		tmp = t_2
	elif t <= -3.3e-122:
		tmp = t_3
	elif t <= 6.2e-298:
		tmp = t_1
	elif t <= 3.7e-238:
		tmp = t_2
	elif t <= 1.05e-109:
		tmp = t_1
	elif t <= 6.8e+38:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -0.000135)
		tmp = t_3;
	elseif (t <= -6.3e-108)
		tmp = t_2;
	elseif (t <= -3.3e-122)
		tmp = t_3;
	elseif (t <= 6.2e-298)
		tmp = t_1;
	elseif (t <= 3.7e-238)
		tmp = t_2;
	elseif (t <= 1.05e-109)
		tmp = t_1;
	elseif (t <= 6.8e+38)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -0.000135)
		tmp = t_3;
	elseif (t <= -6.3e-108)
		tmp = t_2;
	elseif (t <= -3.3e-122)
		tmp = t_3;
	elseif (t <= 6.2e-298)
		tmp = t_1;
	elseif (t <= 3.7e-238)
		tmp = t_2;
	elseif (t <= 1.05e-109)
		tmp = t_1;
	elseif (t <= 6.8e+38)
		tmp = x * ((y * z) - (t * a));
	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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.000135], t$95$3, If[LessEqual[t, -6.3e-108], t$95$2, If[LessEqual[t, -3.3e-122], t$95$3, If[LessEqual[t, 6.2e-298], t$95$1, If[LessEqual[t, 3.7e-238], t$95$2, If[LessEqual[t, 1.05e-109], t$95$1, If[LessEqual[t, 6.8e+38], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.35000000000000002e-4 or -6.2999999999999997e-108 < t < -3.29999999999999999e-122 or 6.79999999999999992e38 < t

   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. associate-+l- 65.8%

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

      2. *-commutative 65.8%

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

      3. sub-neg 65.8%

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

      4. sub-neg 65.8%

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

      5. *-commutative 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in y around 0 67.1%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in t around inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. unsub-neg 63.7%

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

      3. *-commutative 63.7%

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

   9. Simplified 63.7%

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

   if -1.35000000000000002e-4 < t < -6.2999999999999997e-108 or 6.2000000000000003e-298 < t < 3.70000000000000024e-238

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. sub-neg 77.1%

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

      4. sub-neg 77.1%

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

      5. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in z around inf 54.0%

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

   if -3.29999999999999999e-122 < t < 6.2000000000000003e-298 or 3.70000000000000024e-238 < t < 1.04999999999999998e-109

   1. Initial program 80.2%

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

      1. associate-+l- 80.2%

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

      2. *-commutative 80.2%

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

      3. sub-neg 80.2%

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

      4. sub-neg 80.2%

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

      5. *-commutative 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in c around inf 68.9%

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

   if 1.04999999999999998e-109 < t < 6.79999999999999992e38

   1. Initial program 77.4%

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

      1. associate-+l- 77.4%

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

      2. *-commutative 77.4%

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

      3. sub-neg 77.4%

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

      4. sub-neg 77.4%

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

      5. *-commutative 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in a around 0 88.7%

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

      1. mul-1-neg 88.7%

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

   6. Simplified 88.7%

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

   7. Taylor expanded in x around inf 56.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.000135:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-298}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-238}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-109}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 10: 52.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;t \leq -0.0052:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -2.16 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-240}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+39}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= t -0.0052)
     t_2
     (if (<= t -5.7e-108)
       (* z (- (* x y) (* b c)))
       (if (<= t -2.16e-122)
         t_2
         (if (<= t 6.5e-302)
           t_1
           (if (<= t 2e-240)
             t_3
             (if (<= t 3.3e-110) t_1 (if (<= t 1.32e+39) t_3 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 = c * ((a * j) - (z * b));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (t <= -0.0052) {
		tmp = t_2;
	} else if (t <= -5.7e-108) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -2.16e-122) {
		tmp = t_2;
	} else if (t <= 6.5e-302) {
		tmp = t_1;
	} else if (t <= 2e-240) {
		tmp = t_3;
	} else if (t <= 3.3e-110) {
		tmp = t_1;
	} else if (t <= 1.32e+39) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    t_2 = t * ((b * i) - (x * a))
    t_3 = y * ((x * z) - (i * j))
    if (t <= (-0.0052d0)) then
        tmp = t_2
    else if (t <= (-5.7d-108)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= (-2.16d-122)) then
        tmp = t_2
    else if (t <= 6.5d-302) then
        tmp = t_1
    else if (t <= 2d-240) then
        tmp = t_3
    else if (t <= 3.3d-110) then
        tmp = t_1
    else if (t <= 1.32d+39) then
        tmp = t_3
    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 = c * ((a * j) - (z * b));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (t <= -0.0052) {
		tmp = t_2;
	} else if (t <= -5.7e-108) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -2.16e-122) {
		tmp = t_2;
	} else if (t <= 6.5e-302) {
		tmp = t_1;
	} else if (t <= 2e-240) {
		tmp = t_3;
	} else if (t <= 3.3e-110) {
		tmp = t_1;
	} else if (t <= 1.32e+39) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = t * ((b * i) - (x * a))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if t <= -0.0052:
		tmp = t_2
	elif t <= -5.7e-108:
		tmp = z * ((x * y) - (b * c))
	elif t <= -2.16e-122:
		tmp = t_2
	elif t <= 6.5e-302:
		tmp = t_1
	elif t <= 2e-240:
		tmp = t_3
	elif t <= 3.3e-110:
		tmp = t_1
	elif t <= 1.32e+39:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (t <= -0.0052)
		tmp = t_2;
	elseif (t <= -5.7e-108)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= -2.16e-122)
		tmp = t_2;
	elseif (t <= 6.5e-302)
		tmp = t_1;
	elseif (t <= 2e-240)
		tmp = t_3;
	elseif (t <= 3.3e-110)
		tmp = t_1;
	elseif (t <= 1.32e+39)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = t * ((b * i) - (x * a));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (t <= -0.0052)
		tmp = t_2;
	elseif (t <= -5.7e-108)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= -2.16e-122)
		tmp = t_2;
	elseif (t <= 6.5e-302)
		tmp = t_1;
	elseif (t <= 2e-240)
		tmp = t_3;
	elseif (t <= 3.3e-110)
		tmp = t_1;
	elseif (t <= 1.32e+39)
		tmp = t_3;
	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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.0052], t$95$2, If[LessEqual[t, -5.7e-108], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.16e-122], t$95$2, If[LessEqual[t, 6.5e-302], t$95$1, If[LessEqual[t, 2e-240], t$95$3, If[LessEqual[t, 3.3e-110], t$95$1, If[LessEqual[t, 1.32e+39], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.0051999999999999998 or -5.7e-108 < t < -2.1600000000000001e-122 or 1.32e39 < t

   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. associate-+l- 65.8%

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

      2. *-commutative 65.8%

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

      3. sub-neg 65.8%

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

      4. sub-neg 65.8%

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

      5. *-commutative 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in y around 0 67.1%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in t around inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. unsub-neg 63.7%

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

      3. *-commutative 63.7%

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

   9. Simplified 63.7%

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

   if -0.0051999999999999998 < t < -5.7e-108

   1. Initial program 59.7%

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

      1. associate-+l- 59.7%

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

      2. *-commutative 59.7%

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

      3. sub-neg 59.7%

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

      4. sub-neg 59.7%

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

      5. *-commutative 59.7%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in z around inf 52.5%

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

   if -2.1600000000000001e-122 < t < 6.4999999999999995e-302 or 1.9999999999999999e-240 < t < 3.2999999999999999e-110

   1. Initial program 80.2%

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

      1. associate-+l- 80.2%

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

      2. *-commutative 80.2%

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

      3. sub-neg 80.2%

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

      4. sub-neg 80.2%

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

      5. *-commutative 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in c around inf 68.9%

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

   if 6.4999999999999995e-302 < t < 1.9999999999999999e-240 or 3.2999999999999999e-110 < t < 1.32e39

   1. Initial program 84.0%

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

      1. associate-+l- 84.0%

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

      2. *-commutative 84.0%

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

      3. sub-neg 84.0%

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

      4. sub-neg 84.0%

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

      5. *-commutative 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in y around -inf 73.7%

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

      1. mul-1-neg 73.7%

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

      2. *-commutative 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. mul-1-neg 73.7%

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

      5. unsub-neg 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0052:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -2.16 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-302}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-110}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 11: 60.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;x \leq -2.65 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* c (* a j))))
        (t_2 (- (* j (- (* a c) (* y i))) (* c (* z b)))))
   (if (<= x -2.65e+53)
     t_1
     (if (<= x 1.1e-236)
       t_2
       (if (<= x 5.4e-214)
         (* b (- (* t i) (* z c)))
         (if (<= x 2.7e-49) 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 = (x * ((y * z) - (t * a))) + (c * (a * j));
	double t_2 = (j * ((a * c) - (y * i))) - (c * (z * b));
	double tmp;
	if (x <= -2.65e+53) {
		tmp = t_1;
	} else if (x <= 1.1e-236) {
		tmp = t_2;
	} else if (x <= 5.4e-214) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 2.7e-49) {
		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 = (x * ((y * z) - (t * a))) + (c * (a * j))
    t_2 = (j * ((a * c) - (y * i))) - (c * (z * b))
    if (x <= (-2.65d+53)) then
        tmp = t_1
    else if (x <= 1.1d-236) then
        tmp = t_2
    else if (x <= 5.4d-214) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 2.7d-49) 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 = (x * ((y * z) - (t * a))) + (c * (a * j));
	double t_2 = (j * ((a * c) - (y * i))) - (c * (z * b));
	double tmp;
	if (x <= -2.65e+53) {
		tmp = t_1;
	} else if (x <= 1.1e-236) {
		tmp = t_2;
	} else if (x <= 5.4e-214) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 2.7e-49) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (c * (a * j))
	t_2 = (j * ((a * c) - (y * i))) - (c * (z * b))
	tmp = 0
	if x <= -2.65e+53:
		tmp = t_1
	elif x <= 1.1e-236:
		tmp = t_2
	elif x <= 5.4e-214:
		tmp = b * ((t * i) - (z * c))
	elif x <= 2.7e-49:
		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(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(c * Float64(a * j)))
	t_2 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(c * Float64(z * b)))
	tmp = 0.0
	if (x <= -2.65e+53)
		tmp = t_1;
	elseif (x <= 1.1e-236)
		tmp = t_2;
	elseif (x <= 5.4e-214)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 2.7e-49)
		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 = (x * ((y * z) - (t * a))) + (c * (a * j));
	t_2 = (j * ((a * c) - (y * i))) - (c * (z * b));
	tmp = 0.0;
	if (x <= -2.65e+53)
		tmp = t_1;
	elseif (x <= 1.1e-236)
		tmp = t_2;
	elseif (x <= 5.4e-214)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 2.7e-49)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.65e+53], t$95$1, If[LessEqual[x, 1.1e-236], t$95$2, If[LessEqual[x, 5.4e-214], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-49], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6500000000000001e53 or 2.7e-49 < x

   1. Initial program 74.1%

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

      1. +-commutative 74.1%

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

      2. fma-def 74.8%

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

      3. *-commutative 74.8%

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

      4. *-commutative 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in b around 0 69.0%

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

   5. Taylor expanded in i around 0 68.2%

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

   if -2.6500000000000001e53 < x < 1.09999999999999996e-236 or 5.4000000000000001e-214 < x < 2.7e-49

   1. Initial program 69.4%

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

      1. +-commutative 69.4%

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

      2. fma-def 70.3%

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

      3. *-commutative 70.3%

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

      4. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in t around -inf 83.6%

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

   5. Taylor expanded in j around inf 63.0%

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

   if 1.09999999999999996e-236 < x < 5.4000000000000001e-214

   1. Initial program 82.1%

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

      1. associate-+l- 82.1%

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

      2. *-commutative 82.1%

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

      3. sub-neg 82.1%

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

      4. sub-neg 82.1%

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

      5. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in b around inf 90.9%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 12: 29.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;j \leq -9.2 \cdot 10^{+85}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-309}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+248} \lor \neg \left(j \leq 6.1 \cdot 10^{+305}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= j -9.2e+85)
     (* (* y j) (- i))
     (if (<= j -9e-309)
       t_1
       (if (<= j 4.7e-204)
         (* y (* x z))
         (if (<= j 4.4e-80)
           (* i (* t b))
           (if (<= j 7.8e-26)
             (* x (* y z))
             (if (<= j 1.2e+67)
               t_1
               (if (or (<= j 4.5e+248) (not (<= j 6.1e+305)))
                 (* a (* c j))
                 (* y (* i (- j))))))))))))

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 * (x * -t);
	double tmp;
	if (j <= -9.2e+85) {
		tmp = (y * j) * -i;
	} else if (j <= -9e-309) {
		tmp = t_1;
	} else if (j <= 4.7e-204) {
		tmp = y * (x * z);
	} else if (j <= 4.4e-80) {
		tmp = i * (t * b);
	} else if (j <= 7.8e-26) {
		tmp = x * (y * z);
	} else if (j <= 1.2e+67) {
		tmp = t_1;
	} else if ((j <= 4.5e+248) || !(j <= 6.1e+305)) {
		tmp = a * (c * j);
	} else {
		tmp = y * (i * -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) :: t_1
    real(8) :: tmp
    t_1 = a * (x * -t)
    if (j <= (-9.2d+85)) then
        tmp = (y * j) * -i
    else if (j <= (-9d-309)) then
        tmp = t_1
    else if (j <= 4.7d-204) then
        tmp = y * (x * z)
    else if (j <= 4.4d-80) then
        tmp = i * (t * b)
    else if (j <= 7.8d-26) then
        tmp = x * (y * z)
    else if (j <= 1.2d+67) then
        tmp = t_1
    else if ((j <= 4.5d+248) .or. (.not. (j <= 6.1d+305))) then
        tmp = a * (c * j)
    else
        tmp = y * (i * -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 t_1 = a * (x * -t);
	double tmp;
	if (j <= -9.2e+85) {
		tmp = (y * j) * -i;
	} else if (j <= -9e-309) {
		tmp = t_1;
	} else if (j <= 4.7e-204) {
		tmp = y * (x * z);
	} else if (j <= 4.4e-80) {
		tmp = i * (t * b);
	} else if (j <= 7.8e-26) {
		tmp = x * (y * z);
	} else if (j <= 1.2e+67) {
		tmp = t_1;
	} else if ((j <= 4.5e+248) || !(j <= 6.1e+305)) {
		tmp = a * (c * j);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if j <= -9.2e+85:
		tmp = (y * j) * -i
	elif j <= -9e-309:
		tmp = t_1
	elif j <= 4.7e-204:
		tmp = y * (x * z)
	elif j <= 4.4e-80:
		tmp = i * (t * b)
	elif j <= 7.8e-26:
		tmp = x * (y * z)
	elif j <= 1.2e+67:
		tmp = t_1
	elif (j <= 4.5e+248) or not (j <= 6.1e+305):
		tmp = a * (c * j)
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (j <= -9.2e+85)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (j <= -9e-309)
		tmp = t_1;
	elseif (j <= 4.7e-204)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 4.4e-80)
		tmp = Float64(i * Float64(t * b));
	elseif (j <= 7.8e-26)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 1.2e+67)
		tmp = t_1;
	elseif ((j <= 4.5e+248) || !(j <= 6.1e+305))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * -t);
	tmp = 0.0;
	if (j <= -9.2e+85)
		tmp = (y * j) * -i;
	elseif (j <= -9e-309)
		tmp = t_1;
	elseif (j <= 4.7e-204)
		tmp = y * (x * z);
	elseif (j <= 4.4e-80)
		tmp = i * (t * b);
	elseif (j <= 7.8e-26)
		tmp = x * (y * z);
	elseif (j <= 1.2e+67)
		tmp = t_1;
	elseif ((j <= 4.5e+248) || ~((j <= 6.1e+305)))
		tmp = a * (c * j);
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.2e+85], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[j, -9e-309], t$95$1, If[LessEqual[j, 4.7e-204], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-80], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.8e-26], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.2e+67], t$95$1, If[Or[LessEqual[j, 4.5e+248], N[Not[LessEqual[j, 6.1e+305]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -9.1999999999999996e85

   1. Initial program 76.9%

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

      1. +-commutative 76.9%

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

      2. fma-def 79.5%

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

      3. *-commutative 79.5%

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

      4. *-commutative 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in i around 0 79.8%

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

   5. Taylor expanded in i around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. *-commutative 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

   7. Simplified 47.3%

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

   if -9.1999999999999996e85 < j < -9.0000000000000021e-309 or 7.79999999999999973e-26 < j < 1.20000000000000001e67

   1. Initial program 75.3%

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

      1. associate-+l- 75.3%

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

      2. *-commutative 75.3%

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

      3. sub-neg 75.3%

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

      4. sub-neg 75.3%

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

      5. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in a around inf 42.9%

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

      1. +-commutative 42.9%

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

      2. mul-1-neg 42.9%

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

      3. unsub-neg 42.9%

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

   6. Simplified 42.9%

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

   7. Taylor expanded in c around 0 38.1%

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

      1. *-commutative 38.1%

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

      2. associate-*r* 38.1%

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

      3. neg-mul-1 38.1%

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

   9. Simplified 38.1%

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

   if -9.0000000000000021e-309 < j < 4.69999999999999992e-204

   1. Initial program 69.4%

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

      1. associate-+l- 69.4%

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

      2. *-commutative 69.4%

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

      3. sub-neg 69.4%

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

      4. sub-neg 69.4%

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

      5. *-commutative 69.4%

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

   3. Simplified 69.4%

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

   4. Taylor expanded in y around -inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. *-commutative 75.6%

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

      3. distribute-rgt-neg-in 75.6%

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

      4. mul-1-neg 75.6%

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

      5. unsub-neg 75.6%

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

   6. Simplified 75.6%

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

   7. Taylor expanded in i around 0 75.6%

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

      1. neg-mul-1 75.6%

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

      2. distribute-rgt-neg-in 75.6%

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

   9. Simplified 75.6%

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

   if 4.69999999999999992e-204 < j < 4.4000000000000002e-80

   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. associate-+l- 63.5%

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

      2. *-commutative 63.5%

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

      3. sub-neg 63.5%

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

      4. sub-neg 63.5%

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

      5. *-commutative 63.5%

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

   3. Simplified 63.5%

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

   4. Taylor expanded in i around inf 46.1%

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

      1. distribute-lft-out-- 46.1%

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

   6. Simplified 46.1%

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

   7. Taylor expanded in y around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. distribute-rgt-neg-in 39.4%

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

   9. Simplified 39.4%

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

   if 4.4000000000000002e-80 < j < 7.79999999999999973e-26

   1. Initial program 80.6%

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

      1. associate-+l- 80.6%

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

      2. *-commutative 80.6%

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

      3. sub-neg 80.6%

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

      4. sub-neg 80.6%

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

      5. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in a around 0 74.0%

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

      1. mul-1-neg 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in x around inf 55.4%

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

   8. Taylor expanded in y around inf 54.8%

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

      1. *-commutative 54.8%

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

   10. Simplified 54.8%

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

   if 1.20000000000000001e67 < j < 4.4999999999999996e248 or 6.1000000000000002e305 < j

   1. Initial program 64.6%

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

      1. associate-+l- 64.6%

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

      2. *-commutative 64.6%

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

      3. sub-neg 64.6%

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

      4. sub-neg 64.6%

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

      5. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in a around inf 61.5%

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

      1. +-commutative 61.5%

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

      2. mul-1-neg 61.5%

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

      3. unsub-neg 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in c around inf 49.1%

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

      1. *-commutative 49.1%

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

   9. Simplified 49.1%

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

   if 4.4999999999999996e248 < j < 6.1000000000000002e305

   1. Initial program 73.2%

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

      1. associate-+l- 73.2%

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

      2. *-commutative 73.2%

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

      3. sub-neg 73.2%

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

      4. sub-neg 73.2%

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

      5. *-commutative 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in y around -inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. *-commutative 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

      4. mul-1-neg 73.5%

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

      5. unsub-neg 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in i around inf 65.4%

      \[\leadsto \color{blue}{\left(i \cdot j\right)} \cdot \left(-y\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+85}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-309}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+248} \lor \neg \left(j \leq 6.1 \cdot 10^{+305}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 13: 51.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -0.0086:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -0.0086)
     t_3
     (if (<= t -3.5e-122)
       (* i (- (* t b) (* y j)))
       (if (<= t 1.7e-300)
         t_1
         (if (<= t 9.8e-240)
           t_2
           (if (<= t 1.95e-113) t_1 (if (<= t 8e+39) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -0.0086) {
		tmp = t_3;
	} else if (t <= -3.5e-122) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= 1.7e-300) {
		tmp = t_1;
	} else if (t <= 9.8e-240) {
		tmp = t_2;
	} else if (t <= 1.95e-113) {
		tmp = t_1;
	} else if (t <= 8e+39) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    t_2 = y * ((x * z) - (i * j))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-0.0086d0)) then
        tmp = t_3
    else if (t <= (-3.5d-122)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= 1.7d-300) then
        tmp = t_1
    else if (t <= 9.8d-240) then
        tmp = t_2
    else if (t <= 1.95d-113) then
        tmp = t_1
    else if (t <= 8d+39) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -0.0086) {
		tmp = t_3;
	} else if (t <= -3.5e-122) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= 1.7e-300) {
		tmp = t_1;
	} else if (t <= 9.8e-240) {
		tmp = t_2;
	} else if (t <= 1.95e-113) {
		tmp = t_1;
	} else if (t <= 8e+39) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = y * ((x * z) - (i * j))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -0.0086:
		tmp = t_3
	elif t <= -3.5e-122:
		tmp = i * ((t * b) - (y * j))
	elif t <= 1.7e-300:
		tmp = t_1
	elif t <= 9.8e-240:
		tmp = t_2
	elif t <= 1.95e-113:
		tmp = t_1
	elif t <= 8e+39:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -0.0086)
		tmp = t_3;
	elseif (t <= -3.5e-122)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= 1.7e-300)
		tmp = t_1;
	elseif (t <= 9.8e-240)
		tmp = t_2;
	elseif (t <= 1.95e-113)
		tmp = t_1;
	elseif (t <= 8e+39)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = y * ((x * z) - (i * j));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -0.0086)
		tmp = t_3;
	elseif (t <= -3.5e-122)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= 1.7e-300)
		tmp = t_1;
	elseif (t <= 9.8e-240)
		tmp = t_2;
	elseif (t <= 1.95e-113)
		tmp = t_1;
	elseif (t <= 8e+39)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.0086], t$95$3, If[LessEqual[t, -3.5e-122], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-300], t$95$1, If[LessEqual[t, 9.8e-240], t$95$2, If[LessEqual[t, 1.95e-113], t$95$1, If[LessEqual[t, 8e+39], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.0086 or 7.99999999999999952e39 < t

   1. Initial program 63.9%

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

      1. associate-+l- 63.9%

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

      2. *-commutative 63.9%

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

      3. sub-neg 63.9%

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

      4. sub-neg 63.9%

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

      5. *-commutative 63.9%

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

   3. Simplified 63.9%

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

   4. Taylor expanded in y around 0 65.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in t around inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. unsub-neg 64.1%

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

      3. *-commutative 64.1%

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

   9. Simplified 64.1%

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

   if -0.0086 < t < -3.5000000000000001e-122

   1. Initial program 70.0%

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

      1. associate-+l- 70.0%

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

      2. *-commutative 70.0%

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

      3. sub-neg 70.0%

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

      4. sub-neg 70.0%

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

      5. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in i around inf 51.4%

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

      1. distribute-lft-out-- 51.4%

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

   6. Simplified 51.4%

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

   if -3.5000000000000001e-122 < t < 1.70000000000000009e-300 or 9.80000000000000023e-240 < t < 1.9499999999999999e-113

   1. Initial program 80.5%

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

      1. associate-+l- 80.5%

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

      2. *-commutative 80.5%

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

      3. sub-neg 80.5%

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

      4. sub-neg 80.5%

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

      5. *-commutative 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in c around inf 68.0%

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

   if 1.70000000000000009e-300 < t < 9.80000000000000023e-240 or 1.9499999999999999e-113 < t < 7.99999999999999952e39

   1. Initial program 84.0%

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

      1. associate-+l- 84.0%

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

      2. *-commutative 84.0%

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

      3. sub-neg 84.0%

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

      4. sub-neg 84.0%

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

      5. *-commutative 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in y around -inf 73.7%

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

      1. mul-1-neg 73.7%

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

      2. *-commutative 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. mul-1-neg 73.7%

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

      5. unsub-neg 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0086:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-300}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 14: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -1.25 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+248} \lor \neg \left(j \leq 6.1 \cdot 10^{+305}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= j -1.25e+86)
     t_1
     (if (<= j 5.5e-305)
       (* a (* x (- t)))
       (if (<= j 8.7e-192)
         (* z (* x y))
         (if (<= j 2.8e-72)
           (* z (* b (- c)))
           (if (<= j 3.4e+67)
             (* x (* y z))
             (if (or (<= j 7e+248) (not (<= j 6.1e+305)))
               (* a (* c j))
               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 * (i * -j);
	double tmp;
	if (j <= -1.25e+86) {
		tmp = t_1;
	} else if (j <= 5.5e-305) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = z * (x * y);
	} else if (j <= 2.8e-72) {
		tmp = z * (b * -c);
	} else if (j <= 3.4e+67) {
		tmp = x * (y * z);
	} else if ((j <= 7e+248) || !(j <= 6.1e+305)) {
		tmp = a * (c * j);
	} 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 * (i * -j)
    if (j <= (-1.25d+86)) then
        tmp = t_1
    else if (j <= 5.5d-305) then
        tmp = a * (x * -t)
    else if (j <= 8.7d-192) then
        tmp = z * (x * y)
    else if (j <= 2.8d-72) then
        tmp = z * (b * -c)
    else if (j <= 3.4d+67) then
        tmp = x * (y * z)
    else if ((j <= 7d+248) .or. (.not. (j <= 6.1d+305))) then
        tmp = a * (c * j)
    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 * (i * -j);
	double tmp;
	if (j <= -1.25e+86) {
		tmp = t_1;
	} else if (j <= 5.5e-305) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = z * (x * y);
	} else if (j <= 2.8e-72) {
		tmp = z * (b * -c);
	} else if (j <= 3.4e+67) {
		tmp = x * (y * z);
	} else if ((j <= 7e+248) || !(j <= 6.1e+305)) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if j <= -1.25e+86:
		tmp = t_1
	elif j <= 5.5e-305:
		tmp = a * (x * -t)
	elif j <= 8.7e-192:
		tmp = z * (x * y)
	elif j <= 2.8e-72:
		tmp = z * (b * -c)
	elif j <= 3.4e+67:
		tmp = x * (y * z)
	elif (j <= 7e+248) or not (j <= 6.1e+305):
		tmp = a * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (j <= -1.25e+86)
		tmp = t_1;
	elseif (j <= 5.5e-305)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (j <= 8.7e-192)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 2.8e-72)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (j <= 3.4e+67)
		tmp = Float64(x * Float64(y * z));
	elseif ((j <= 7e+248) || !(j <= 6.1e+305))
		tmp = Float64(a * Float64(c * j));
	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 * (i * -j);
	tmp = 0.0;
	if (j <= -1.25e+86)
		tmp = t_1;
	elseif (j <= 5.5e-305)
		tmp = a * (x * -t);
	elseif (j <= 8.7e-192)
		tmp = z * (x * y);
	elseif (j <= 2.8e-72)
		tmp = z * (b * -c);
	elseif (j <= 3.4e+67)
		tmp = x * (y * z);
	elseif ((j <= 7e+248) || ~((j <= 6.1e+305)))
		tmp = a * (c * j);
	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[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.25e+86], t$95$1, If[LessEqual[j, 5.5e-305], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.7e-192], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e-72], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e+67], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 7e+248], N[Not[LessEqual[j, 6.1e+305]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.2499999999999999e86 or 7.00000000000000044e248 < j < 6.1000000000000002e305

   1. Initial program 76.1%

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

      1. associate-+l- 76.1%

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

      2. *-commutative 76.1%

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

      3. sub-neg 76.1%

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

      4. sub-neg 76.1%

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

      5. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in y around -inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. *-commutative 53.3%

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

      3. distribute-rgt-neg-in 53.3%

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

      4. mul-1-neg 53.3%

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

      5. unsub-neg 53.3%

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

   6. Simplified 53.3%

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

   7. Taylor expanded in i around inf 45.8%

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

   if -1.2499999999999999e86 < j < 5.5e-305

   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. associate-+l- 73.3%

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

      2. *-commutative 73.3%

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

      3. sub-neg 73.3%

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

      4. sub-neg 73.3%

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

      5. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in a around inf 44.0%

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

      1. +-commutative 44.0%

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

      2. mul-1-neg 44.0%

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

      3. unsub-neg 44.0%

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

   6. Simplified 44.0%

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

   7. Taylor expanded in c around 0 38.1%

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

      1. *-commutative 38.1%

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

      2. associate-*r* 38.1%

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

      3. neg-mul-1 38.1%

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

   9. Simplified 38.1%

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

   if 5.5e-305 < j < 8.7000000000000001e-192

   1. Initial program 69.3%

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

      1. associate-+l- 69.3%

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

      2. *-commutative 69.3%

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

      3. sub-neg 69.3%

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

      4. sub-neg 69.3%

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

      5. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in z around inf 74.3%

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

   5. Taylor expanded in y around inf 69.1%

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

   if 8.7000000000000001e-192 < j < 2.7999999999999998e-72

   1. Initial program 64.3%

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

      1. associate-+l- 64.3%

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

      2. *-commutative 64.3%

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

      3. sub-neg 64.3%

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

      4. sub-neg 64.3%

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

      5. *-commutative 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in z around inf 45.5%

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

   5. Taylor expanded in y around 0 38.1%

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

      1. mul-1-neg 38.1%

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

      2. distribute-lft-neg-out 38.1%

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

      3. *-commutative 38.1%

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

   7. Simplified 38.1%

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

   if 2.7999999999999998e-72 < j < 3.4000000000000002e67

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. *-commutative 82.2%

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

      3. sub-neg 82.2%

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

      4. sub-neg 82.2%

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

      5. *-commutative 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in a around 0 82.2%

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

      1. mul-1-neg 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in x around inf 47.4%

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

   8. Taylor expanded in y around inf 37.9%

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

      1. *-commutative 37.9%

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

   10. Simplified 37.9%

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

   if 3.4000000000000002e67 < j < 7.00000000000000044e248 or 6.1000000000000002e305 < j

   1. Initial program 64.6%

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

      1. associate-+l- 64.6%

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

      2. *-commutative 64.6%

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

      3. sub-neg 64.6%

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

      4. sub-neg 64.6%

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

      5. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in a around inf 61.5%

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

      1. +-commutative 61.5%

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

      2. mul-1-neg 61.5%

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

      3. unsub-neg 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in c around inf 49.1%

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

      1. *-commutative 49.1%

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

   9. Simplified 49.1%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+248} \lor \neg \left(j \leq 6.1 \cdot 10^{+305}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 15: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8.2 \cdot 10^{+85}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+248} \lor \neg \left(j \leq 8.2 \cdot 10^{+307}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -8.2e+85)
   (* (* y j) (- i))
   (if (<= j 1.8e-305)
     (* a (* x (- t)))
     (if (<= j 8.7e-192)
       (* z (* x y))
       (if (<= j 2.8e-79)
         (* z (* b (- c)))
         (if (<= j 9e+66)
           (* x (* y z))
           (if (or (<= j 1.05e+248) (not (<= j 8.2e+307)))
             (* a (* c j))
             (* y (* i (- 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 (j <= -8.2e+85) {
		tmp = (y * j) * -i;
	} else if (j <= 1.8e-305) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = z * (x * y);
	} else if (j <= 2.8e-79) {
		tmp = z * (b * -c);
	} else if (j <= 9e+66) {
		tmp = x * (y * z);
	} else if ((j <= 1.05e+248) || !(j <= 8.2e+307)) {
		tmp = a * (c * j);
	} else {
		tmp = y * (i * -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 (j <= (-8.2d+85)) then
        tmp = (y * j) * -i
    else if (j <= 1.8d-305) then
        tmp = a * (x * -t)
    else if (j <= 8.7d-192) then
        tmp = z * (x * y)
    else if (j <= 2.8d-79) then
        tmp = z * (b * -c)
    else if (j <= 9d+66) then
        tmp = x * (y * z)
    else if ((j <= 1.05d+248) .or. (.not. (j <= 8.2d+307))) then
        tmp = a * (c * j)
    else
        tmp = y * (i * -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 (j <= -8.2e+85) {
		tmp = (y * j) * -i;
	} else if (j <= 1.8e-305) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = z * (x * y);
	} else if (j <= 2.8e-79) {
		tmp = z * (b * -c);
	} else if (j <= 9e+66) {
		tmp = x * (y * z);
	} else if ((j <= 1.05e+248) || !(j <= 8.2e+307)) {
		tmp = a * (c * j);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -8.2e+85:
		tmp = (y * j) * -i
	elif j <= 1.8e-305:
		tmp = a * (x * -t)
	elif j <= 8.7e-192:
		tmp = z * (x * y)
	elif j <= 2.8e-79:
		tmp = z * (b * -c)
	elif j <= 9e+66:
		tmp = x * (y * z)
	elif (j <= 1.05e+248) or not (j <= 8.2e+307):
		tmp = a * (c * j)
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -8.2e+85)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (j <= 1.8e-305)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (j <= 8.7e-192)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 2.8e-79)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (j <= 9e+66)
		tmp = Float64(x * Float64(y * z));
	elseif ((j <= 1.05e+248) || !(j <= 8.2e+307))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -8.2e+85)
		tmp = (y * j) * -i;
	elseif (j <= 1.8e-305)
		tmp = a * (x * -t);
	elseif (j <= 8.7e-192)
		tmp = z * (x * y);
	elseif (j <= 2.8e-79)
		tmp = z * (b * -c);
	elseif (j <= 9e+66)
		tmp = x * (y * z);
	elseif ((j <= 1.05e+248) || ~((j <= 8.2e+307)))
		tmp = a * (c * j);
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -8.2e+85], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[j, 1.8e-305], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.7e-192], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e-79], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e+66], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 1.05e+248], N[Not[LessEqual[j, 8.2e+307]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -8.19999999999999957e85

   1. Initial program 76.9%

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

      1. +-commutative 76.9%

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

      2. fma-def 79.5%

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

      3. *-commutative 79.5%

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

      4. *-commutative 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in i around 0 79.8%

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

   5. Taylor expanded in i around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. *-commutative 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

   7. Simplified 47.3%

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

   if -8.19999999999999957e85 < j < 1.80000000000000002e-305

   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. associate-+l- 73.3%

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

      2. *-commutative 73.3%

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

      3. sub-neg 73.3%

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

      4. sub-neg 73.3%

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

      5. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in a around inf 44.0%

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

      1. +-commutative 44.0%

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

      2. mul-1-neg 44.0%

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

      3. unsub-neg 44.0%

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

   6. Simplified 44.0%

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

   7. Taylor expanded in c around 0 38.1%

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

      1. *-commutative 38.1%

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

      2. associate-*r* 38.1%

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

      3. neg-mul-1 38.1%

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

   9. Simplified 38.1%

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

   if 1.80000000000000002e-305 < j < 8.7000000000000001e-192

   1. Initial program 69.3%

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

      1. associate-+l- 69.3%

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

      2. *-commutative 69.3%

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

      3. sub-neg 69.3%

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

      4. sub-neg 69.3%

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

      5. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in z around inf 74.3%

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

   5. Taylor expanded in y around inf 69.1%

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

   if 8.7000000000000001e-192 < j < 2.80000000000000012e-79

   1. Initial program 64.3%

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

      1. associate-+l- 64.3%

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

      2. *-commutative 64.3%

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

      3. sub-neg 64.3%

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

      4. sub-neg 64.3%

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

      5. *-commutative 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in z around inf 45.5%

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

   5. Taylor expanded in y around 0 38.1%

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

      1. mul-1-neg 38.1%

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

      2. distribute-lft-neg-out 38.1%

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

      3. *-commutative 38.1%

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

   7. Simplified 38.1%

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

   if 2.80000000000000012e-79 < j < 8.9999999999999997e66

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. *-commutative 82.2%

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

      3. sub-neg 82.2%

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

      4. sub-neg 82.2%

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

      5. *-commutative 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in a around 0 82.2%

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

      1. mul-1-neg 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in x around inf 47.4%

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

   8. Taylor expanded in y around inf 37.9%

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

      1. *-commutative 37.9%

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

   10. Simplified 37.9%

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

   if 8.9999999999999997e66 < j < 1.04999999999999994e248 or 8.1999999999999996e307 < j

   1. Initial program 64.6%

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

      1. associate-+l- 64.6%

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

      2. *-commutative 64.6%

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

      3. sub-neg 64.6%

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

      4. sub-neg 64.6%

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

      5. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in a around inf 61.5%

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

      1. +-commutative 61.5%

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

      2. mul-1-neg 61.5%

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

      3. unsub-neg 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in c around inf 49.1%

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

      1. *-commutative 49.1%

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

   9. Simplified 49.1%

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

   if 1.04999999999999994e248 < j < 8.1999999999999996e307

   1. Initial program 73.2%

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

      1. associate-+l- 73.2%

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

      2. *-commutative 73.2%

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

      3. sub-neg 73.2%

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

      4. sub-neg 73.2%

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

      5. *-commutative 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in y around -inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. *-commutative 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

      4. mul-1-neg 73.5%

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

      5. unsub-neg 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in i around inf 65.4%

      \[\leadsto \color{blue}{\left(i \cdot j\right)} \cdot \left(-y\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.2 \cdot 10^{+85}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+248} \lor \neg \left(j \leq 8.2 \cdot 10^{+307}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 16: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;j \leq -6.8 \cdot 10^{+85}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+248} \lor \neg \left(j \leq 2.6 \cdot 10^{+306}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= j -6.8e+85)
     (* (* y j) (- i))
     (if (<= j 2.3e-304)
       (* a (* x (- t)))
       (if (<= j 8.7e-192)
         t_1
         (if (<= j 1.2e-72)
           (* z (* b (- c)))
           (if (<= j 5.5e+67)
             t_1
             (if (or (<= j 3.8e+248) (not (<= j 2.6e+306)))
               (* a (* c j))
               (* y (* i (- j)))))))))))

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);
	double tmp;
	if (j <= -6.8e+85) {
		tmp = (y * j) * -i;
	} else if (j <= 2.3e-304) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = t_1;
	} else if (j <= 1.2e-72) {
		tmp = z * (b * -c);
	} else if (j <= 5.5e+67) {
		tmp = t_1;
	} else if ((j <= 3.8e+248) || !(j <= 2.6e+306)) {
		tmp = a * (c * j);
	} else {
		tmp = y * (i * -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) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (j <= (-6.8d+85)) then
        tmp = (y * j) * -i
    else if (j <= 2.3d-304) then
        tmp = a * (x * -t)
    else if (j <= 8.7d-192) then
        tmp = t_1
    else if (j <= 1.2d-72) then
        tmp = z * (b * -c)
    else if (j <= 5.5d+67) then
        tmp = t_1
    else if ((j <= 3.8d+248) .or. (.not. (j <= 2.6d+306))) then
        tmp = a * (c * j)
    else
        tmp = y * (i * -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 t_1 = y * (x * z);
	double tmp;
	if (j <= -6.8e+85) {
		tmp = (y * j) * -i;
	} else if (j <= 2.3e-304) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = t_1;
	} else if (j <= 1.2e-72) {
		tmp = z * (b * -c);
	} else if (j <= 5.5e+67) {
		tmp = t_1;
	} else if ((j <= 3.8e+248) || !(j <= 2.6e+306)) {
		tmp = a * (c * j);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if j <= -6.8e+85:
		tmp = (y * j) * -i
	elif j <= 2.3e-304:
		tmp = a * (x * -t)
	elif j <= 8.7e-192:
		tmp = t_1
	elif j <= 1.2e-72:
		tmp = z * (b * -c)
	elif j <= 5.5e+67:
		tmp = t_1
	elif (j <= 3.8e+248) or not (j <= 2.6e+306):
		tmp = a * (c * j)
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (j <= -6.8e+85)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (j <= 2.3e-304)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (j <= 8.7e-192)
		tmp = t_1;
	elseif (j <= 1.2e-72)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (j <= 5.5e+67)
		tmp = t_1;
	elseif ((j <= 3.8e+248) || !(j <= 2.6e+306))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (j <= -6.8e+85)
		tmp = (y * j) * -i;
	elseif (j <= 2.3e-304)
		tmp = a * (x * -t);
	elseif (j <= 8.7e-192)
		tmp = t_1;
	elseif (j <= 1.2e-72)
		tmp = z * (b * -c);
	elseif (j <= 5.5e+67)
		tmp = t_1;
	elseif ((j <= 3.8e+248) || ~((j <= 2.6e+306)))
		tmp = a * (c * j);
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.8e+85], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[j, 2.3e-304], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.7e-192], t$95$1, If[LessEqual[j, 1.2e-72], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e+67], t$95$1, If[Or[LessEqual[j, 3.8e+248], N[Not[LessEqual[j, 2.6e+306]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -6.8000000000000007e85

   1. Initial program 76.9%

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

      1. +-commutative 76.9%

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

      2. fma-def 79.5%

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

      3. *-commutative 79.5%

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

      4. *-commutative 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in i around 0 79.8%

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

   5. Taylor expanded in i around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. *-commutative 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

   7. Simplified 47.3%

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

   if -6.8000000000000007e85 < j < 2.3e-304

   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. associate-+l- 73.3%

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

      2. *-commutative 73.3%

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

      3. sub-neg 73.3%

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

      4. sub-neg 73.3%

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

      5. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in a around inf 44.0%

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

      1. +-commutative 44.0%

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

      2. mul-1-neg 44.0%

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

      3. unsub-neg 44.0%

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

   6. Simplified 44.0%

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

   7. Taylor expanded in c around 0 38.1%

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

      1. *-commutative 38.1%

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

      2. associate-*r* 38.1%

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

      3. neg-mul-1 38.1%

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

   9. Simplified 38.1%

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

   if 2.3e-304 < j < 8.7000000000000001e-192 or 1.2e-72 < j < 5.49999999999999968e67

   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. associate-+l- 77.5%

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

      2. *-commutative 77.5%

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

      3. sub-neg 77.5%

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

      4. sub-neg 77.5%

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

      5. *-commutative 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in y around -inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. *-commutative 60.1%

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

      3. distribute-rgt-neg-in 60.1%

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

      4. mul-1-neg 60.1%

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

      5. unsub-neg 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in i around 0 49.4%

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

      1. neg-mul-1 49.4%

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

      2. distribute-rgt-neg-in 49.4%

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

   9. Simplified 49.4%

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

   if 8.7000000000000001e-192 < j < 1.2e-72

   1. Initial program 64.3%

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

      1. associate-+l- 64.3%

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

      2. *-commutative 64.3%

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

      3. sub-neg 64.3%

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

      4. sub-neg 64.3%

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

      5. *-commutative 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in z around inf 45.5%

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

   5. Taylor expanded in y around 0 38.1%

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

      1. mul-1-neg 38.1%

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

      2. distribute-lft-neg-out 38.1%

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

      3. *-commutative 38.1%

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

   7. Simplified 38.1%

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

   if 5.49999999999999968e67 < j < 3.8000000000000001e248 or 2.60000000000000008e306 < j

   1. Initial program 64.6%

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

      1. associate-+l- 64.6%

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

      2. *-commutative 64.6%

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

      3. sub-neg 64.6%

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

      4. sub-neg 64.6%

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

      5. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in a around inf 61.5%

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

      1. +-commutative 61.5%

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

      2. mul-1-neg 61.5%

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

      3. unsub-neg 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in c around inf 49.1%

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

      1. *-commutative 49.1%

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

   9. Simplified 49.1%

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

   if 3.8000000000000001e248 < j < 2.60000000000000008e306

   1. Initial program 73.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 73.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in y around -inf 73.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j + -1 \cdot \left(z \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 73.5%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j + -1 \cdot \left(z \cdot x\right)\right)} \]

      2. *-commutative 73.5%

         \[\leadsto -\color{blue}{\left(i \cdot j + -1 \cdot \left(z \cdot x\right)\right) \cdot y} \]

      3. distribute-rgt-neg-in 73.5%

         \[\leadsto \color{blue}{\left(i \cdot j + -1 \cdot \left(z \cdot x\right)\right) \cdot \left(-y\right)} \]

      4. mul-1-neg 73.5%

         \[\leadsto \left(i \cdot j + \color{blue}{\left(-z \cdot x\right)}\right) \cdot \left(-y\right) \]

      5. unsub-neg 73.5%

         \[\leadsto \color{blue}{\left(i \cdot j - z \cdot x\right)} \cdot \left(-y\right) \]

   6. Simplified 73.5%

      \[\leadsto \color{blue}{\left(i \cdot j - z \cdot x\right) \cdot \left(-y\right)} \]

   7. Taylor expanded in i around inf 65.4%

      \[\leadsto \color{blue}{\left(i \cdot j\right)} \cdot \left(-y\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.8 \cdot 10^{+85}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+248} \lor \neg \left(j \leq 2.6 \cdot 10^{+306}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 17: 42.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 85000000000000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= t -2.3e-33)
     t_2
     (if (<= t 3.6e-299)
       t_1
       (if (<= t 3.3e-239)
         (* x (* y z))
         (if (<= t 2.2e-105)
           t_1
           (if (<= t 85000000000000.0) (* z (* x y)) 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 = c * ((a * j) - (z * b));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (t <= -2.3e-33) {
		tmp = t_2;
	} else if (t <= 3.6e-299) {
		tmp = t_1;
	} else if (t <= 3.3e-239) {
		tmp = x * (y * z);
	} else if (t <= 2.2e-105) {
		tmp = t_1;
	} else if (t <= 85000000000000.0) {
		tmp = z * (x * y);
	} 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 = c * ((a * j) - (z * b))
    t_2 = a * ((c * j) - (x * t))
    if (t <= (-2.3d-33)) then
        tmp = t_2
    else if (t <= 3.6d-299) then
        tmp = t_1
    else if (t <= 3.3d-239) then
        tmp = x * (y * z)
    else if (t <= 2.2d-105) then
        tmp = t_1
    else if (t <= 85000000000000.0d0) then
        tmp = z * (x * y)
    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 = c * ((a * j) - (z * b));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (t <= -2.3e-33) {
		tmp = t_2;
	} else if (t <= 3.6e-299) {
		tmp = t_1;
	} else if (t <= 3.3e-239) {
		tmp = x * (y * z);
	} else if (t <= 2.2e-105) {
		tmp = t_1;
	} else if (t <= 85000000000000.0) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if t <= -2.3e-33:
		tmp = t_2
	elif t <= 3.6e-299:
		tmp = t_1
	elif t <= 3.3e-239:
		tmp = x * (y * z)
	elif t <= 2.2e-105:
		tmp = t_1
	elif t <= 85000000000000.0:
		tmp = z * (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (t <= -2.3e-33)
		tmp = t_2;
	elseif (t <= 3.6e-299)
		tmp = t_1;
	elseif (t <= 3.3e-239)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 2.2e-105)
		tmp = t_1;
	elseif (t <= 85000000000000.0)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (t <= -2.3e-33)
		tmp = t_2;
	elseif (t <= 3.6e-299)
		tmp = t_1;
	elseif (t <= 3.3e-239)
		tmp = x * (y * z);
	elseif (t <= 2.2e-105)
		tmp = t_1;
	elseif (t <= 85000000000000.0)
		tmp = z * (x * y);
	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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e-33], t$95$2, If[LessEqual[t, 3.6e-299], t$95$1, If[LessEqual[t, 3.3e-239], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-105], t$95$1, If[LessEqual[t, 85000000000000.0], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.29999999999999986e-33 or 8.5e13 < t

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 63.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 63.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 63.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 63.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 63.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 63.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 55.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 55.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 55.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -2.29999999999999986e-33 < t < 3.6e-299 or 3.29999999999999995e-239 < t < 2.20000000000000004e-105

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 79.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 79.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 79.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 79.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 57.2%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if 3.6e-299 < t < 3.29999999999999995e-239

   1. Initial program 99.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 99.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 99.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 99.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 99.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 71.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   6. Simplified 71.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   7. Taylor expanded in x around inf 55.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   8. Taylor expanded in y around inf 55.4%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 55.4%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   10. Simplified 55.4%

       \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   if 2.20000000000000004e-105 < t < 8.5e13

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 79.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 79.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 79.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 79.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 79.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 47.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 46.8%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 85000000000000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 18: 52.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -3e-32)
     t_3
     (if (<= z -2.2e-243)
       t_2
       (if (<= z 1.12e-248)
         t_1
         (if (<= z 2.05e-156) t_2 (if (<= z 1.35e-9) 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 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3e-32) {
		tmp = t_3;
	} else if (z <= -2.2e-243) {
		tmp = t_2;
	} else if (z <= 1.12e-248) {
		tmp = t_1;
	} else if (z <= 2.05e-156) {
		tmp = t_2;
	} else if (z <= 1.35e-9) {
		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 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-3d-32)) then
        tmp = t_3
    else if (z <= (-2.2d-243)) then
        tmp = t_2
    else if (z <= 1.12d-248) then
        tmp = t_1
    else if (z <= 2.05d-156) then
        tmp = t_2
    else if (z <= 1.35d-9) 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 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3e-32) {
		tmp = t_3;
	} else if (z <= -2.2e-243) {
		tmp = t_2;
	} else if (z <= 1.12e-248) {
		tmp = t_1;
	} else if (z <= 2.05e-156) {
		tmp = t_2;
	} else if (z <= 1.35e-9) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -3e-32:
		tmp = t_3
	elif z <= -2.2e-243:
		tmp = t_2
	elif z <= 1.12e-248:
		tmp = t_1
	elif z <= 2.05e-156:
		tmp = t_2
	elif z <= 1.35e-9:
		tmp = t_1
	else:
		tmp = t_3
	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)))
	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 <= -3e-32)
		tmp = t_3;
	elseif (z <= -2.2e-243)
		tmp = t_2;
	elseif (z <= 1.12e-248)
		tmp = t_1;
	elseif (z <= 2.05e-156)
		tmp = t_2;
	elseif (z <= 1.35e-9)
		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 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -3e-32)
		tmp = t_3;
	elseif (z <= -2.2e-243)
		tmp = t_2;
	elseif (z <= 1.12e-248)
		tmp = t_1;
	elseif (z <= 2.05e-156)
		tmp = t_2;
	elseif (z <= 1.35e-9)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $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, -3e-32], t$95$3, If[LessEqual[z, -2.2e-243], t$95$2, If[LessEqual[z, 1.12e-248], t$95$1, If[LessEqual[z, 2.05e-156], t$95$2, If[LessEqual[z, 1.35e-9], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e-32 or 1.3500000000000001e-9 < z

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 66.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 66.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 66.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 66.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 66.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 66.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 64.2%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -3e-32 < z < -2.1999999999999999e-243 or 1.12e-248 < z < 2.0500000000000001e-156

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 75.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 75.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 75.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 75.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 75.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in y around 0 82.6%

      \[\leadsto \color{blue}{\left(\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   6. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, c \cdot j - t \cdot x, y \cdot \mathsf{fma}\left(z, x, j \cdot \left(-i\right)\right)\right) + b \cdot \mathsf{fma}\left(i, t, c \cdot \left(-z\right)\right)} \]

   7. Taylor expanded in t around inf 57.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 57.7%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      2. unsub-neg 57.7%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

      3. *-commutative 57.7%

         \[\leadsto t \cdot \left(i \cdot b - \color{blue}{x \cdot a}\right) \]

   9. Simplified 57.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - x \cdot a\right)} \]

   if -2.1999999999999999e-243 < z < 1.12e-248 or 2.0500000000000001e-156 < z < 1.3500000000000001e-9

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 80.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 80.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 80.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in i around 0 70.2%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - c \cdot \left(b \cdot z\right)}\right) \]

   5. Taylor expanded in j around inf 61.9%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-32}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-243}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-248}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-156}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 19: 48.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -3.3e-122)
     t_2
     (if (<= t 3.6e-299)
       t_1
       (if (<= t 1.05e-240) (* x (* y z)) (if (<= t 1.2e-107) 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 = c * ((a * j) - (z * b));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -3.3e-122) {
		tmp = t_2;
	} else if (t <= 3.6e-299) {
		tmp = t_1;
	} else if (t <= 1.05e-240) {
		tmp = x * (y * z);
	} else if (t <= 1.2e-107) {
		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 = c * ((a * j) - (z * b))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-3.3d-122)) then
        tmp = t_2
    else if (t <= 3.6d-299) then
        tmp = t_1
    else if (t <= 1.05d-240) then
        tmp = x * (y * z)
    else if (t <= 1.2d-107) 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 = c * ((a * j) - (z * b));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -3.3e-122) {
		tmp = t_2;
	} else if (t <= 3.6e-299) {
		tmp = t_1;
	} else if (t <= 1.05e-240) {
		tmp = x * (y * z);
	} else if (t <= 1.2e-107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -3.3e-122:
		tmp = t_2
	elif t <= 3.6e-299:
		tmp = t_1
	elif t <= 1.05e-240:
		tmp = x * (y * z)
	elif t <= 1.2e-107:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.3e-122)
		tmp = t_2;
	elseif (t <= 3.6e-299)
		tmp = t_1;
	elseif (t <= 1.05e-240)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 1.2e-107)
		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 = c * ((a * j) - (z * b));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -3.3e-122)
		tmp = t_2;
	elseif (t <= 3.6e-299)
		tmp = t_1;
	elseif (t <= 1.05e-240)
		tmp = x * (y * z);
	elseif (t <= 1.2e-107)
		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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-122], t$95$2, If[LessEqual[t, 3.6e-299], t$95$1, If[LessEqual[t, 1.05e-240], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-107], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.29999999999999999e-122 or 1.19999999999999997e-107 < t

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 67.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 67.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 67.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 67.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 67.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in y around 0 69.4%

      \[\leadsto \color{blue}{\left(\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   6. Simplified 72.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, c \cdot j - t \cdot x, y \cdot \mathsf{fma}\left(z, x, j \cdot \left(-i\right)\right)\right) + b \cdot \mathsf{fma}\left(i, t, c \cdot \left(-z\right)\right)} \]

   7. Taylor expanded in t around inf 54.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 54.2%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      2. unsub-neg 54.2%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

      3. *-commutative 54.2%

         \[\leadsto t \cdot \left(i \cdot b - \color{blue}{x \cdot a}\right) \]

   9. Simplified 54.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - x \cdot a\right)} \]

   if -3.29999999999999999e-122 < t < 3.6e-299 or 1.04999999999999997e-240 < t < 1.19999999999999997e-107

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 80.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 80.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 80.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 80.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 80.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 68.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if 3.6e-299 < t < 1.04999999999999997e-240

   1. Initial program 99.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 99.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 99.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 99.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 99.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 71.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   6. Simplified 71.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   7. Taylor expanded in x around inf 55.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   8. Taylor expanded in y around inf 55.4%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 55.4%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   10. Simplified 55.4%

       \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-107}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 20: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{-204}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))) (t_2 (* a (* c j))))
   (if (<= j -9.5e+85)
     t_2
     (if (<= j 1.75e-304)
       t_1
       (if (<= j 3.15e-204)
         (* z (* x y))
         (if (<= j 4.2e-74) t_1 (if (<= j 9.5e+66) (* x (* y z)) 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 * (x * -t);
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -9.5e+85) {
		tmp = t_2;
	} else if (j <= 1.75e-304) {
		tmp = t_1;
	} else if (j <= 3.15e-204) {
		tmp = z * (x * y);
	} else if (j <= 4.2e-74) {
		tmp = t_1;
	} else if (j <= 9.5e+66) {
		tmp = x * (y * z);
	} 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 * (x * -t)
    t_2 = a * (c * j)
    if (j <= (-9.5d+85)) then
        tmp = t_2
    else if (j <= 1.75d-304) then
        tmp = t_1
    else if (j <= 3.15d-204) then
        tmp = z * (x * y)
    else if (j <= 4.2d-74) then
        tmp = t_1
    else if (j <= 9.5d+66) then
        tmp = x * (y * z)
    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 * (x * -t);
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -9.5e+85) {
		tmp = t_2;
	} else if (j <= 1.75e-304) {
		tmp = t_1;
	} else if (j <= 3.15e-204) {
		tmp = z * (x * y);
	} else if (j <= 4.2e-74) {
		tmp = t_1;
	} else if (j <= 9.5e+66) {
		tmp = x * (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	t_2 = a * (c * j)
	tmp = 0
	if j <= -9.5e+85:
		tmp = t_2
	elif j <= 1.75e-304:
		tmp = t_1
	elif j <= 3.15e-204:
		tmp = z * (x * y)
	elif j <= 4.2e-74:
		tmp = t_1
	elif j <= 9.5e+66:
		tmp = x * (y * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -9.5e+85)
		tmp = t_2;
	elseif (j <= 1.75e-304)
		tmp = t_1;
	elseif (j <= 3.15e-204)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 4.2e-74)
		tmp = t_1;
	elseif (j <= 9.5e+66)
		tmp = Float64(x * Float64(y * z));
	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 * (x * -t);
	t_2 = a * (c * j);
	tmp = 0.0;
	if (j <= -9.5e+85)
		tmp = t_2;
	elseif (j <= 1.75e-304)
		tmp = t_1;
	elseif (j <= 3.15e-204)
		tmp = z * (x * y);
	elseif (j <= 4.2e-74)
		tmp = t_1;
	elseif (j <= 9.5e+66)
		tmp = x * (y * z);
	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[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.5e+85], t$95$2, If[LessEqual[j, 1.75e-304], t$95$1, If[LessEqual[j, 3.15e-204], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.2e-74], t$95$1, If[LessEqual[j, 9.5e+66], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.49999999999999945e85 or 9.50000000000000051e66 < j

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 48.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 48.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 39.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.2%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 39.2%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -9.49999999999999945e85 < j < 1.75e-304 or 3.14999999999999996e-204 < j < 4.2e-74

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 41.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 41.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 41.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 35.9%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.9%

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(x \cdot t\right)}\right) \]

      2. associate-*r* 35.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot x\right) \cdot t\right)} \]

      3. neg-mul-1 35.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(-x\right)} \cdot t\right) \]

   9. Simplified 35.9%

      \[\leadsto a \cdot \color{blue}{\left(\left(-x\right) \cdot t\right)} \]

   if 1.75e-304 < j < 3.14999999999999996e-204

   1. Initial program 69.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 81.7%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 75.5%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if 4.2e-74 < j < 9.50000000000000051e66

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 82.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 82.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   6. Simplified 82.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   7. Taylor expanded in x around inf 47.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   8. Taylor expanded in y around inf 37.9%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 37.9%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   10. Simplified 37.9%

       \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+85}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{-204}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 21: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -6.8 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{-107}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -6.8e+85)
     t_1
     (if (<= j 1.5e-308)
       (* a (* x (- t)))
       (if (<= j 8.7e-192)
         (* z (* x y))
         (if (<= j 9.6e-107)
           (* c (- (* z b)))
           (if (<= j 4.5e+67) (* x (* y z)) 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);
	double tmp;
	if (j <= -6.8e+85) {
		tmp = t_1;
	} else if (j <= 1.5e-308) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = z * (x * y);
	} else if (j <= 9.6e-107) {
		tmp = c * -(z * b);
	} else if (j <= 4.5e+67) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (j <= (-6.8d+85)) then
        tmp = t_1
    else if (j <= 1.5d-308) then
        tmp = a * (x * -t)
    else if (j <= 8.7d-192) then
        tmp = z * (x * y)
    else if (j <= 9.6d-107) then
        tmp = c * -(z * b)
    else if (j <= 4.5d+67) then
        tmp = x * (y * z)
    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);
	double tmp;
	if (j <= -6.8e+85) {
		tmp = t_1;
	} else if (j <= 1.5e-308) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = z * (x * y);
	} else if (j <= 9.6e-107) {
		tmp = c * -(z * b);
	} else if (j <= 4.5e+67) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -6.8e+85:
		tmp = t_1
	elif j <= 1.5e-308:
		tmp = a * (x * -t)
	elif j <= 8.7e-192:
		tmp = z * (x * y)
	elif j <= 9.6e-107:
		tmp = c * -(z * b)
	elif j <= 4.5e+67:
		tmp = x * (y * z)
	else:
		tmp = t_1
	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 (j <= -6.8e+85)
		tmp = t_1;
	elseif (j <= 1.5e-308)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (j <= 8.7e-192)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 9.6e-107)
		tmp = Float64(c * Float64(-Float64(z * b)));
	elseif (j <= 4.5e+67)
		tmp = Float64(x * Float64(y * z));
	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);
	tmp = 0.0;
	if (j <= -6.8e+85)
		tmp = t_1;
	elseif (j <= 1.5e-308)
		tmp = a * (x * -t);
	elseif (j <= 8.7e-192)
		tmp = z * (x * y);
	elseif (j <= 9.6e-107)
		tmp = c * -(z * b);
	elseif (j <= 4.5e+67)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.8e+85], t$95$1, If[LessEqual[j, 1.5e-308], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.7e-192], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.6e-107], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], If[LessEqual[j, 4.5e+67], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -6.8000000000000007e85 or 4.4999999999999998e67 < j

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 48.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 48.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 39.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.2%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 39.2%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -6.8000000000000007e85 < j < 1.4999999999999999e-308

   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. associate-+l- 73.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 44.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 44.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 44.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 44.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 38.1%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(x \cdot t\right)}\right) \]

      2. associate-*r* 38.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot x\right) \cdot t\right)} \]

      3. neg-mul-1 38.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-x\right)} \cdot t\right) \]

   9. Simplified 38.1%

      \[\leadsto a \cdot \color{blue}{\left(\left(-x\right) \cdot t\right)} \]

   if 1.4999999999999999e-308 < j < 8.7000000000000001e-192

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 74.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 69.1%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if 8.7000000000000001e-192 < j < 9.59999999999999977e-107

   1. Initial program 56.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 56.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 56.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 56.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 56.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 56.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 56.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 51.1%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around 0 41.3%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.3%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. *-commutative 41.3%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

      3. *-commutative 41.3%

         \[\leadsto -\color{blue}{\left(b \cdot z\right) \cdot c} \]

      4. distribute-rgt-neg-in 41.3%

         \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \left(-c\right)} \]

   7. Simplified 41.3%

      \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \left(-c\right)} \]

   if 9.59999999999999977e-107 < j < 4.4999999999999998e67

   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. associate-+l- 82.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 82.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 82.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 82.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 82.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 78.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 78.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   6. Simplified 78.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   7. Taylor expanded in x around inf 44.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   8. Taylor expanded in y around inf 34.0%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   10. Simplified 34.0%

       \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.8 \cdot 10^{+85}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{-107}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 22: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -1e+86)
     t_1
     (if (<= j 2.5e-305)
       (* a (* x (- t)))
       (if (<= j 8.7e-192)
         (* z (* x y))
         (if (<= j 9.2e-79)
           (* z (* b (- c)))
           (if (<= j 1.2e+67) (* x (* y z)) 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);
	double tmp;
	if (j <= -1e+86) {
		tmp = t_1;
	} else if (j <= 2.5e-305) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = z * (x * y);
	} else if (j <= 9.2e-79) {
		tmp = z * (b * -c);
	} else if (j <= 1.2e+67) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (j <= (-1d+86)) then
        tmp = t_1
    else if (j <= 2.5d-305) then
        tmp = a * (x * -t)
    else if (j <= 8.7d-192) then
        tmp = z * (x * y)
    else if (j <= 9.2d-79) then
        tmp = z * (b * -c)
    else if (j <= 1.2d+67) then
        tmp = x * (y * z)
    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);
	double tmp;
	if (j <= -1e+86) {
		tmp = t_1;
	} else if (j <= 2.5e-305) {
		tmp = a * (x * -t);
	} else if (j <= 8.7e-192) {
		tmp = z * (x * y);
	} else if (j <= 9.2e-79) {
		tmp = z * (b * -c);
	} else if (j <= 1.2e+67) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -1e+86:
		tmp = t_1
	elif j <= 2.5e-305:
		tmp = a * (x * -t)
	elif j <= 8.7e-192:
		tmp = z * (x * y)
	elif j <= 9.2e-79:
		tmp = z * (b * -c)
	elif j <= 1.2e+67:
		tmp = x * (y * z)
	else:
		tmp = t_1
	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 (j <= -1e+86)
		tmp = t_1;
	elseif (j <= 2.5e-305)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (j <= 8.7e-192)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 9.2e-79)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (j <= 1.2e+67)
		tmp = Float64(x * Float64(y * z));
	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);
	tmp = 0.0;
	if (j <= -1e+86)
		tmp = t_1;
	elseif (j <= 2.5e-305)
		tmp = a * (x * -t);
	elseif (j <= 8.7e-192)
		tmp = z * (x * y);
	elseif (j <= 9.2e-79)
		tmp = z * (b * -c);
	elseif (j <= 1.2e+67)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1e+86], t$95$1, If[LessEqual[j, 2.5e-305], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.7e-192], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.2e-79], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.2e+67], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1e86 or 1.20000000000000001e67 < j

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 48.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 48.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 39.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.2%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 39.2%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -1e86 < j < 2.49999999999999993e-305

   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. associate-+l- 73.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 44.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 44.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 44.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 44.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 38.1%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(x \cdot t\right)}\right) \]

      2. associate-*r* 38.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot x\right) \cdot t\right)} \]

      3. neg-mul-1 38.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-x\right)} \cdot t\right) \]

   9. Simplified 38.1%

      \[\leadsto a \cdot \color{blue}{\left(\left(-x\right) \cdot t\right)} \]

   if 2.49999999999999993e-305 < j < 8.7000000000000001e-192

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 74.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 69.1%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if 8.7000000000000001e-192 < j < 9.20000000000000047e-79

   1. Initial program 64.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 64.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 64.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 64.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 64.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 64.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 45.5%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around 0 38.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg 38.1%

         \[\leadsto \color{blue}{\left(-c \cdot b\right)} \cdot z \]

      2. distribute-lft-neg-out 38.1%

         \[\leadsto \color{blue}{\left(\left(-c\right) \cdot b\right)} \cdot z \]

      3. *-commutative 38.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(-c\right)\right)} \cdot z \]

   7. Simplified 38.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(-c\right)\right)} \cdot z \]

   if 9.20000000000000047e-79 < j < 1.20000000000000001e67

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 82.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 82.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 82.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   6. Simplified 82.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   7. Taylor expanded in x around inf 47.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   8. Taylor expanded in y around inf 37.9%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 37.9%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   10. Simplified 37.9%

       \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 23: 40.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i 2.2e+125) (* a (- (* c j) (* x t))) (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= 2.2e+125) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= 2.2d+125) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= 2.2e+125) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= 2.2e+125:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= 2.2e+125)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= 2.2e+125)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, 2.2e+125], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 2.19999999999999991e125

   1. Initial program 73.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 73.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 45.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 45.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if 2.19999999999999991e125 < i

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 67.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 67.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 67.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 67.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 67.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 73.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 73.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Simplified 73.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   7. Taylor expanded in y around 0 47.3%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(t \cdot b\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 47.3%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-t \cdot b\right)}\right) \]

      2. distribute-rgt-neg-in 47.3%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(t \cdot \left(-b\right)\right)}\right) \]

   9. Simplified 47.3%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(t \cdot \left(-b\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 24: 29.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-33} \lor \neg \left(z \leq 8 \cdot 10^{-38}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -2e-33) (not (<= z 8e-38))) (* z (* x y)) (* c (* a 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 ((z <= -2e-33) || !(z <= 8e-38)) {
		tmp = z * (x * y);
	} else {
		tmp = c * (a * 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 ((z <= (-2d-33)) .or. (.not. (z <= 8d-38))) then
        tmp = z * (x * y)
    else
        tmp = c * (a * 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 ((z <= -2e-33) || !(z <= 8e-38)) {
		tmp = z * (x * y);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -2e-33) or not (z <= 8e-38):
		tmp = z * (x * y)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -2e-33) || !(z <= 8e-38))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -2e-33) || ~((z <= 8e-38)))
		tmp = z * (x * y);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -2e-33], N[Not[LessEqual[z, 8e-38]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-33 or 7.9999999999999997e-38 < z

   1. Initial program 66.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 66.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 66.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 66.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 66.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 66.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 66.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 62.5%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 42.1%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -2.0000000000000001e-33 < z < 7.9999999999999997e-38

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in b around 0 64.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around inf 27.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-33} \lor \neg \left(z \leq 8 \cdot 10^{-38}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 25: 29.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -6.5e-34)
   (* x (* y z))
   (if (<= z 2.3e-44) (* c (* a j)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6.5e-34) {
		tmp = x * (y * z);
	} else if (z <= 2.3e-44) {
		tmp = c * (a * j);
	} else {
		tmp = z * (x * y);
	}
	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 (z <= (-6.5d-34)) then
        tmp = x * (y * z)
    else if (z <= 2.3d-44) then
        tmp = c * (a * j)
    else
        tmp = z * (x * y)
    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 (z <= -6.5e-34) {
		tmp = x * (y * z);
	} else if (z <= 2.3e-44) {
		tmp = c * (a * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -6.5e-34:
		tmp = x * (y * z)
	elif z <= 2.3e-44:
		tmp = c * (a * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -6.5e-34)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 2.3e-44)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -6.5e-34)
		tmp = x * (y * z);
	elseif (z <= 2.3e-44)
		tmp = c * (a * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -6.5e-34], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-44], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.49999999999999985e-34

   1. Initial program 57.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 57.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 57.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 57.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 57.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 57.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 57.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 60.6%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 60.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   6. Simplified 60.6%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)}\right) \]

   7. Taylor expanded in x around inf 50.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   8. Taylor expanded in y around inf 38.5%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 38.5%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   10. Simplified 38.5%

       \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   if -6.49999999999999985e-34 < z < 2.29999999999999998e-44

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in b around 0 64.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + \left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around inf 27.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 2.29999999999999998e-44 < z

   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. associate-+l- 76.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 66.8%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 48.1%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 26: 21.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. associate-+l- 72.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   2. *-commutative 72.4%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   3. sub-neg 72.4%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

   4. sub-neg 72.4%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

   5. *-commutative 72.4%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

3. Simplified 72.4%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

4. Taylor expanded in a around inf 41.3%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 41.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 41.3%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 41.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

6. Simplified 41.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

7. Taylor expanded in c around inf 20.5%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 20.5%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

9. Simplified 20.5%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

10. Final simplification 20.5%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 58.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023268 
(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)))))