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

Percentage Accurate: 73.0% → 80.3%

Time: 37.2s

Alternatives: 23

Speedup: 0.5×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.0% 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: 80.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + t_1)
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = (a * ((c * j) - (x * t))) + t_1
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + t_1);
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = (a * ((c * j) - (x * t))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $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 89.9%

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

   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. Add Preprocessing

   3. Taylor expanded in y around 0 39.7%

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

      1. cancel-sign-sub-inv 39.7%

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

      2. *-commutative 39.7%

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

      3. *-commutative 39.7%

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

      4. cancel-sign-sub-inv 39.7%

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

      5. sub-neg 39.7%

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

      6. distribute-rgt-neg-out 39.7%

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

      7. mul-1-neg 39.7%

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

      8. distribute-rgt-neg-in 39.7%

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

      9. mul-1-neg 39.7%

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

      10. distribute-lft-in 48.4%

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

      11. +-commutative 48.4%

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

      12. mul-1-neg 48.4%

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

      13. unsub-neg 48.4%

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

      14. *-commutative 48.4%

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

   5. Simplified 48.4%

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

4. Final simplification 80.5%

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

Alternative 2: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -390000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-283}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* c (- (* a j) (* z b))))
        (t_4 (* t (- (* b i) (* x a)))))
   (if (<= t -390000000.0)
     t_4
     (if (<= t -5e-173)
       t_3
       (if (<= t -1.1e-294)
         t_2
         (if (<= t 1.7e-283)
           t_3
           (if (<= t 3.3e-235)
             t_2
             (if (<= t 2.7e-23)
               t_1
               (if (<= t 3.5e+17) t_3 (if (<= t 3.1e+63) t_1 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double t_4 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -390000000.0) {
		tmp = t_4;
	} else if (t <= -5e-173) {
		tmp = t_3;
	} else if (t <= -1.1e-294) {
		tmp = t_2;
	} else if (t <= 1.7e-283) {
		tmp = t_3;
	} else if (t <= 3.3e-235) {
		tmp = t_2;
	} else if (t <= 2.7e-23) {
		tmp = t_1;
	} else if (t <= 3.5e+17) {
		tmp = t_3;
	} else if (t <= 3.1e+63) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = y * ((x * z) - (i * j))
    t_3 = c * ((a * j) - (z * b))
    t_4 = t * ((b * i) - (x * a))
    if (t <= (-390000000.0d0)) then
        tmp = t_4
    else if (t <= (-5d-173)) then
        tmp = t_3
    else if (t <= (-1.1d-294)) then
        tmp = t_2
    else if (t <= 1.7d-283) then
        tmp = t_3
    else if (t <= 3.3d-235) then
        tmp = t_2
    else if (t <= 2.7d-23) then
        tmp = t_1
    else if (t <= 3.5d+17) then
        tmp = t_3
    else if (t <= 3.1d+63) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double t_4 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -390000000.0) {
		tmp = t_4;
	} else if (t <= -5e-173) {
		tmp = t_3;
	} else if (t <= -1.1e-294) {
		tmp = t_2;
	} else if (t <= 1.7e-283) {
		tmp = t_3;
	} else if (t <= 3.3e-235) {
		tmp = t_2;
	} else if (t <= 2.7e-23) {
		tmp = t_1;
	} else if (t <= 3.5e+17) {
		tmp = t_3;
	} else if (t <= 3.1e+63) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = y * ((x * z) - (i * j))
	t_3 = c * ((a * j) - (z * b))
	t_4 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -390000000.0:
		tmp = t_4
	elif t <= -5e-173:
		tmp = t_3
	elif t <= -1.1e-294:
		tmp = t_2
	elif t <= 1.7e-283:
		tmp = t_3
	elif t <= 3.3e-235:
		tmp = t_2
	elif t <= 2.7e-23:
		tmp = t_1
	elif t <= 3.5e+17:
		tmp = t_3
	elif t <= 3.1e+63:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_4 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -390000000.0)
		tmp = t_4;
	elseif (t <= -5e-173)
		tmp = t_3;
	elseif (t <= -1.1e-294)
		tmp = t_2;
	elseif (t <= 1.7e-283)
		tmp = t_3;
	elseif (t <= 3.3e-235)
		tmp = t_2;
	elseif (t <= 2.7e-23)
		tmp = t_1;
	elseif (t <= 3.5e+17)
		tmp = t_3;
	elseif (t <= 3.1e+63)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = y * ((x * z) - (i * j));
	t_3 = c * ((a * j) - (z * b));
	t_4 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -390000000.0)
		tmp = t_4;
	elseif (t <= -5e-173)
		tmp = t_3;
	elseif (t <= -1.1e-294)
		tmp = t_2;
	elseif (t <= 1.7e-283)
		tmp = t_3;
	elseif (t <= 3.3e-235)
		tmp = t_2;
	elseif (t <= 2.7e-23)
		tmp = t_1;
	elseif (t <= 3.5e+17)
		tmp = t_3;
	elseif (t <= 3.1e+63)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -390000000.0], t$95$4, If[LessEqual[t, -5e-173], t$95$3, If[LessEqual[t, -1.1e-294], t$95$2, If[LessEqual[t, 1.7e-283], t$95$3, If[LessEqual[t, 3.3e-235], t$95$2, If[LessEqual[t, 2.7e-23], t$95$1, If[LessEqual[t, 3.5e+17], t$95$3, If[LessEqual[t, 3.1e+63], t$95$1, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.9e8 or 3.1000000000000001e63 < 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. Add Preprocessing

   3. Taylor expanded in a around -inf 67.3%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

   8. Simplified 68.7%

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

   if -3.9e8 < t < -5.0000000000000002e-173 or -1.1e-294 < t < 1.6999999999999999e-283 or 2.69999999999999985e-23 < t < 3.5e17

   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. Add Preprocessing

   3. Taylor expanded in c around inf 69.3%

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

      1. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   if -5.0000000000000002e-173 < t < -1.1e-294 or 1.6999999999999999e-283 < t < 3.30000000000000028e-235

   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. Add Preprocessing

   3. Taylor expanded in y around inf 64.5%

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

      1. +-commutative 64.5%

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

      2. mul-1-neg 64.5%

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

      3. unsub-neg 64.5%

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

   5. Simplified 64.5%

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

   if 3.30000000000000028e-235 < t < 2.69999999999999985e-23 or 3.5e17 < t < 3.1000000000000001e63

   1. Initial program 71.6%

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

   3. Taylor expanded in a around -inf 71.6%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in x around inf 66.2%

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

      1. *-commutative 66.2%

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

   8. Simplified 66.2%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -390000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-173}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-283}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-235}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t_1 + t_2\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+222}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+136}:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) - z \cdot \left(b \cdot c - x \cdot y\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-11}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-175}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-137}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (+ t_1 t_2))
        (t_4 (* y (- (* x z) (* i j)))))
   (if (<= y -8.2e+222)
     t_4
     (if (<= y -8.8e+136)
       (- (- (* b (* t i)) (* z (- (* b c) (* x y)))) (* i (* y j)))
       (if (<= y -1.55e-11)
         (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
         (if (<= y -1.4e-175)
           t_3
           (if (<= y -1.06e-223)
             (+ (* x (- (* y z) (* t a))) t_2)
             (if (<= y 1.9e-137) t_3 (+ t_1 t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_1 + t_2;
	double t_4 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -8.2e+222) {
		tmp = t_4;
	} else if (y <= -8.8e+136) {
		tmp = ((b * (t * i)) - (z * ((b * c) - (x * y)))) - (i * (y * j));
	} else if (y <= -1.55e-11) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= -1.4e-175) {
		tmp = t_3;
	} else if (y <= -1.06e-223) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else if (y <= 1.9e-137) {
		tmp = t_3;
	} else {
		tmp = t_1 + t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    t_3 = t_1 + t_2
    t_4 = y * ((x * z) - (i * j))
    if (y <= (-8.2d+222)) then
        tmp = t_4
    else if (y <= (-8.8d+136)) then
        tmp = ((b * (t * i)) - (z * ((b * c) - (x * y)))) - (i * (y * j))
    else if (y <= (-1.55d-11)) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else if (y <= (-1.4d-175)) then
        tmp = t_3
    else if (y <= (-1.06d-223)) then
        tmp = (x * ((y * z) - (t * a))) + t_2
    else if (y <= 1.9d-137) then
        tmp = t_3
    else
        tmp = t_1 + t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_1 + t_2;
	double t_4 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -8.2e+222) {
		tmp = t_4;
	} else if (y <= -8.8e+136) {
		tmp = ((b * (t * i)) - (z * ((b * c) - (x * y)))) - (i * (y * j));
	} else if (y <= -1.55e-11) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= -1.4e-175) {
		tmp = t_3;
	} else if (y <= -1.06e-223) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else if (y <= 1.9e-137) {
		tmp = t_3;
	} else {
		tmp = t_1 + t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	t_3 = t_1 + t_2
	t_4 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -8.2e+222:
		tmp = t_4
	elif y <= -8.8e+136:
		tmp = ((b * (t * i)) - (z * ((b * c) - (x * y)))) - (i * (y * j))
	elif y <= -1.55e-11:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	elif y <= -1.4e-175:
		tmp = t_3
	elif y <= -1.06e-223:
		tmp = (x * ((y * z) - (t * a))) + t_2
	elif y <= 1.9e-137:
		tmp = t_3
	else:
		tmp = t_1 + t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(t_1 + t_2)
	t_4 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -8.2e+222)
		tmp = t_4;
	elseif (y <= -8.8e+136)
		tmp = Float64(Float64(Float64(b * Float64(t * i)) - Float64(z * Float64(Float64(b * c) - Float64(x * y)))) - Float64(i * Float64(y * j)));
	elseif (y <= -1.55e-11)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (y <= -1.4e-175)
		tmp = t_3;
	elseif (y <= -1.06e-223)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2);
	elseif (y <= 1.9e-137)
		tmp = t_3;
	else
		tmp = Float64(t_1 + t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	t_3 = t_1 + t_2;
	t_4 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -8.2e+222)
		tmp = t_4;
	elseif (y <= -8.8e+136)
		tmp = ((b * (t * i)) - (z * ((b * c) - (x * y)))) - (i * (y * j));
	elseif (y <= -1.55e-11)
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	elseif (y <= -1.4e-175)
		tmp = t_3;
	elseif (y <= -1.06e-223)
		tmp = (x * ((y * z) - (t * a))) + t_2;
	elseif (y <= 1.9e-137)
		tmp = t_3;
	else
		tmp = t_1 + t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+222], t$95$4, If[LessEqual[y, -8.8e+136], N[(N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.55e-11], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-175], t$95$3, If[LessEqual[y, -1.06e-223], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[y, 1.9e-137], t$95$3, N[(t$95$1 + t$95$4), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.19999999999999974e222

   1. Initial program 37.6%

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

   3. Taylor expanded in y around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

   5. Simplified 73.4%

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

   if -8.19999999999999974e222 < y < -8.7999999999999998e136

   1. Initial program 78.8%

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

   3. Taylor expanded in a around -inf 73.5%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around 0 84.0%

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

   7. Taylor expanded in a around 0 82.8%

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

   if -8.7999999999999998e136 < y < -1.55000000000000014e-11

   1. Initial program 68.7%

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

   3. Taylor expanded in b around 0 82.4%

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

   if -1.55000000000000014e-11 < y < -1.4e-175 or -1.05999999999999994e-223 < y < 1.89999999999999999e-137

   1. Initial program 78.2%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. cancel-sign-sub-inv 83.9%

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

      2. *-commutative 83.9%

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

      3. *-commutative 83.9%

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

      4. cancel-sign-sub-inv 83.9%

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

      5. sub-neg 83.9%

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

      6. distribute-rgt-neg-out 83.9%

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

      7. mul-1-neg 83.9%

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

      8. distribute-rgt-neg-in 83.9%

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

      9. mul-1-neg 83.9%

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

      10. distribute-lft-in 86.1%

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

      11. +-commutative 86.1%

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

      12. mul-1-neg 86.1%

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

      13. unsub-neg 86.1%

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

      14. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   if -1.4e-175 < y < -1.05999999999999994e-223

   1. Initial program 69.7%

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

   3. Taylor expanded in j around 0 89.7%

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

   if 1.89999999999999999e-137 < y

   1. Initial program 67.1%

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

   3. Taylor expanded in a around -inf 66.9%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in b around 0 71.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+136}:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) - z \cdot \left(b \cdot c - x \cdot y\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-11}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-175}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-137}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.9e-34)
     t_2
     (if (<= b 8.5e-263)
       t_1
       (if (<= b 5.1e-222)
         (* x (* y z))
         (if (<= b 8.5e-170)
           t_1
           (if (<= b 1.1e-123)
             t_2
             (if (<= b 2.25e-57)
               t_1
               (if (<= b 1.25e+65) (* c (- (* a j) (* z b))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.9e-34) {
		tmp = t_2;
	} else if (b <= 8.5e-263) {
		tmp = t_1;
	} else if (b <= 5.1e-222) {
		tmp = x * (y * z);
	} else if (b <= 8.5e-170) {
		tmp = t_1;
	} else if (b <= 1.1e-123) {
		tmp = t_2;
	} else if (b <= 2.25e-57) {
		tmp = t_1;
	} else if (b <= 1.25e+65) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.9d-34)) then
        tmp = t_2
    else if (b <= 8.5d-263) then
        tmp = t_1
    else if (b <= 5.1d-222) then
        tmp = x * (y * z)
    else if (b <= 8.5d-170) then
        tmp = t_1
    else if (b <= 1.1d-123) then
        tmp = t_2
    else if (b <= 2.25d-57) then
        tmp = t_1
    else if (b <= 1.25d+65) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.9e-34) {
		tmp = t_2;
	} else if (b <= 8.5e-263) {
		tmp = t_1;
	} else if (b <= 5.1e-222) {
		tmp = x * (y * z);
	} else if (b <= 8.5e-170) {
		tmp = t_1;
	} else if (b <= 1.1e-123) {
		tmp = t_2;
	} else if (b <= 2.25e-57) {
		tmp = t_1;
	} else if (b <= 1.25e+65) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.9e-34:
		tmp = t_2
	elif b <= 8.5e-263:
		tmp = t_1
	elif b <= 5.1e-222:
		tmp = x * (y * z)
	elif b <= 8.5e-170:
		tmp = t_1
	elif b <= 1.1e-123:
		tmp = t_2
	elif b <= 2.25e-57:
		tmp = t_1
	elif b <= 1.25e+65:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.9e-34)
		tmp = t_2;
	elseif (b <= 8.5e-263)
		tmp = t_1;
	elseif (b <= 5.1e-222)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 8.5e-170)
		tmp = t_1;
	elseif (b <= 1.1e-123)
		tmp = t_2;
	elseif (b <= 2.25e-57)
		tmp = t_1;
	elseif (b <= 1.25e+65)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.9e-34)
		tmp = t_2;
	elseif (b <= 8.5e-263)
		tmp = t_1;
	elseif (b <= 5.1e-222)
		tmp = x * (y * z);
	elseif (b <= 8.5e-170)
		tmp = t_1;
	elseif (b <= 1.1e-123)
		tmp = t_2;
	elseif (b <= 2.25e-57)
		tmp = t_1;
	elseif (b <= 1.25e+65)
		tmp = c * ((a * j) - (z * b));
	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[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e-34], t$95$2, If[LessEqual[b, 8.5e-263], t$95$1, If[LessEqual[b, 5.1e-222], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-170], t$95$1, If[LessEqual[b, 1.1e-123], t$95$2, If[LessEqual[b, 2.25e-57], t$95$1, If[LessEqual[b, 1.25e+65], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9000000000000001e-34 or 8.5e-170 < b < 1.10000000000000003e-123 or 1.24999999999999993e65 < b

   1. Initial program 72.3%

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

   3. Taylor expanded in b around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if -1.9000000000000001e-34 < b < 8.49999999999999975e-263 or 5.1000000000000002e-222 < b < 8.5e-170 or 1.10000000000000003e-123 < b < 2.24999999999999986e-57

   1. Initial program 67.8%

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

   3. Taylor expanded in a around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

      4. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   if 8.49999999999999975e-263 < b < 5.1000000000000002e-222

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in x around inf 71.7%

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

   if 2.24999999999999986e-57 < b < 1.24999999999999993e65

   1. Initial program 64.9%

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

   3. Taylor expanded in c around inf 44.7%

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

      1. *-commutative 44.7%

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

   5. Simplified 44.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{-34}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-263}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -4.5e-35)
     t_3
     (if (<= b 6.4e-263)
       t_1
       (if (<= b 5.8e-222)
         (* x (* y z))
         (if (<= b 8.2e-170)
           t_1
           (if (<= b 3e-78)
             t_2
             (if (<= b 2.4e+59)
               (* c (- (* a j) (* z b)))
               (if (<= b 2.8e+121) 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 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.5e-35) {
		tmp = t_3;
	} else if (b <= 6.4e-263) {
		tmp = t_1;
	} else if (b <= 5.8e-222) {
		tmp = x * (y * z);
	} else if (b <= 8.2e-170) {
		tmp = t_1;
	} else if (b <= 3e-78) {
		tmp = t_2;
	} else if (b <= 2.4e+59) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 2.8e+121) {
		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 = a * ((c * j) - (x * t))
    t_2 = i * ((t * b) - (y * j))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-4.5d-35)) then
        tmp = t_3
    else if (b <= 6.4d-263) then
        tmp = t_1
    else if (b <= 5.8d-222) then
        tmp = x * (y * z)
    else if (b <= 8.2d-170) then
        tmp = t_1
    else if (b <= 3d-78) then
        tmp = t_2
    else if (b <= 2.4d+59) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 2.8d+121) 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 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.5e-35) {
		tmp = t_3;
	} else if (b <= 6.4e-263) {
		tmp = t_1;
	} else if (b <= 5.8e-222) {
		tmp = x * (y * z);
	} else if (b <= 8.2e-170) {
		tmp = t_1;
	} else if (b <= 3e-78) {
		tmp = t_2;
	} else if (b <= 2.4e+59) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 2.8e+121) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = i * ((t * b) - (y * j))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.5e-35:
		tmp = t_3
	elif b <= 6.4e-263:
		tmp = t_1
	elif b <= 5.8e-222:
		tmp = x * (y * z)
	elif b <= 8.2e-170:
		tmp = t_1
	elif b <= 3e-78:
		tmp = t_2
	elif b <= 2.4e+59:
		tmp = c * ((a * j) - (z * b))
	elif b <= 2.8e+121:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.5e-35)
		tmp = t_3;
	elseif (b <= 6.4e-263)
		tmp = t_1;
	elseif (b <= 5.8e-222)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 8.2e-170)
		tmp = t_1;
	elseif (b <= 3e-78)
		tmp = t_2;
	elseif (b <= 2.4e+59)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 2.8e+121)
		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 = a * ((c * j) - (x * t));
	t_2 = i * ((t * b) - (y * j));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.5e-35)
		tmp = t_3;
	elseif (b <= 6.4e-263)
		tmp = t_1;
	elseif (b <= 5.8e-222)
		tmp = x * (y * z);
	elseif (b <= 8.2e-170)
		tmp = t_1;
	elseif (b <= 3e-78)
		tmp = t_2;
	elseif (b <= 2.4e+59)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 2.8e+121)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e-35], t$95$3, If[LessEqual[b, 6.4e-263], t$95$1, If[LessEqual[b, 5.8e-222], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-170], t$95$1, If[LessEqual[b, 3e-78], t$95$2, If[LessEqual[b, 2.4e+59], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+121], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.5000000000000001e-35 or 2.80000000000000006e121 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   if -4.5000000000000001e-35 < b < 6.4000000000000001e-263 or 5.8000000000000004e-222 < b < 8.19999999999999931e-170

   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. Add Preprocessing

   3. Taylor expanded in a around inf 56.1%

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

      1. +-commutative 56.1%

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

      2. mul-1-neg 56.1%

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

      3. unsub-neg 56.1%

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

      4. *-commutative 56.1%

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

   5. Simplified 56.1%

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

   if 6.4000000000000001e-263 < b < 5.8000000000000004e-222

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in x around inf 71.7%

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

   if 8.19999999999999931e-170 < b < 2.99999999999999988e-78 or 2.4000000000000002e59 < b < 2.80000000000000006e121

   1. Initial program 76.4%

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

   3. Taylor expanded in a around -inf 63.9%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in i around inf 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

   8. Simplified 53.4%

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

   if 2.99999999999999988e-78 < b < 2.4000000000000002e59

   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. Add Preprocessing

   3. Taylor expanded in c around inf 43.2%

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

      1. *-commutative 43.2%

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

   5. Simplified 43.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-263}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-78}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+121}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;t \leq -430000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* x (- (* y z) (* t a)))))
   (if (<= t -430000000.0)
     t_2
     (if (<= t -2.7e-175)
       t_1
       (if (<= t -6.2e-293)
         (* i (- (* t b) (* y j)))
         (if (<= t 6.2e-232)
           t_1
           (if (<= t 8.4e-25)
             t_3
             (if (<= t 3.5e+17) t_1 (if (<= t 4.7e+64) 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 = x * ((y * z) - (t * a));
	double tmp;
	if (t <= -430000000.0) {
		tmp = t_2;
	} else if (t <= -2.7e-175) {
		tmp = t_1;
	} else if (t <= -6.2e-293) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= 6.2e-232) {
		tmp = t_1;
	} else if (t <= 8.4e-25) {
		tmp = t_3;
	} else if (t <= 3.5e+17) {
		tmp = t_1;
	} else if (t <= 4.7e+64) {
		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 = x * ((y * z) - (t * a))
    if (t <= (-430000000.0d0)) then
        tmp = t_2
    else if (t <= (-2.7d-175)) then
        tmp = t_1
    else if (t <= (-6.2d-293)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= 6.2d-232) then
        tmp = t_1
    else if (t <= 8.4d-25) then
        tmp = t_3
    else if (t <= 3.5d+17) then
        tmp = t_1
    else if (t <= 4.7d+64) 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 = x * ((y * z) - (t * a));
	double tmp;
	if (t <= -430000000.0) {
		tmp = t_2;
	} else if (t <= -2.7e-175) {
		tmp = t_1;
	} else if (t <= -6.2e-293) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= 6.2e-232) {
		tmp = t_1;
	} else if (t <= 8.4e-25) {
		tmp = t_3;
	} else if (t <= 3.5e+17) {
		tmp = t_1;
	} else if (t <= 4.7e+64) {
		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 = x * ((y * z) - (t * a))
	tmp = 0
	if t <= -430000000.0:
		tmp = t_2
	elif t <= -2.7e-175:
		tmp = t_1
	elif t <= -6.2e-293:
		tmp = i * ((t * b) - (y * j))
	elif t <= 6.2e-232:
		tmp = t_1
	elif t <= 8.4e-25:
		tmp = t_3
	elif t <= 3.5e+17:
		tmp = t_1
	elif t <= 4.7e+64:
		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(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (t <= -430000000.0)
		tmp = t_2;
	elseif (t <= -2.7e-175)
		tmp = t_1;
	elseif (t <= -6.2e-293)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= 6.2e-232)
		tmp = t_1;
	elseif (t <= 8.4e-25)
		tmp = t_3;
	elseif (t <= 3.5e+17)
		tmp = t_1;
	elseif (t <= 4.7e+64)
		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 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (t <= -430000000.0)
		tmp = t_2;
	elseif (t <= -2.7e-175)
		tmp = t_1;
	elseif (t <= -6.2e-293)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= 6.2e-232)
		tmp = t_1;
	elseif (t <= 8.4e-25)
		tmp = t_3;
	elseif (t <= 3.5e+17)
		tmp = t_1;
	elseif (t <= 4.7e+64)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -430000000.0], t$95$2, If[LessEqual[t, -2.7e-175], t$95$1, If[LessEqual[t, -6.2e-293], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-232], t$95$1, If[LessEqual[t, 8.4e-25], t$95$3, If[LessEqual[t, 3.5e+17], t$95$1, If[LessEqual[t, 4.7e+64], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.3e8 or 4.70000000000000029e64 < 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. Add Preprocessing

   3. Taylor expanded in a around -inf 67.3%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

   8. Simplified 68.7%

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

   if -4.3e8 < t < -2.69999999999999999e-175 or -6.19999999999999965e-293 < t < 6.1999999999999998e-232 or 8.40000000000000009e-25 < t < 3.5e17

   1. Initial program 71.4%

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

   3. Taylor expanded in c around inf 63.4%

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

      1. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   if -2.69999999999999999e-175 < t < -6.19999999999999965e-293

   1. Initial program 85.0%

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

   3. Taylor expanded in a around -inf 77.5%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in i around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

   8. Simplified 48.6%

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

   if 6.1999999999999998e-232 < t < 8.40000000000000009e-25 or 3.5e17 < t < 4.70000000000000029e64

   1. Initial program 71.6%

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

   3. Taylor expanded in a around -inf 71.6%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in x around inf 66.2%

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

      1. *-commutative 66.2%

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

   8. Simplified 66.2%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -430000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;y \leq -0.000145:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-99}:\\ \;\;\;\;t_2 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+97}:\\ \;\;\;\;t_2 + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z (- (* x y) (* b c))) (* i (* y j))))
        (t_2 (* a (- (* c j) (* x t)))))
   (if (<= y -0.000145)
     (* y (- (* x z) (* i j)))
     (if (<= y 5.8e-99)
       (+ t_2 (* b (- (* t i) (* z c))))
       (if (<= y 200.0)
         t_1
         (if (<= y 5e+25)
           (* t (- (* b i) (* x a)))
           (if (<= y 1.1e+97) (+ t_2 (* 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 = (z * ((x * y) - (b * c))) - (i * (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -0.000145) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 5.8e-99) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if (y <= 200.0) {
		tmp = t_1;
	} else if (y <= 5e+25) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.1e+97) {
		tmp = t_2 + (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) :: t_2
    real(8) :: tmp
    t_1 = (z * ((x * y) - (b * c))) - (i * (y * j))
    t_2 = a * ((c * j) - (x * t))
    if (y <= (-0.000145d0)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= 5.8d-99) then
        tmp = t_2 + (b * ((t * i) - (z * c)))
    else if (y <= 200.0d0) then
        tmp = t_1
    else if (y <= 5d+25) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 1.1d+97) then
        tmp = t_2 + (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 = (z * ((x * y) - (b * c))) - (i * (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -0.000145) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 5.8e-99) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if (y <= 200.0) {
		tmp = t_1;
	} else if (y <= 5e+25) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.1e+97) {
		tmp = t_2 + (x * (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * ((x * y) - (b * c))) - (i * (y * j))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if y <= -0.000145:
		tmp = y * ((x * z) - (i * j))
	elif y <= 5.8e-99:
		tmp = t_2 + (b * ((t * i) - (z * c)))
	elif y <= 200.0:
		tmp = t_1
	elif y <= 5e+25:
		tmp = t * ((b * i) - (x * a))
	elif y <= 1.1e+97:
		tmp = t_2 + (x * (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(i * Float64(y * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (y <= -0.000145)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= 5.8e-99)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (y <= 200.0)
		tmp = t_1;
	elseif (y <= 5e+25)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 1.1e+97)
		tmp = Float64(t_2 + 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 = (z * ((x * y) - (b * c))) - (i * (y * j));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (y <= -0.000145)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= 5.8e-99)
		tmp = t_2 + (b * ((t * i) - (z * c)));
	elseif (y <= 200.0)
		tmp = t_1;
	elseif (y <= 5e+25)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 1.1e+97)
		tmp = t_2 + (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[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.000145], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-99], N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 200.0], t$95$1, If[LessEqual[y, 5e+25], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+97], N[(t$95$2 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.45e-4

   1. Initial program 60.9%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

   5. Simplified 64.0%

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

   if -1.45e-4 < y < 5.79999999999999971e-99

   1. Initial program 77.9%

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

   3. Taylor expanded in y around 0 76.4%

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

      1. cancel-sign-sub-inv 76.4%

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

      2. *-commutative 76.4%

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

      3. *-commutative 76.4%

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

      4. cancel-sign-sub-inv 76.4%

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

      5. sub-neg 76.4%

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

      6. distribute-rgt-neg-out 76.4%

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

      7. mul-1-neg 76.4%

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

      8. distribute-rgt-neg-in 76.4%

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

      9. mul-1-neg 76.4%

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

      10. distribute-lft-in 80.1%

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

      11. +-commutative 80.1%

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

      12. mul-1-neg 80.1%

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

      13. unsub-neg 80.1%

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

      14. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   if 5.79999999999999971e-99 < y < 200 or 1.1e97 < y

   1. Initial program 63.7%

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

   3. Taylor expanded in a around -inf 62.2%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around 0 66.7%

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

   7. Taylor expanded in a around 0 66.8%

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

   8. Taylor expanded in t around 0 71.2%

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

   if 200 < y < 5.00000000000000024e25

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in t around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if 5.00000000000000024e25 < y < 1.1e97

   1. Initial program 72.7%

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

   3. Taylor expanded in a around -inf 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in z around 0 81.8%

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

   7. Taylor expanded in x around inf 82.7%

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

      1. *-commutative 82.7%

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

   9. Simplified 82.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000145:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 200:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t_1 + t_2\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-138}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+98}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (+ t_1 t_2)))
   (if (<= y -2.7e-9)
     (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
     (if (<= y -8.4e-172)
       t_3
       (if (<= y -3.5e-223)
         (+ (* x (- (* y z) (* t a))) t_2)
         (if (<= y 7e-138)
           t_3
           (if (<= y 9.5e+98)
             (+ t_1 (* x (* y z)))
             (- (* z (- (* x y) (* b c))) (* i (* y 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 * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_1 + t_2;
	double tmp;
	if (y <= -2.7e-9) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= -8.4e-172) {
		tmp = t_3;
	} else if (y <= -3.5e-223) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else if (y <= 7e-138) {
		tmp = t_3;
	} else if (y <= 9.5e+98) {
		tmp = t_1 + (x * (y * z));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * 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) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    t_3 = t_1 + t_2
    if (y <= (-2.7d-9)) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else if (y <= (-8.4d-172)) then
        tmp = t_3
    else if (y <= (-3.5d-223)) then
        tmp = (x * ((y * z) - (t * a))) + t_2
    else if (y <= 7d-138) then
        tmp = t_3
    else if (y <= 9.5d+98) then
        tmp = t_1 + (x * (y * z))
    else
        tmp = (z * ((x * y) - (b * c))) - (i * (y * 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 * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_1 + t_2;
	double tmp;
	if (y <= -2.7e-9) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= -8.4e-172) {
		tmp = t_3;
	} else if (y <= -3.5e-223) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else if (y <= 7e-138) {
		tmp = t_3;
	} else if (y <= 9.5e+98) {
		tmp = t_1 + (x * (y * z));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	t_3 = t_1 + t_2
	tmp = 0
	if y <= -2.7e-9:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	elif y <= -8.4e-172:
		tmp = t_3
	elif y <= -3.5e-223:
		tmp = (x * ((y * z) - (t * a))) + t_2
	elif y <= 7e-138:
		tmp = t_3
	elif y <= 9.5e+98:
		tmp = t_1 + (x * (y * z))
	else:
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(t_1 + t_2)
	tmp = 0.0
	if (y <= -2.7e-9)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (y <= -8.4e-172)
		tmp = t_3;
	elseif (y <= -3.5e-223)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2);
	elseif (y <= 7e-138)
		tmp = t_3;
	elseif (y <= 9.5e+98)
		tmp = Float64(t_1 + Float64(x * Float64(y * z)));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(i * Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	t_3 = t_1 + t_2;
	tmp = 0.0;
	if (y <= -2.7e-9)
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	elseif (y <= -8.4e-172)
		tmp = t_3;
	elseif (y <= -3.5e-223)
		tmp = (x * ((y * z) - (t * a))) + t_2;
	elseif (y <= 7e-138)
		tmp = t_3;
	elseif (y <= 9.5e+98)
		tmp = t_1 + (x * (y * z));
	else
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + t$95$2), $MachinePrecision]}, If[LessEqual[y, -2.7e-9], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.4e-172], t$95$3, If[LessEqual[y, -3.5e-223], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[y, 7e-138], t$95$3, If[LessEqual[y, 9.5e+98], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7000000000000002e-9

   1. Initial program 60.9%

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

   3. Taylor expanded in b around 0 67.4%

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

   if -2.7000000000000002e-9 < y < -8.3999999999999998e-172 or -3.50000000000000009e-223 < y < 6.9999999999999997e-138

   1. Initial program 78.2%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. cancel-sign-sub-inv 83.9%

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

      2. *-commutative 83.9%

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

      3. *-commutative 83.9%

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

      4. cancel-sign-sub-inv 83.9%

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

      5. sub-neg 83.9%

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

      6. distribute-rgt-neg-out 83.9%

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

      7. mul-1-neg 83.9%

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

      8. distribute-rgt-neg-in 83.9%

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

      9. mul-1-neg 83.9%

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

      10. distribute-lft-in 86.1%

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

      11. +-commutative 86.1%

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

      12. mul-1-neg 86.1%

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

      13. unsub-neg 86.1%

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

      14. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   if -8.3999999999999998e-172 < y < -3.50000000000000009e-223

   1. Initial program 69.7%

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

   3. Taylor expanded in j around 0 89.7%

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

   if 6.9999999999999997e-138 < y < 9.5000000000000001e98

   1. Initial program 69.1%

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

   3. Taylor expanded in a around -inf 71.2%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in z around 0 75.2%

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

   7. Taylor expanded in x around inf 65.5%

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

      1. *-commutative 65.5%

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

   9. Simplified 65.5%

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

   if 9.5000000000000001e98 < y

   1. Initial program 64.9%

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

   3. Taylor expanded in a around -inf 62.5%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in z around 0 64.9%

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

   7. Taylor expanded in a around 0 67.2%

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

   8. Taylor expanded in t around 0 71.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + z \cdot \left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-172}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-138}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1800000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 0.000255:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -1800000000.0)
     t_2
     (if (<= t -3.3e-175)
       t_1
       (if (<= t -5.2e-293)
         (* i (- (* t b) (* y j)))
         (if (<= t 1.5e-113)
           t_1
           (if (<= t 1.3e-26) (* x (* y z)) (if (<= t 0.000255) 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 <= -1800000000.0) {
		tmp = t_2;
	} else if (t <= -3.3e-175) {
		tmp = t_1;
	} else if (t <= -5.2e-293) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= 1.5e-113) {
		tmp = t_1;
	} else if (t <= 1.3e-26) {
		tmp = x * (y * z);
	} else if (t <= 0.000255) {
		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 <= (-1800000000.0d0)) then
        tmp = t_2
    else if (t <= (-3.3d-175)) then
        tmp = t_1
    else if (t <= (-5.2d-293)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= 1.5d-113) then
        tmp = t_1
    else if (t <= 1.3d-26) then
        tmp = x * (y * z)
    else if (t <= 0.000255d0) 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 <= -1800000000.0) {
		tmp = t_2;
	} else if (t <= -3.3e-175) {
		tmp = t_1;
	} else if (t <= -5.2e-293) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= 1.5e-113) {
		tmp = t_1;
	} else if (t <= 1.3e-26) {
		tmp = x * (y * z);
	} else if (t <= 0.000255) {
		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 <= -1800000000.0:
		tmp = t_2
	elif t <= -3.3e-175:
		tmp = t_1
	elif t <= -5.2e-293:
		tmp = i * ((t * b) - (y * j))
	elif t <= 1.5e-113:
		tmp = t_1
	elif t <= 1.3e-26:
		tmp = x * (y * z)
	elif t <= 0.000255:
		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 <= -1800000000.0)
		tmp = t_2;
	elseif (t <= -3.3e-175)
		tmp = t_1;
	elseif (t <= -5.2e-293)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= 1.5e-113)
		tmp = t_1;
	elseif (t <= 1.3e-26)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 0.000255)
		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 <= -1800000000.0)
		tmp = t_2;
	elseif (t <= -3.3e-175)
		tmp = t_1;
	elseif (t <= -5.2e-293)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= 1.5e-113)
		tmp = t_1;
	elseif (t <= 1.3e-26)
		tmp = x * (y * z);
	elseif (t <= 0.000255)
		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, -1800000000.0], t$95$2, If[LessEqual[t, -3.3e-175], t$95$1, If[LessEqual[t, -5.2e-293], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-113], t$95$1, If[LessEqual[t, 1.3e-26], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.000255], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.8e9 or 2.55e-4 < t

   1. Initial program 65.5%

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

   3. Taylor expanded in a around -inf 67.7%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in t around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

   8. Simplified 67.5%

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

   if -1.8e9 < t < -3.29999999999999999e-175 or -5.1999999999999996e-293 < t < 1.5e-113 or 1.30000000000000005e-26 < t < 2.55e-4

   1. Initial program 69.5%

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

   3. Taylor expanded in c around inf 59.8%

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

      1. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   if -3.29999999999999999e-175 < t < -5.1999999999999996e-293

   1. Initial program 85.0%

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

   3. Taylor expanded in a around -inf 77.5%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in i around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

   8. Simplified 48.6%

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

   if 1.5e-113 < t < 1.30000000000000005e-26

   1. Initial program 73.8%

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

   3. Taylor expanded in y around inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in x around inf 57.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1800000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 0.000255:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{-69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-283}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -1.1e-69)
     t_3
     (if (<= t -1.15e-173)
       t_2
       (if (<= t -8.5e-297)
         t_1
         (if (<= t 1.46e-283)
           (* c (- (* a j) (* z b)))
           (if (<= t 1.8e-229) t_1 (if (<= t 1.52e-12) 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 = y * ((x * z) - (i * j));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.1e-69) {
		tmp = t_3;
	} else if (t <= -1.15e-173) {
		tmp = t_2;
	} else if (t <= -8.5e-297) {
		tmp = t_1;
	} else if (t <= 1.46e-283) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.8e-229) {
		tmp = t_1;
	} else if (t <= 1.52e-12) {
		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 = y * ((x * z) - (i * j))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-1.1d-69)) then
        tmp = t_3
    else if (t <= (-1.15d-173)) then
        tmp = t_2
    else if (t <= (-8.5d-297)) then
        tmp = t_1
    else if (t <= 1.46d-283) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 1.8d-229) then
        tmp = t_1
    else if (t <= 1.52d-12) 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 = y * ((x * z) - (i * j));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.1e-69) {
		tmp = t_3;
	} else if (t <= -1.15e-173) {
		tmp = t_2;
	} else if (t <= -8.5e-297) {
		tmp = t_1;
	} else if (t <= 1.46e-283) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.8e-229) {
		tmp = t_1;
	} else if (t <= 1.52e-12) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.1e-69:
		tmp = t_3
	elif t <= -1.15e-173:
		tmp = t_2
	elif t <= -8.5e-297:
		tmp = t_1
	elif t <= 1.46e-283:
		tmp = c * ((a * j) - (z * b))
	elif t <= 1.8e-229:
		tmp = t_1
	elif t <= 1.52e-12:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	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 <= -1.1e-69)
		tmp = t_3;
	elseif (t <= -1.15e-173)
		tmp = t_2;
	elseif (t <= -8.5e-297)
		tmp = t_1;
	elseif (t <= 1.46e-283)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 1.8e-229)
		tmp = t_1;
	elseif (t <= 1.52e-12)
		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 = y * ((x * z) - (i * j));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.1e-69)
		tmp = t_3;
	elseif (t <= -1.15e-173)
		tmp = t_2;
	elseif (t <= -8.5e-297)
		tmp = t_1;
	elseif (t <= 1.46e-283)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 1.8e-229)
		tmp = t_1;
	elseif (t <= 1.52e-12)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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, -1.1e-69], t$95$3, If[LessEqual[t, -1.15e-173], t$95$2, If[LessEqual[t, -8.5e-297], t$95$1, If[LessEqual[t, 1.46e-283], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-229], t$95$1, If[LessEqual[t, 1.52e-12], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1e-69 or 1.52e-12 < t

   1. Initial program 65.0%

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

   3. Taylor expanded in a around -inf 66.9%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. *-commutative 65.4%

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

   8. Simplified 65.4%

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

   if -1.1e-69 < t < -1.14999999999999994e-173 or 1.80000000000000001e-229 < t < 1.52e-12

   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. Add Preprocessing

   3. Taylor expanded in z around inf 69.0%

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

   if -1.14999999999999994e-173 < t < -8.49999999999999991e-297 or 1.46000000000000004e-283 < t < 1.80000000000000001e-229

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. +-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

   5. Simplified 65.4%

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

   if -8.49999999999999991e-297 < t < 1.46000000000000004e-283

   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. Add Preprocessing

   3. Taylor expanded in c around inf 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-283}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t_1 + t_2\\ \mathbf{if}\;y \leq -1.86 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-137}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (+ t_1 t_2)))
   (if (<= y -1.86e-10)
     (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
     (if (<= y -3.7e-176)
       t_3
       (if (<= y -3.8e-224)
         (+ (* x (- (* y z) (* t a))) t_2)
         (if (<= y 1.02e-137) t_3 (+ t_1 (* 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_1 + t_2;
	double tmp;
	if (y <= -1.86e-10) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= -3.7e-176) {
		tmp = t_3;
	} else if (y <= -3.8e-224) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else if (y <= 1.02e-137) {
		tmp = t_3;
	} else {
		tmp = t_1 + (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) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    t_3 = t_1 + t_2
    if (y <= (-1.86d-10)) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else if (y <= (-3.7d-176)) then
        tmp = t_3
    else if (y <= (-3.8d-224)) then
        tmp = (x * ((y * z) - (t * a))) + t_2
    else if (y <= 1.02d-137) then
        tmp = t_3
    else
        tmp = t_1 + (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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_1 + t_2;
	double tmp;
	if (y <= -1.86e-10) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= -3.7e-176) {
		tmp = t_3;
	} else if (y <= -3.8e-224) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else if (y <= 1.02e-137) {
		tmp = t_3;
	} else {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	t_3 = t_1 + t_2
	tmp = 0
	if y <= -1.86e-10:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	elif y <= -3.7e-176:
		tmp = t_3
	elif y <= -3.8e-224:
		tmp = (x * ((y * z) - (t * a))) + t_2
	elif y <= 1.02e-137:
		tmp = t_3
	else:
		tmp = t_1 + (y * ((x * z) - (i * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(t_1 + t_2)
	tmp = 0.0
	if (y <= -1.86e-10)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (y <= -3.7e-176)
		tmp = t_3;
	elseif (y <= -3.8e-224)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2);
	elseif (y <= 1.02e-137)
		tmp = t_3;
	else
		tmp = Float64(t_1 + 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 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	t_3 = t_1 + t_2;
	tmp = 0.0;
	if (y <= -1.86e-10)
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	elseif (y <= -3.7e-176)
		tmp = t_3;
	elseif (y <= -3.8e-224)
		tmp = (x * ((y * z) - (t * a))) + t_2;
	elseif (y <= 1.02e-137)
		tmp = t_3;
	else
		tmp = t_1 + (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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + t$95$2), $MachinePrecision]}, If[LessEqual[y, -1.86e-10], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.7e-176], t$95$3, If[LessEqual[y, -3.8e-224], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[y, 1.02e-137], t$95$3, N[(t$95$1 + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.86000000000000004e-10

   1. Initial program 60.9%

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

   3. Taylor expanded in b around 0 67.4%

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

   if -1.86000000000000004e-10 < y < -3.69999999999999984e-176 or -3.80000000000000002e-224 < y < 1.02e-137

   1. Initial program 78.2%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. cancel-sign-sub-inv 83.9%

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

      2. *-commutative 83.9%

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

      3. *-commutative 83.9%

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

      4. cancel-sign-sub-inv 83.9%

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

      5. sub-neg 83.9%

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

      6. distribute-rgt-neg-out 83.9%

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

      7. mul-1-neg 83.9%

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

      8. distribute-rgt-neg-in 83.9%

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

      9. mul-1-neg 83.9%

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

      10. distribute-lft-in 86.1%

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

      11. +-commutative 86.1%

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

      12. mul-1-neg 86.1%

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

      13. unsub-neg 86.1%

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

      14. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   if -3.69999999999999984e-176 < y < -3.80000000000000002e-224

   1. Initial program 69.7%

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

   3. Taylor expanded in j around 0 89.7%

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

   if 1.02e-137 < y

   1. Initial program 67.1%

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

   3. Taylor expanded in a around -inf 66.9%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in b around 0 71.6%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.86 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-176}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-137}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.72 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -1.72e+49)
     t_1
     (if (<= b -1.15e-59)
       (- (* z (- (* x y) (* b c))) (* i (* y j)))
       (if (<= b 1.28e+79) (+ (* a (- (* c j) (* x t))) (* 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.72e+49) {
		tmp = t_1;
	} else if (b <= -1.15e-59) {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	} else if (b <= 1.28e+79) {
		tmp = (a * ((c * j) - (x * t))) + (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 = b * ((t * i) - (z * c))
    if (b <= (-1.72d+49)) then
        tmp = t_1
    else if (b <= (-1.15d-59)) then
        tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
    else if (b <= 1.28d+79) then
        tmp = (a * ((c * j) - (x * t))) + (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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.72e+49) {
		tmp = t_1;
	} else if (b <= -1.15e-59) {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	} else if (b <= 1.28e+79) {
		tmp = (a * ((c * j) - (x * t))) + (x * (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.72e+49:
		tmp = t_1
	elif b <= -1.15e-59:
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
	elif b <= 1.28e+79:
		tmp = (a * ((c * j) - (x * t))) + (x * (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.72e+49)
		tmp = t_1;
	elseif (b <= -1.15e-59)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(i * Float64(y * j)));
	elseif (b <= 1.28e+79)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + 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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.72e+49)
		tmp = t_1;
	elseif (b <= -1.15e-59)
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	elseif (b <= 1.28e+79)
		tmp = (a * ((c * j) - (x * t))) + (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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.72e+49], t$95$1, If[LessEqual[b, -1.15e-59], 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, 1.28e+79], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.71999999999999991e49 or 1.27999999999999998e79 < b

   1. Initial program 69.0%

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

   3. Taylor expanded in b around inf 69.3%

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

      1. *-commutative 69.3%

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

      2. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   if -1.71999999999999991e49 < b < -1.1499999999999999e-59

   1. Initial program 81.7%

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

   3. Taylor expanded in a around -inf 77.7%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around 0 82.3%

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

   7. Taylor expanded in a around 0 73.9%

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

   8. Taylor expanded in t around 0 69.3%

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

   if -1.1499999999999999e-59 < b < 1.27999999999999998e79

   1. Initial program 67.9%

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

   3. Taylor expanded in a around -inf 70.0%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in z around 0 75.2%

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

   7. Taylor expanded in x around inf 64.0%

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

      1. *-commutative 64.0%

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

   9. Simplified 64.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-137}:\\ \;\;\;\;t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+99}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= y -6.5e-10)
     (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
     (if (<= y 1.9e-137)
       (+ t_1 (* b (- (* t i) (* z c))))
       (if (<= y 3.1e+99)
         (+ t_1 (* x (* y z)))
         (- (* z (- (* x y) (* b c))) (* i (* y 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 * ((c * j) - (x * t));
	double tmp;
	if (y <= -6.5e-10) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= 1.9e-137) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (y <= 3.1e+99) {
		tmp = t_1 + (x * (y * z));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * 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 * ((c * j) - (x * t))
    if (y <= (-6.5d-10)) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else if (y <= 1.9d-137) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if (y <= 3.1d+99) then
        tmp = t_1 + (x * (y * z))
    else
        tmp = (z * ((x * y) - (b * c))) - (i * (y * 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 * ((c * j) - (x * t));
	double tmp;
	if (y <= -6.5e-10) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= 1.9e-137) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (y <= 3.1e+99) {
		tmp = t_1 + (x * (y * z));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if y <= -6.5e-10:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	elif y <= 1.9e-137:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif y <= 3.1e+99:
		tmp = t_1 + (x * (y * z))
	else:
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (y <= -6.5e-10)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (y <= 1.9e-137)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (y <= 3.1e+99)
		tmp = Float64(t_1 + Float64(x * Float64(y * z)));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(i * Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (y <= -6.5e-10)
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	elseif (y <= 1.9e-137)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif (y <= 3.1e+99)
		tmp = t_1 + (x * (y * z));
	else
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-10], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-137], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+99], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.5000000000000003e-10

   1. Initial program 60.9%

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

   3. Taylor expanded in b around 0 67.4%

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

   if -6.5000000000000003e-10 < y < 1.89999999999999999e-137

   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. Add Preprocessing

   3. Taylor expanded in y around 0 78.7%

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

      1. cancel-sign-sub-inv 78.7%

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

      2. *-commutative 78.7%

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

      3. *-commutative 78.7%

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

      4. cancel-sign-sub-inv 78.7%

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

      5. sub-neg 78.7%

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

      6. distribute-rgt-neg-out 78.7%

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

      7. mul-1-neg 78.7%

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

      8. distribute-rgt-neg-in 78.7%

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

      9. mul-1-neg 78.7%

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

      10. distribute-lft-in 81.6%

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

      11. +-commutative 81.6%

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

      12. mul-1-neg 81.6%

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

      13. unsub-neg 81.6%

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

      14. *-commutative 81.6%

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

   5. Simplified 81.6%

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

   if 1.89999999999999999e-137 < y < 3.1000000000000001e99

   1. Initial program 69.1%

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

   3. Taylor expanded in a around -inf 71.2%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in z around 0 75.2%

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

   7. Taylor expanded in x around inf 65.5%

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

      1. *-commutative 65.5%

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

   9. Simplified 65.5%

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

   if 3.1000000000000001e99 < y

   1. Initial program 64.9%

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

   3. Taylor expanded in a around -inf 62.5%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in z around 0 64.9%

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

   7. Taylor expanded in a around 0 67.2%

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

   8. Taylor expanded in t around 0 71.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + z \cdot \left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-137}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;y \leq -3.95 \cdot 10^{+146}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= y -3.95e+146)
     (* i (* y (- j)))
     (if (<= y 4.6e-200)
       t_1
       (if (<= y 4.2e-156)
         (* i (* t b))
         (if (<= y 2.8e+113) t_1 (* x (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -3.95e+146) {
		tmp = i * (y * -j);
	} else if (y <= 4.6e-200) {
		tmp = t_1;
	} else if (y <= 4.2e-156) {
		tmp = i * (t * b);
	} else if (y <= 2.8e+113) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (y <= (-3.95d+146)) then
        tmp = i * (y * -j)
    else if (y <= 4.6d-200) then
        tmp = t_1
    else if (y <= 4.2d-156) then
        tmp = i * (t * b)
    else if (y <= 2.8d+113) then
        tmp = t_1
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -3.95e+146) {
		tmp = i * (y * -j);
	} else if (y <= 4.6e-200) {
		tmp = t_1;
	} else if (y <= 4.2e-156) {
		tmp = i * (t * b);
	} else if (y <= 2.8e+113) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if y <= -3.95e+146:
		tmp = i * (y * -j)
	elif y <= 4.6e-200:
		tmp = t_1
	elif y <= 4.2e-156:
		tmp = i * (t * b)
	elif y <= 2.8e+113:
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (y <= -3.95e+146)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= 4.6e-200)
		tmp = t_1;
	elseif (y <= 4.2e-156)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 2.8e+113)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (y <= -3.95e+146)
		tmp = i * (y * -j);
	elseif (y <= 4.6e-200)
		tmp = t_1;
	elseif (y <= 4.2e-156)
		tmp = i * (t * b);
	elseif (y <= 2.8e+113)
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.95e+146], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-200], t$95$1, If[LessEqual[y, 4.2e-156], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+113], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.9499999999999999e146

   1. Initial program 55.6%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in x around 0 53.6%

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

      1. associate-*r* 53.6%

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

      2. neg-mul-1 53.6%

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

   8. Simplified 53.6%

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

   if -3.9499999999999999e146 < y < 4.60000000000000015e-200 or 4.20000000000000025e-156 < y < 2.79999999999999998e113

   1. Initial program 72.5%

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

   3. Taylor expanded in a around inf 43.5%

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

      1. +-commutative 43.5%

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

      2. mul-1-neg 43.5%

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

      3. unsub-neg 43.5%

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

      4. *-commutative 43.5%

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

   5. Simplified 43.5%

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

   if 4.60000000000000015e-200 < y < 4.20000000000000025e-156

   1. Initial program 93.0%

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

   3. Taylor expanded in a around -inf 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in i around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in b around inf 62.3%

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

       1. *-commutative 62.3%

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

   11. Simplified 62.3%

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

   if 2.79999999999999998e113 < y

   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. Add Preprocessing

   3. Taylor expanded in y around inf 74.3%

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

      1. +-commutative 74.3%

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

      2. mul-1-neg 74.3%

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

      3. unsub-neg 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in x around inf 46.2%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{+146}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.05e-32)
     t_2
     (if (<= b 5.2e-263)
       t_1
       (if (<= b 1.5e-221) (* x (* y z)) (if (<= b 8.2e-170) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.05e-32) {
		tmp = t_2;
	} else if (b <= 5.2e-263) {
		tmp = t_1;
	} else if (b <= 1.5e-221) {
		tmp = x * (y * z);
	} else if (b <= 8.2e-170) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.05d-32)) then
        tmp = t_2
    else if (b <= 5.2d-263) then
        tmp = t_1
    else if (b <= 1.5d-221) then
        tmp = x * (y * z)
    else if (b <= 8.2d-170) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.05e-32) {
		tmp = t_2;
	} else if (b <= 5.2e-263) {
		tmp = t_1;
	} else if (b <= 1.5e-221) {
		tmp = x * (y * z);
	} else if (b <= 8.2e-170) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.05e-32:
		tmp = t_2
	elif b <= 5.2e-263:
		tmp = t_1
	elif b <= 1.5e-221:
		tmp = x * (y * z)
	elif b <= 8.2e-170:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.05e-32)
		tmp = t_2;
	elseif (b <= 5.2e-263)
		tmp = t_1;
	elseif (b <= 1.5e-221)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 8.2e-170)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.05e-32)
		tmp = t_2;
	elseif (b <= 5.2e-263)
		tmp = t_1;
	elseif (b <= 1.5e-221)
		tmp = x * (y * z);
	elseif (b <= 8.2e-170)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e-32], t$95$2, If[LessEqual[b, 5.2e-263], t$95$1, If[LessEqual[b, 1.5e-221], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-170], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05e-32 or 8.19999999999999931e-170 < b

   1. Initial program 70.1%

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

   3. Taylor expanded in b around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   if -1.05e-32 < b < 5.2000000000000001e-263 or 1.5000000000000001e-221 < b < 8.19999999999999931e-170

   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. Add Preprocessing

   3. Taylor expanded in a around inf 56.1%

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

      1. +-commutative 56.1%

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

      2. mul-1-neg 56.1%

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

      3. unsub-neg 56.1%

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

      4. *-commutative 56.1%

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

   5. Simplified 56.1%

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

   if 5.2000000000000001e-263 < b < 1.5000000000000001e-221

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in x around inf 71.7%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-263}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -2.75e-71)
     t_2
     (if (<= t -3.9e-174)
       t_1
       (if (<= t 2.85e-285)
         (* j (- (* a c) (* y i)))
         (if (<= t 1e-12) 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 = z * ((x * y) - (b * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.75e-71) {
		tmp = t_2;
	} else if (t <= -3.9e-174) {
		tmp = t_1;
	} else if (t <= 2.85e-285) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 1e-12) {
		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 = z * ((x * y) - (b * c))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-2.75d-71)) then
        tmp = t_2
    else if (t <= (-3.9d-174)) then
        tmp = t_1
    else if (t <= 2.85d-285) then
        tmp = j * ((a * c) - (y * i))
    else if (t <= 1d-12) 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 = z * ((x * y) - (b * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.75e-71) {
		tmp = t_2;
	} else if (t <= -3.9e-174) {
		tmp = t_1;
	} else if (t <= 2.85e-285) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 1e-12) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.75e-71:
		tmp = t_2
	elif t <= -3.9e-174:
		tmp = t_1
	elif t <= 2.85e-285:
		tmp = j * ((a * c) - (y * i))
	elif t <= 1e-12:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.75e-71)
		tmp = t_2;
	elseif (t <= -3.9e-174)
		tmp = t_1;
	elseif (t <= 2.85e-285)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (t <= 1e-12)
		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 = z * ((x * y) - (b * c));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.75e-71)
		tmp = t_2;
	elseif (t <= -3.9e-174)
		tmp = t_1;
	elseif (t <= 2.85e-285)
		tmp = j * ((a * c) - (y * i));
	elseif (t <= 1e-12)
		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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.75e-71], t$95$2, If[LessEqual[t, -3.9e-174], t$95$1, If[LessEqual[t, 2.85e-285], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-12], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7499999999999999e-71 or 9.9999999999999998e-13 < t

   1. Initial program 65.0%

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

   3. Taylor expanded in a around -inf 66.9%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. *-commutative 65.4%

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

   8. Simplified 65.4%

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

   if -2.7499999999999999e-71 < t < -3.8999999999999999e-174 or 2.85000000000000013e-285 < t < 9.9999999999999998e-13

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 68.4%

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

   if -3.8999999999999999e-174 < t < 2.85000000000000013e-285

   1. Initial program 83.7%

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

   3. Taylor expanded in a around -inf 75.5%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in j around inf 56.7%

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

      1. distribute-lft-out-- 56.7%

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

      2. *-commutative 56.7%

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

   8. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y - c \cdot a\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-174}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 10^{-12}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+83}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.02e+81)
   (* j (* a c))
   (if (<= a -3.8e-141)
     (* t (* b i))
     (if (<= a 4.9e-219)
       (* x (* y z))
       (if (<= a 4.5e+83) (* b (* z (- c))) (* a (* x (- t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.02e+81) {
		tmp = j * (a * c);
	} else if (a <= -3.8e-141) {
		tmp = t * (b * i);
	} else if (a <= 4.9e-219) {
		tmp = x * (y * z);
	} else if (a <= 4.5e+83) {
		tmp = b * (z * -c);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.02d+81)) then
        tmp = j * (a * c)
    else if (a <= (-3.8d-141)) then
        tmp = t * (b * i)
    else if (a <= 4.9d-219) then
        tmp = x * (y * z)
    else if (a <= 4.5d+83) then
        tmp = b * (z * -c)
    else
        tmp = a * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.02e+81) {
		tmp = j * (a * c);
	} else if (a <= -3.8e-141) {
		tmp = t * (b * i);
	} else if (a <= 4.9e-219) {
		tmp = x * (y * z);
	} else if (a <= 4.5e+83) {
		tmp = b * (z * -c);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.02e+81:
		tmp = j * (a * c)
	elif a <= -3.8e-141:
		tmp = t * (b * i)
	elif a <= 4.9e-219:
		tmp = x * (y * z)
	elif a <= 4.5e+83:
		tmp = b * (z * -c)
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.02e+81)
		tmp = Float64(j * Float64(a * c));
	elseif (a <= -3.8e-141)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 4.9e-219)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 4.5e+83)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.02e+81)
		tmp = j * (a * c);
	elseif (a <= -3.8e-141)
		tmp = t * (b * i);
	elseif (a <= 4.9e-219)
		tmp = x * (y * z);
	elseif (a <= 4.5e+83)
		tmp = b * (z * -c);
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.02e+81], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-141], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e-219], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+83], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.01999999999999992e81

   1. Initial program 49.2%

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

   3. Taylor expanded in a around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in c around inf 37.8%

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

      1. *-commutative 37.8%

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

   8. Simplified 37.8%

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

   9. Taylor expanded in a around 0 37.8%

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

       1. associate-*r* 38.0%

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

   11. Simplified 38.0%

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

   if -1.01999999999999992e81 < a < -3.79999999999999987e-141

   1. Initial program 76.5%

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

   3. Taylor expanded in a around -inf 76.8%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in i around inf 51.0%

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

      1. +-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in b around inf 42.5%

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

       1. *-commutative 42.5%

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

   11. Simplified 42.5%

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

   12. Taylor expanded in i around 0 42.5%

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

       1. associate-*r* 42.6%

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

   14. Simplified 42.6%

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

   if -3.79999999999999987e-141 < a < 4.8999999999999999e-219

   1. Initial program 82.2%

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

   3. Taylor expanded in y around inf 50.0%

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

      1. +-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in x around inf 42.4%

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

   if 4.8999999999999999e-219 < a < 4.4999999999999999e83

   1. Initial program 75.4%

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

   3. Taylor expanded in a around -inf 67.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in z around 0 75.4%

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

   7. Taylor expanded in a around 0 65.9%

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

   8. Taylor expanded in c around inf 42.0%

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

      1. mul-1-neg 42.0%

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

   10. Simplified 42.0%

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

   if 4.4999999999999999e83 < a

   1. Initial program 68.4%

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

   3. Taylor expanded in a around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in c around 0 44.2%

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

      1. mul-1-neg 44.2%

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

      2. *-commutative 44.2%

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

      3. distribute-rgt-neg-in 44.2%

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

      4. distribute-rgt-neg-in 44.2%

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

   8. Simplified 44.2%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+83}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -8 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{+85}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))))
   (if (<= a -8e+107)
     t_1
     (if (<= a -2.75e-132)
       (* t (* b i))
       (if (<= a 4.6e-219)
         (* x (* y z))
         (if (<= a 1e+85) (* b (* z (- c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (a <= -8e+107) {
		tmp = t_1;
	} else if (a <= -2.75e-132) {
		tmp = t * (b * i);
	} else if (a <= 4.6e-219) {
		tmp = x * (y * z);
	} else if (a <= 1e+85) {
		tmp = b * (z * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x * -a)
    if (a <= (-8d+107)) then
        tmp = t_1
    else if (a <= (-2.75d-132)) then
        tmp = t * (b * i)
    else if (a <= 4.6d-219) then
        tmp = x * (y * z)
    else if (a <= 1d+85) then
        tmp = b * (z * -c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (a <= -8e+107) {
		tmp = t_1;
	} else if (a <= -2.75e-132) {
		tmp = t * (b * i);
	} else if (a <= 4.6e-219) {
		tmp = x * (y * z);
	} else if (a <= 1e+85) {
		tmp = b * (z * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	tmp = 0
	if a <= -8e+107:
		tmp = t_1
	elif a <= -2.75e-132:
		tmp = t * (b * i)
	elif a <= 4.6e-219:
		tmp = x * (y * z)
	elif a <= 1e+85:
		tmp = b * (z * -c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (a <= -8e+107)
		tmp = t_1;
	elseif (a <= -2.75e-132)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 4.6e-219)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 1e+85)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (x * -a);
	tmp = 0.0;
	if (a <= -8e+107)
		tmp = t_1;
	elseif (a <= -2.75e-132)
		tmp = t * (b * i);
	elseif (a <= 4.6e-219)
		tmp = x * (y * z);
	elseif (a <= 1e+85)
		tmp = b * (z * -c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+107], t$95$1, If[LessEqual[a, -2.75e-132], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-219], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+85], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.9999999999999998e107 or 1e85 < a

   1. Initial program 59.5%

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

   3. Taylor expanded in a around -inf 68.9%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. *-commutative 56.1%

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

   8. Simplified 56.1%

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

   9. Taylor expanded in i around 0 45.6%

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

       1. mul-1-neg 45.6%

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

       2. *-commutative 45.6%

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

       3. distribute-rgt-neg-in 45.6%

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

   11. Simplified 45.6%

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

   if -7.9999999999999998e107 < a < -2.75e-132

   1. Initial program 71.8%

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

   3. Taylor expanded in a around -inf 74.6%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in i around inf 47.4%

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

      1. +-commutative 47.4%

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

      2. mul-1-neg 47.4%

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

      3. unsub-neg 47.4%

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

   8. Simplified 47.4%

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

   9. Taylor expanded in b around inf 39.8%

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

       1. *-commutative 39.8%

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

   11. Simplified 39.8%

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

   12. Taylor expanded in i around 0 39.8%

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

       1. associate-*r* 39.9%

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

   14. Simplified 39.9%

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

   if -2.75e-132 < a < 4.59999999999999977e-219

   1. Initial program 82.2%

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

   3. Taylor expanded in y around inf 50.0%

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

      1. +-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in x around inf 42.4%

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

   if 4.59999999999999977e-219 < a < 1e85

   1. Initial program 75.4%

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

   3. Taylor expanded in a around -inf 67.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in z around 0 75.4%

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

   7. Taylor expanded in a around 0 65.9%

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

   8. Taylor expanded in c around inf 42.0%

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

      1. mul-1-neg 42.0%

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

   10. Simplified 42.0%

       \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{+85}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -1900000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -1900000000.0)
     t_1
     (if (<= t -2.25e-297)
       (* b (* z (- c)))
       (if (<= t 2.25e-284)
         (* j (* a c))
         (if (<= t 2.45e+79) (* 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 = b * (t * i);
	double tmp;
	if (t <= -1900000000.0) {
		tmp = t_1;
	} else if (t <= -2.25e-297) {
		tmp = b * (z * -c);
	} else if (t <= 2.25e-284) {
		tmp = j * (a * c);
	} else if (t <= 2.45e+79) {
		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 = b * (t * i)
    if (t <= (-1900000000.0d0)) then
        tmp = t_1
    else if (t <= (-2.25d-297)) then
        tmp = b * (z * -c)
    else if (t <= 2.25d-284) then
        tmp = j * (a * c)
    else if (t <= 2.45d+79) 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 = b * (t * i);
	double tmp;
	if (t <= -1900000000.0) {
		tmp = t_1;
	} else if (t <= -2.25e-297) {
		tmp = b * (z * -c);
	} else if (t <= 2.25e-284) {
		tmp = j * (a * c);
	} else if (t <= 2.45e+79) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if t <= -1900000000.0:
		tmp = t_1
	elif t <= -2.25e-297:
		tmp = b * (z * -c)
	elif t <= 2.25e-284:
		tmp = j * (a * c)
	elif t <= 2.45e+79:
		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(b * Float64(t * i))
	tmp = 0.0
	if (t <= -1900000000.0)
		tmp = t_1;
	elseif (t <= -2.25e-297)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (t <= 2.25e-284)
		tmp = Float64(j * Float64(a * c));
	elseif (t <= 2.45e+79)
		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 = b * (t * i);
	tmp = 0.0;
	if (t <= -1900000000.0)
		tmp = t_1;
	elseif (t <= -2.25e-297)
		tmp = b * (z * -c);
	elseif (t <= 2.25e-284)
		tmp = j * (a * c);
	elseif (t <= 2.45e+79)
		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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1900000000.0], t$95$1, If[LessEqual[t, -2.25e-297], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e-284], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e+79], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9e9 or 2.4499999999999999e79 < t

   1. Initial program 63.0%

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

   3. Taylor expanded in a around -inf 66.3%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in i around inf 53.5%

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

      1. +-commutative 53.5%

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

      2. mul-1-neg 53.5%

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

      3. unsub-neg 53.5%

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

   8. Simplified 53.5%

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

   9. Taylor expanded in b around inf 43.7%

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

       1. *-commutative 43.7%

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

   11. Simplified 43.7%

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

   12. Taylor expanded in i around 0 46.2%

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

   if -1.9e9 < t < -2.24999999999999988e-297

   1. Initial program 81.2%

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

   3. Taylor expanded in a around -inf 76.5%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around 0 77.9%

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

   7. Taylor expanded in a around 0 69.0%

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

   8. Taylor expanded in c around inf 31.9%

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

      1. mul-1-neg 31.9%

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

   10. Simplified 31.9%

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

   if -2.24999999999999988e-297 < t < 2.25e-284

   1. Initial program 70.3%

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

   3. Taylor expanded in a around inf 61.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. 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%

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

      4. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in c around inf 61.4%

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

      1. *-commutative 61.4%

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

   8. Simplified 61.4%

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

   9. Taylor expanded in a around 0 61.4%

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

       1. associate-*r* 70.9%

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

   11. Simplified 70.9%

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

   if 2.25e-284 < t < 2.4499999999999999e79

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in x around inf 41.4%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1900000000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 60.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+32} \lor \neg \left(b \leq 1.45 \cdot 10^{+79}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.5e+32) (not (<= b 1.45e+79)))
   (* b (- (* t i) (* z c)))
   (+ (* a (- (* c j) (* x t))) (* x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.5e+32) || !(b <= 1.45e+79)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (x * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.5d+32)) .or. (.not. (b <= 1.45d+79))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = (a * ((c * j) - (x * t))) + (x * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.5e+32) || !(b <= 1.45e+79)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (x * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.5e+32) or not (b <= 1.45e+79):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = (a * ((c * j) - (x * t))) + (x * (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.5e+32) || !(b <= 1.45e+79))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(x * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.5e+32) || ~((b <= 1.45e+79)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = (a * ((c * j) - (x * t))) + (x * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.5e+32], N[Not[LessEqual[b, 1.45e+79]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.5000000000000001e32 or 1.44999999999999996e79 < b

   1. Initial program 70.5%

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

   3. Taylor expanded in b around inf 68.9%

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

      1. *-commutative 68.9%

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

      2. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   if -3.5000000000000001e32 < b < 1.44999999999999996e79

   1. Initial program 68.9%

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

   3. Taylor expanded in a around -inf 70.1%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in z around 0 75.4%

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

   7. Taylor expanded in x around inf 61.5%

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

      1. *-commutative 61.5%

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

   9. Simplified 61.5%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+32} \lor \neg \left(b \leq 1.45 \cdot 10^{+79}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+215} \lor \neg \left(c \leq 2.5 \cdot 10^{-22}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.2e+215) (not (<= c 2.5e-22))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.2e+215) || !(c <= 2.5e-22)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * 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) :: tmp
    if ((c <= (-1.2d+215)) .or. (.not. (c <= 2.5d-22))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * 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 tmp;
	if ((c <= -1.2e+215) || !(c <= 2.5e-22)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.2e+215) or not (c <= 2.5e-22):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.2e+215) || !(c <= 2.5e-22))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.2e+215) || ~((c <= 2.5e-22)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.2e+215], N[Not[LessEqual[c, 2.5e-22]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.2e215 or 2.49999999999999977e-22 < c

   1. Initial program 56.5%

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

   3. Taylor expanded in a around inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

      4. *-commutative 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in c around inf 43.0%

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

      1. *-commutative 43.0%

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

   8. Simplified 43.0%

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

   if -1.2e215 < c < 2.49999999999999977e-22

   1. Initial program 76.5%

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

   3. Taylor expanded in a around -inf 77.6%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in i around inf 47.7%

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

      1. +-commutative 47.7%

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

      2. mul-1-neg 47.7%

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

      3. unsub-neg 47.7%

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

   8. Simplified 47.7%

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

   9. Taylor expanded in b around inf 28.7%

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

       1. *-commutative 28.7%

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

   11. Simplified 28.7%

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

   12. Taylor expanded in i around 0 29.2%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+215} \lor \neg \left(c \leq 2.5 \cdot 10^{-22}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-46} \lor \neg \left(t \leq 2.8 \cdot 10^{+81}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -3.3e-46) (not (<= t 2.8e+81))) (* b (* t i)) (* x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -3.3e-46) || !(t <= 2.8e+81)) {
		tmp = b * (t * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-3.3d-46)) .or. (.not. (t <= 2.8d+81))) then
        tmp = b * (t * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -3.3e-46) || !(t <= 2.8e+81)) {
		tmp = b * (t * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -3.3e-46) or not (t <= 2.8e+81):
		tmp = b * (t * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -3.3e-46) || !(t <= 2.8e+81))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -3.3e-46) || ~((t <= 2.8e+81)))
		tmp = b * (t * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -3.3e-46], N[Not[LessEqual[t, 2.8e+81]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.30000000000000013e-46 or 2.79999999999999995e81 < 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. Add Preprocessing

   3. Taylor expanded in a around -inf 66.1%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in i around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in b around inf 42.4%

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

       1. *-commutative 42.4%

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

   11. Simplified 42.4%

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

   12. Taylor expanded in i around 0 44.6%

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

   if -3.30000000000000013e-46 < t < 2.79999999999999995e81

   1. Initial program 74.5%

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

   3. Taylor expanded in y around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in x around inf 34.2%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-46} \lor \neg \left(t \leq 2.8 \cdot 10^{+81}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.3% 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 69.6%

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

3. Taylor expanded in a around inf 36.4%

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

   1. +-commutative 36.4%

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

   2. mul-1-neg 36.4%

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

   3. unsub-neg 36.4%

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

   4. *-commutative 36.4%

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

5. Simplified 36.4%

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

6. Taylor expanded in c around inf 20.8%

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

   1. *-commutative 20.8%

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

8. Simplified 20.8%

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

9. Final simplification 20.8%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

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 2024021 
(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)))))