Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.1% → 94.8%

Time: 12.8s

Alternatives: 15

Speedup: 0.4×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := z \cdot t - x\\ \mathbf{if}\;\frac{\frac{t\_1}{t\_2} - x}{-1 - x} \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\frac{x - \frac{1}{\frac{t\_2}{t\_1}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} + \frac{\frac{x}{z}}{-1 - x}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (- (* z t) x)))
   (if (<= (/ (- (/ t_1 t_2) x) (- -1.0 x)) 5e+263)
     (/ (- x (/ 1.0 (/ t_2 t_1))) (+ x 1.0))
     (+ (/ x (+ x 1.0)) (/ (+ (/ y (+ x 1.0)) (/ (/ x z) (- -1.0 x))) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * z);
	double t_2 = (z * t) - x;
	double tmp;
	if ((((t_1 / t_2) - x) / (-1.0 - x)) <= 5e+263) {
		tmp = (x - (1.0 / (t_2 / t_1))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = (z * t) - x
    if ((((t_1 / t_2) - x) / ((-1.0d0) - x)) <= 5d+263) then
        tmp = (x - (1.0d0 / (t_2 / t_1))) / (x + 1.0d0)
    else
        tmp = (x / (x + 1.0d0)) + (((y / (x + 1.0d0)) + ((x / z) / ((-1.0d0) - x))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * z);
	double t_2 = (z * t) - x;
	double tmp;
	if ((((t_1 / t_2) - x) / (-1.0 - x)) <= 5e+263) {
		tmp = (x - (1.0 / (t_2 / t_1))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * z)
	t_2 = (z * t) - x
	tmp = 0
	if (((t_1 / t_2) - x) / (-1.0 - x)) <= 5e+263:
		tmp = (x - (1.0 / (t_2 / t_1))) / (x + 1.0)
	else:
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (Float64(Float64(Float64(t_1 / t_2) - x) / Float64(-1.0 - x)) <= 5e+263)
		tmp = Float64(Float64(x - Float64(1.0 / Float64(t_2 / t_1))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(Float64(y / Float64(x + 1.0)) + Float64(Float64(x / z) / Float64(-1.0 - x))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * z);
	t_2 = (z * t) - x;
	tmp = 0.0;
	if ((((t_1 / t_2) - x) / (-1.0 - x)) <= 5e+263)
		tmp = (x - (1.0 / (t_2 / t_1))) / (x + 1.0);
	else
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[N[(N[(N[(t$95$1 / t$95$2), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision], 5e+263], N[(N[(x - N[(1.0 / N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000022e263

   1. Initial program 96.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 96.9%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 96.9%

         \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{z \cdot t - x}{y \cdot z - x}}}}{x + 1} \]

      2. inv-pow 96.9%

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

      3. fma-neg 96.9%

         \[\leadsto \frac{x + {\left(\frac{z \cdot t - x}{\color{blue}{\mathsf{fma}\left(y, z, -x\right)}}\right)}^{-1}}{x + 1} \]

   6. Applied egg-rr 96.9%

      \[\leadsto \frac{x + \color{blue}{{\left(\frac{z \cdot t - x}{\mathsf{fma}\left(y, z, -x\right)}\right)}^{-1}}}{x + 1} \]
   7. Step-by-step derivation

      1. unpow-1 96.9%

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

      2. div-sub 96.0%

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

      3. *-commutative 96.0%

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

      4. div-sub 96.9%

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

      5. fma-neg 96.9%

         \[\leadsto \frac{x + \frac{1}{\frac{t \cdot z - x}{\color{blue}{y \cdot z - x}}}}{x + 1} \]

      6. *-commutative 96.9%

         \[\leadsto \frac{x + \frac{1}{\frac{t \cdot z - x}{\color{blue}{z \cdot y} - x}}}{x + 1} \]

   8. Simplified 96.9%

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t \cdot z - x}{z \cdot y - x}}}}{x + 1} \]

   if 5.00000000000000022e263 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 30.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 30.6%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 30.6%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around -inf 84.1%

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

      1. +-commutative 84.1%

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

      2. mul-1-neg 84.1%

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

      3. unsub-neg 84.1%

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

      4. +-commutative 84.1%

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

      5. sub-neg 84.1%

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

      6. mul-1-neg 84.1%

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

      7. distribute-neg-frac2 84.1%

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

      8. distribute-neg-in 84.1%

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

      9. metadata-eval 84.1%

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

      10. unsub-neg 84.1%

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

      11. mul-1-neg 84.1%

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

      12. remove-double-neg 84.1%

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

      13. associate-/r* 84.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{-1 - x} + \color{blue}{\frac{\frac{x}{z}}{1 + x}}}{t} \]

      14. +-commutative 84.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{-1 - x} + \frac{\frac{x}{z}}{\color{blue}{x + 1}}}{t} \]

   7. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{x}{x + 1} - \frac{\frac{y}{-1 - x} + \frac{\frac{x}{z}}{x + 1}}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{x - y \cdot z}{z \cdot t - x} - x}{-1 - x} \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\frac{x - \frac{1}{\frac{z \cdot t - x}{x - y \cdot z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} + \frac{\frac{x}{z}}{-1 - x}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := z \cdot t - x\\ \mathbf{if}\;\frac{\frac{t\_1}{t\_2} - x}{-1 - x} \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\frac{x - \frac{1}{\frac{t\_2}{t\_1}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (- (* z t) x)))
   (if (<= (/ (- (/ t_1 t_2) x) (- -1.0 x)) 5e+263)
     (/ (- x (/ 1.0 (/ t_2 t_1))) (+ x 1.0))
     (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * z);
	double t_2 = (z * t) - x;
	double tmp;
	if ((((t_1 / t_2) - x) / (-1.0 - x)) <= 5e+263) {
		tmp = (x - (1.0 / (t_2 / t_1))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = (z * t) - x
    if ((((t_1 / t_2) - x) / ((-1.0d0) - x)) <= 5d+263) then
        tmp = (x - (1.0d0 / (t_2 / t_1))) / (x + 1.0d0)
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * z);
	double t_2 = (z * t) - x;
	double tmp;
	if ((((t_1 / t_2) - x) / (-1.0 - x)) <= 5e+263) {
		tmp = (x - (1.0 / (t_2 / t_1))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * z)
	t_2 = (z * t) - x
	tmp = 0
	if (((t_1 / t_2) - x) / (-1.0 - x)) <= 5e+263:
		tmp = (x - (1.0 / (t_2 / t_1))) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (Float64(Float64(Float64(t_1 / t_2) - x) / Float64(-1.0 - x)) <= 5e+263)
		tmp = Float64(Float64(x - Float64(1.0 / Float64(t_2 / t_1))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * z);
	t_2 = (z * t) - x;
	tmp = 0.0;
	if ((((t_1 / t_2) - x) / (-1.0 - x)) <= 5e+263)
		tmp = (x - (1.0 / (t_2 / t_1))) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[N[(N[(N[(t$95$1 / t$95$2), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision], 5e+263], N[(N[(x - N[(1.0 / N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000022e263

   1. Initial program 96.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 96.9%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 96.9%

         \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{z \cdot t - x}{y \cdot z - x}}}}{x + 1} \]

      2. inv-pow 96.9%

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

      3. fma-neg 96.9%

         \[\leadsto \frac{x + {\left(\frac{z \cdot t - x}{\color{blue}{\mathsf{fma}\left(y, z, -x\right)}}\right)}^{-1}}{x + 1} \]

   6. Applied egg-rr 96.9%

      \[\leadsto \frac{x + \color{blue}{{\left(\frac{z \cdot t - x}{\mathsf{fma}\left(y, z, -x\right)}\right)}^{-1}}}{x + 1} \]
   7. Step-by-step derivation

      1. unpow-1 96.9%

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

      2. div-sub 96.0%

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

      3. *-commutative 96.0%

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

      4. div-sub 96.9%

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

      5. fma-neg 96.9%

         \[\leadsto \frac{x + \frac{1}{\frac{t \cdot z - x}{\color{blue}{y \cdot z - x}}}}{x + 1} \]

      6. *-commutative 96.9%

         \[\leadsto \frac{x + \frac{1}{\frac{t \cdot z - x}{\color{blue}{z \cdot y} - x}}}{x + 1} \]

   8. Simplified 96.9%

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t \cdot z - x}{z \cdot y - x}}}}{x + 1} \]

   if 5.00000000000000022e263 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 30.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 30.6%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 30.6%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.0%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{x - y \cdot z}{z \cdot t - x} - x}{-1 - x} \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\frac{x - \frac{1}{\frac{z \cdot t - x}{x - y \cdot z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x - y \cdot z}{z \cdot t - x} - x}{-1 - x}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ (- x (* y z)) (- (* z t) x)) x) (- -1.0 x))))
   (if (<= t_1 5e+263) t_1 (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((x - (y * z)) / ((z * t) - x)) - x) / (-1.0 - x);
	double tmp;
	if (t_1 <= 5e+263) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((x - (y * z)) / ((z * t) - x)) - x) / ((-1.0d0) - x)
    if (t_1 <= 5d+263) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((x - (y * z)) / ((z * t) - x)) - x) / (-1.0 - x);
	double tmp;
	if (t_1 <= 5e+263) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((x - (y * z)) / ((z * t) - x)) - x) / (-1.0 - x)
	tmp = 0
	if t_1 <= 5e+263:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(x - Float64(y * z)) / Float64(Float64(z * t) - x)) - x) / Float64(-1.0 - x))
	tmp = 0.0
	if (t_1 <= 5e+263)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((x - (y * z)) / ((z * t) - x)) - x) / (-1.0 - x);
	tmp = 0.0;
	if (t_1 <= 5e+263)
		tmp = t_1;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+263], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000022e263

   1. Initial program 96.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 5.00000000000000022e263 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 30.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 30.6%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 30.6%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.0%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{x - y \cdot z}{z \cdot t - x} - x}{-1 - x} \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\frac{\frac{x - y \cdot z}{z \cdot t - x} - x}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* t (+ x 1.0)))))
   (if (<= x -3.6e-40)
     (/ x (+ x 1.0))
     (if (<= x -2.6e-63)
       (/ y t)
       (if (<= x -8e-211)
         x
         (if (<= x 1.6e-120)
           t_1
           (if (<= x 5.4e-83) x (if (<= x 4.3e+17) t_1 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t * (x + 1.0));
	double tmp;
	if (x <= -3.6e-40) {
		tmp = x / (x + 1.0);
	} else if (x <= -2.6e-63) {
		tmp = y / t;
	} else if (x <= -8e-211) {
		tmp = x;
	} else if (x <= 1.6e-120) {
		tmp = t_1;
	} else if (x <= 5.4e-83) {
		tmp = x;
	} else if (x <= 4.3e+17) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (t * (x + 1.0d0))
    if (x <= (-3.6d-40)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-2.6d-63)) then
        tmp = y / t
    else if (x <= (-8d-211)) then
        tmp = x
    else if (x <= 1.6d-120) then
        tmp = t_1
    else if (x <= 5.4d-83) then
        tmp = x
    else if (x <= 4.3d+17) then
        tmp = t_1
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (t * (x + 1.0));
	double tmp;
	if (x <= -3.6e-40) {
		tmp = x / (x + 1.0);
	} else if (x <= -2.6e-63) {
		tmp = y / t;
	} else if (x <= -8e-211) {
		tmp = x;
	} else if (x <= 1.6e-120) {
		tmp = t_1;
	} else if (x <= 5.4e-83) {
		tmp = x;
	} else if (x <= 4.3e+17) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t * (x + 1.0))
	tmp = 0
	if x <= -3.6e-40:
		tmp = x / (x + 1.0)
	elif x <= -2.6e-63:
		tmp = y / t
	elif x <= -8e-211:
		tmp = x
	elif x <= 1.6e-120:
		tmp = t_1
	elif x <= 5.4e-83:
		tmp = x
	elif x <= 4.3e+17:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t * Float64(x + 1.0)))
	tmp = 0.0
	if (x <= -3.6e-40)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -2.6e-63)
		tmp = Float64(y / t);
	elseif (x <= -8e-211)
		tmp = x;
	elseif (x <= 1.6e-120)
		tmp = t_1;
	elseif (x <= 5.4e-83)
		tmp = x;
	elseif (x <= 4.3e+17)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t * (x + 1.0));
	tmp = 0.0;
	if (x <= -3.6e-40)
		tmp = x / (x + 1.0);
	elseif (x <= -2.6e-63)
		tmp = y / t;
	elseif (x <= -8e-211)
		tmp = x;
	elseif (x <= 1.6e-120)
		tmp = t_1;
	elseif (x <= 5.4e-83)
		tmp = x;
	elseif (x <= 4.3e+17)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e-40], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e-63], N[(y / t), $MachinePrecision], If[LessEqual[x, -8e-211], x, If[LessEqual[x, 1.6e-120], t$95$1, If[LessEqual[x, 5.4e-83], x, If[LessEqual[x, 4.3e+17], t$95$1, 1.0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.6e-40

   1. Initial program 90.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.5%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 83.4%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 83.4%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if -3.6e-40 < x < -2.6000000000000001e-63

   1. Initial program 83.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 83.3%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 83.4%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around 0 83.4%

      \[\leadsto \color{blue}{\frac{y}{t}} \]

   if -2.6000000000000001e-63 < x < -8.00000000000000069e-211 or 1.6e-120 < x < 5.39999999999999982e-83

   1. Initial program 97.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 97.1%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 47.7%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 47.7%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 47.7%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   8. Taylor expanded in x around 0 47.7%

      \[\leadsto \color{blue}{x} \]

   if -8.00000000000000069e-211 < x < 1.6e-120 or 5.39999999999999982e-83 < x < 4.3e17

   1. Initial program 89.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.7%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.3%

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

      1. associate-/l* 64.6%

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

      2. +-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in z around inf 62.1%

      \[\leadsto \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 62.1%

         \[\leadsto \frac{y}{t \cdot \color{blue}{\left(x + 1\right)}} \]

   10. Simplified 62.1%

       \[\leadsto \color{blue}{\frac{y}{t \cdot \left(x + 1\right)}} \]

   if 4.3e17 < x

   1. Initial program 86.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 86.2%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 78.1%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* t (+ x 1.0)))))
   (if (<= x -4.9e-39)
     (/ x (+ x 1.0))
     (if (<= x -3.6e-64)
       (/ y t)
       (if (<= x -8e-211)
         (* x (+ 1.0 (/ -1.0 (* z t))))
         (if (<= x 4.4e-120)
           t_1
           (if (<= x 4.1e-83) x (if (<= x 4.3e+17) t_1 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t * (x + 1.0));
	double tmp;
	if (x <= -4.9e-39) {
		tmp = x / (x + 1.0);
	} else if (x <= -3.6e-64) {
		tmp = y / t;
	} else if (x <= -8e-211) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 4.4e-120) {
		tmp = t_1;
	} else if (x <= 4.1e-83) {
		tmp = x;
	} else if (x <= 4.3e+17) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (t * (x + 1.0d0))
    if (x <= (-4.9d-39)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-3.6d-64)) then
        tmp = y / t
    else if (x <= (-8d-211)) then
        tmp = x * (1.0d0 + ((-1.0d0) / (z * t)))
    else if (x <= 4.4d-120) then
        tmp = t_1
    else if (x <= 4.1d-83) then
        tmp = x
    else if (x <= 4.3d+17) then
        tmp = t_1
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (t * (x + 1.0));
	double tmp;
	if (x <= -4.9e-39) {
		tmp = x / (x + 1.0);
	} else if (x <= -3.6e-64) {
		tmp = y / t;
	} else if (x <= -8e-211) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 4.4e-120) {
		tmp = t_1;
	} else if (x <= 4.1e-83) {
		tmp = x;
	} else if (x <= 4.3e+17) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t * (x + 1.0))
	tmp = 0
	if x <= -4.9e-39:
		tmp = x / (x + 1.0)
	elif x <= -3.6e-64:
		tmp = y / t
	elif x <= -8e-211:
		tmp = x * (1.0 + (-1.0 / (z * t)))
	elif x <= 4.4e-120:
		tmp = t_1
	elif x <= 4.1e-83:
		tmp = x
	elif x <= 4.3e+17:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t * Float64(x + 1.0)))
	tmp = 0.0
	if (x <= -4.9e-39)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -3.6e-64)
		tmp = Float64(y / t);
	elseif (x <= -8e-211)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	elseif (x <= 4.4e-120)
		tmp = t_1;
	elseif (x <= 4.1e-83)
		tmp = x;
	elseif (x <= 4.3e+17)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t * (x + 1.0));
	tmp = 0.0;
	if (x <= -4.9e-39)
		tmp = x / (x + 1.0);
	elseif (x <= -3.6e-64)
		tmp = y / t;
	elseif (x <= -8e-211)
		tmp = x * (1.0 + (-1.0 / (z * t)));
	elseif (x <= 4.4e-120)
		tmp = t_1;
	elseif (x <= 4.1e-83)
		tmp = x;
	elseif (x <= 4.3e+17)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.9e-39], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.6e-64], N[(y / t), $MachinePrecision], If[LessEqual[x, -8e-211], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-120], t$95$1, If[LessEqual[x, 4.1e-83], x, If[LessEqual[x, 4.3e+17], t$95$1, 1.0]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.89999999999999974e-39

   1. Initial program 90.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.5%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 83.4%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 83.4%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if -4.89999999999999974e-39 < x < -3.5999999999999998e-64

   1. Initial program 83.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 83.3%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 83.4%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around 0 83.4%

      \[\leadsto \color{blue}{\frac{y}{t}} \]

   if -3.5999999999999998e-64 < x < -8.00000000000000069e-211

   1. Initial program 95.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 95.1%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.6%

      \[\leadsto \color{blue}{\frac{x - \frac{x}{t \cdot z - x}}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 81.6%

         \[\leadsto \frac{x - \frac{x}{t \cdot z - x}}{\color{blue}{x + 1}} \]

   7. Simplified 81.6%

      \[\leadsto \color{blue}{\frac{x - \frac{x}{t \cdot z - x}}{x + 1}} \]

   8. Taylor expanded in x around 0 63.2%

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

   if -8.00000000000000069e-211 < x < 4.40000000000000025e-120 or 4.1e-83 < x < 4.3e17

   1. Initial program 89.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.7%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.3%

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

      1. associate-/l* 64.6%

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

      2. +-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in z around inf 62.1%

      \[\leadsto \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 62.1%

         \[\leadsto \frac{y}{t \cdot \color{blue}{\left(x + 1\right)}} \]

   10. Simplified 62.1%

       \[\leadsto \color{blue}{\frac{y}{t \cdot \left(x + 1\right)}} \]

   if 4.40000000000000025e-120 < x < 4.1e-83

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 52.1%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 52.1%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 52.1%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   8. Taylor expanded in x around 0 52.1%

      \[\leadsto \color{blue}{x} \]

   if 4.3e17 < x

   1. Initial program 86.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 86.2%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 78.1%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3e-39)
   (/ x (+ x 1.0))
   (if (<= x -1.28e-67)
     (/ y t)
     (if (<= x -8e-211)
       x
       (if (<= x 4.4e-120)
         (/ y t)
         (if (<= x 8.4e-84)
           x
           (if (<= x 100000000.0) (/ y t) (- 1.0 (/ 1.0 x)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3e-39) {
		tmp = x / (x + 1.0);
	} else if (x <= -1.28e-67) {
		tmp = y / t;
	} else if (x <= -8e-211) {
		tmp = x;
	} else if (x <= 4.4e-120) {
		tmp = y / t;
	} else if (x <= 8.4e-84) {
		tmp = x;
	} else if (x <= 100000000.0) {
		tmp = y / t;
	} else {
		tmp = 1.0 - (1.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3d-39)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-1.28d-67)) then
        tmp = y / t
    else if (x <= (-8d-211)) then
        tmp = x
    else if (x <= 4.4d-120) then
        tmp = y / t
    else if (x <= 8.4d-84) then
        tmp = x
    else if (x <= 100000000.0d0) then
        tmp = y / t
    else
        tmp = 1.0d0 - (1.0d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3e-39) {
		tmp = x / (x + 1.0);
	} else if (x <= -1.28e-67) {
		tmp = y / t;
	} else if (x <= -8e-211) {
		tmp = x;
	} else if (x <= 4.4e-120) {
		tmp = y / t;
	} else if (x <= 8.4e-84) {
		tmp = x;
	} else if (x <= 100000000.0) {
		tmp = y / t;
	} else {
		tmp = 1.0 - (1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3e-39:
		tmp = x / (x + 1.0)
	elif x <= -1.28e-67:
		tmp = y / t
	elif x <= -8e-211:
		tmp = x
	elif x <= 4.4e-120:
		tmp = y / t
	elif x <= 8.4e-84:
		tmp = x
	elif x <= 100000000.0:
		tmp = y / t
	else:
		tmp = 1.0 - (1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3e-39)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -1.28e-67)
		tmp = Float64(y / t);
	elseif (x <= -8e-211)
		tmp = x;
	elseif (x <= 4.4e-120)
		tmp = Float64(y / t);
	elseif (x <= 8.4e-84)
		tmp = x;
	elseif (x <= 100000000.0)
		tmp = Float64(y / t);
	else
		tmp = Float64(1.0 - Float64(1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3e-39)
		tmp = x / (x + 1.0);
	elseif (x <= -1.28e-67)
		tmp = y / t;
	elseif (x <= -8e-211)
		tmp = x;
	elseif (x <= 4.4e-120)
		tmp = y / t;
	elseif (x <= 8.4e-84)
		tmp = x;
	elseif (x <= 100000000.0)
		tmp = y / t;
	else
		tmp = 1.0 - (1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3e-39], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.28e-67], N[(y / t), $MachinePrecision], If[LessEqual[x, -8e-211], x, If[LessEqual[x, 4.4e-120], N[(y / t), $MachinePrecision], If[LessEqual[x, 8.4e-84], x, If[LessEqual[x, 100000000.0], N[(y / t), $MachinePrecision], N[(1.0 - N[(1.0 / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.00000000000000028e-39

   1. Initial program 90.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.5%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 83.4%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 83.4%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if -3.00000000000000028e-39 < x < -1.28e-67 or -8.00000000000000069e-211 < x < 4.40000000000000025e-120 or 8.39999999999999992e-84 < x < 1e8

   1. Initial program 89.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.9%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 76.3%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around 0 64.0%

      \[\leadsto \color{blue}{\frac{y}{t}} \]

   if -1.28e-67 < x < -8.00000000000000069e-211 or 4.40000000000000025e-120 < x < 8.39999999999999992e-84

   1. Initial program 97.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 97.1%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 47.7%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 47.7%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 47.7%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   8. Taylor expanded in x around 0 47.7%

      \[\leadsto \color{blue}{x} \]

   if 1e8 < x

   1. Initial program 85.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 85.5%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 85.6%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 85.6%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 85.6%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   8. Taylor expanded in x around inf 85.6%

      \[\leadsto \color{blue}{1 - \frac{1}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{-110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-150}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ (* y (/ z x)) (- -1.0 x))))
        (t_2 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.1e-110)
     t_2
     (if (<= t 7.5e-162)
       t_1
       (if (<= t 3.4e-150)
         (/ y (* t (+ x 1.0)))
         (if (<= t 6.2e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((y * (z / x)) / (-1.0 - x));
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.1e-110) {
		tmp = t_2;
	} else if (t <= 7.5e-162) {
		tmp = t_1;
	} else if (t <= 3.4e-150) {
		tmp = y / (t * (x + 1.0));
	} else if (t <= 6.2e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 + ((y * (z / x)) / ((-1.0d0) - x))
    t_2 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.1d-110)) then
        tmp = t_2
    else if (t <= 7.5d-162) then
        tmp = t_1
    else if (t <= 3.4d-150) then
        tmp = y / (t * (x + 1.0d0))
    else if (t <= 6.2d+45) 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 t_1 = 1.0 + ((y * (z / x)) / (-1.0 - x));
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.1e-110) {
		tmp = t_2;
	} else if (t <= 7.5e-162) {
		tmp = t_1;
	} else if (t <= 3.4e-150) {
		tmp = y / (t * (x + 1.0));
	} else if (t <= 6.2e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + ((y * (z / x)) / (-1.0 - x))
	t_2 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -1.1e-110:
		tmp = t_2
	elif t <= 7.5e-162:
		tmp = t_1
	elif t <= 3.4e-150:
		tmp = y / (t * (x + 1.0))
	elif t <= 6.2e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(y * Float64(z / x)) / Float64(-1.0 - x)))
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1.1e-110)
		tmp = t_2;
	elseif (t <= 7.5e-162)
		tmp = t_1;
	elseif (t <= 3.4e-150)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	elseif (t <= 6.2e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((y * (z / x)) / (-1.0 - x));
	t_2 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1.1e-110)
		tmp = t_2;
	elseif (t <= 7.5e-162)
		tmp = t_1;
	elseif (t <= 3.4e-150)
		tmp = y / (t * (x + 1.0));
	elseif (t <= 6.2e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e-110], t$95$2, If[LessEqual[t, 7.5e-162], t$95$1, If[LessEqual[t, 3.4e-150], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e-110 or 6.19999999999999975e45 < t

   1. Initial program 87.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.8%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 90.6%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   if -1.1e-110 < t < 7.49999999999999972e-162 or 3.39999999999999999e-150 < t < 6.19999999999999975e45

   1. Initial program 93.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 93.2%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 76.3%

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

      1. associate-+r+ 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

      4. +-commutative 76.3%

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

      5. associate-/l* 80.2%

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

      6. +-commutative 80.2%

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

   7. Simplified 80.2%

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

      1. div-sub 80.2%

         \[\leadsto \color{blue}{\frac{x + 1}{x + 1} - \frac{y \cdot \frac{z}{x}}{x + 1}} \]

      2. pow1 80.2%

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

      3. pow1 80.2%

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

      4. pow-div 80.2%

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

      5. metadata-eval 80.2%

         \[\leadsto {\left(x + 1\right)}^{\color{blue}{0}} - \frac{y \cdot \frac{z}{x}}{x + 1} \]

      6. metadata-eval 80.2%

         \[\leadsto \color{blue}{1} - \frac{y \cdot \frac{z}{x}}{x + 1} \]

   9. Applied egg-rr 80.2%

      \[\leadsto \color{blue}{1 - \frac{y \cdot \frac{z}{x}}{x + 1}} \]

   if 7.49999999999999972e-162 < t < 3.39999999999999999e-150

   1. Initial program 83.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 83.7%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 83.7%

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

      1. associate-/l* 99.2%

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

      2. +-commutative 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in z around inf 86.6%

      \[\leadsto \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 86.6%

         \[\leadsto \frac{y}{t \cdot \color{blue}{\left(x + 1\right)}} \]

   10. Simplified 86.6%

       \[\leadsto \color{blue}{\frac{y}{t \cdot \left(x + 1\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-110}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-150}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+45}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ (* y (/ z x)) (- -1.0 x))))
        (t_2 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -7.4e-109)
     t_2
     (if (<= t 6e-162)
       t_1
       (if (<= t 5.5e-150)
         (* y (/ z (* (- (* z t) x) (+ x 1.0))))
         (if (<= t 6.2e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((y * (z / x)) / (-1.0 - x));
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -7.4e-109) {
		tmp = t_2;
	} else if (t <= 6e-162) {
		tmp = t_1;
	} else if (t <= 5.5e-150) {
		tmp = y * (z / (((z * t) - x) * (x + 1.0)));
	} else if (t <= 6.2e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 + ((y * (z / x)) / ((-1.0d0) - x))
    t_2 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-7.4d-109)) then
        tmp = t_2
    else if (t <= 6d-162) then
        tmp = t_1
    else if (t <= 5.5d-150) then
        tmp = y * (z / (((z * t) - x) * (x + 1.0d0)))
    else if (t <= 6.2d+45) 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 t_1 = 1.0 + ((y * (z / x)) / (-1.0 - x));
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -7.4e-109) {
		tmp = t_2;
	} else if (t <= 6e-162) {
		tmp = t_1;
	} else if (t <= 5.5e-150) {
		tmp = y * (z / (((z * t) - x) * (x + 1.0)));
	} else if (t <= 6.2e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + ((y * (z / x)) / (-1.0 - x))
	t_2 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -7.4e-109:
		tmp = t_2
	elif t <= 6e-162:
		tmp = t_1
	elif t <= 5.5e-150:
		tmp = y * (z / (((z * t) - x) * (x + 1.0)))
	elif t <= 6.2e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(y * Float64(z / x)) / Float64(-1.0 - x)))
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -7.4e-109)
		tmp = t_2;
	elseif (t <= 6e-162)
		tmp = t_1;
	elseif (t <= 5.5e-150)
		tmp = Float64(y * Float64(z / Float64(Float64(Float64(z * t) - x) * Float64(x + 1.0))));
	elseif (t <= 6.2e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((y * (z / x)) / (-1.0 - x));
	t_2 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -7.4e-109)
		tmp = t_2;
	elseif (t <= 6e-162)
		tmp = t_1;
	elseif (t <= 5.5e-150)
		tmp = y * (z / (((z * t) - x) * (x + 1.0)));
	elseif (t <= 6.2e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e-109], t$95$2, If[LessEqual[t, 6e-162], t$95$1, If[LessEqual[t, 5.5e-150], N[(y * N[(z / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.39999999999999961e-109 or 6.19999999999999975e45 < t

   1. Initial program 87.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.8%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 90.6%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   if -7.39999999999999961e-109 < t < 5.99999999999999997e-162 or 5.4999999999999996e-150 < t < 6.19999999999999975e45

   1. Initial program 93.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 93.2%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 76.3%

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

      1. associate-+r+ 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

      4. +-commutative 76.3%

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

      5. associate-/l* 80.2%

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

      6. +-commutative 80.2%

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

   7. Simplified 80.2%

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

      1. div-sub 80.2%

         \[\leadsto \color{blue}{\frac{x + 1}{x + 1} - \frac{y \cdot \frac{z}{x}}{x + 1}} \]

      2. pow1 80.2%

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

      3. pow1 80.2%

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

      4. pow-div 80.2%

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

      5. metadata-eval 80.2%

         \[\leadsto {\left(x + 1\right)}^{\color{blue}{0}} - \frac{y \cdot \frac{z}{x}}{x + 1} \]

      6. metadata-eval 80.2%

         \[\leadsto \color{blue}{1} - \frac{y \cdot \frac{z}{x}}{x + 1} \]

   9. Applied egg-rr 80.2%

      \[\leadsto \color{blue}{1 - \frac{y \cdot \frac{z}{x}}{x + 1}} \]

   if 5.99999999999999997e-162 < t < 5.4999999999999996e-150

   1. Initial program 83.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 83.7%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 83.7%

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

      1. associate-/l* 99.2%

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

      2. +-commutative 99.2%

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

   7. Simplified 99.2%

      \[\leadsto \color{blue}{y \cdot \frac{z}{\left(x + 1\right) \cdot \left(t \cdot z - x\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-109}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+45}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-121}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.2)
   1.0
   (if (<= x 1.95e-121)
     (/ y t)
     (if (<= x 1.75e-84)
       x
       (if (<= x 100000000.0) (/ y t) (- 1.0 (/ 1.0 x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.2) {
		tmp = 1.0;
	} else if (x <= 1.95e-121) {
		tmp = y / t;
	} else if (x <= 1.75e-84) {
		tmp = x;
	} else if (x <= 100000000.0) {
		tmp = y / t;
	} else {
		tmp = 1.0 - (1.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-0.2d0)) then
        tmp = 1.0d0
    else if (x <= 1.95d-121) then
        tmp = y / t
    else if (x <= 1.75d-84) then
        tmp = x
    else if (x <= 100000000.0d0) then
        tmp = y / t
    else
        tmp = 1.0d0 - (1.0d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.2) {
		tmp = 1.0;
	} else if (x <= 1.95e-121) {
		tmp = y / t;
	} else if (x <= 1.75e-84) {
		tmp = x;
	} else if (x <= 100000000.0) {
		tmp = y / t;
	} else {
		tmp = 1.0 - (1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.2:
		tmp = 1.0
	elif x <= 1.95e-121:
		tmp = y / t
	elif x <= 1.75e-84:
		tmp = x
	elif x <= 100000000.0:
		tmp = y / t
	else:
		tmp = 1.0 - (1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.2)
		tmp = 1.0;
	elseif (x <= 1.95e-121)
		tmp = Float64(y / t);
	elseif (x <= 1.75e-84)
		tmp = x;
	elseif (x <= 100000000.0)
		tmp = Float64(y / t);
	else
		tmp = Float64(1.0 - Float64(1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.2)
		tmp = 1.0;
	elseif (x <= 1.95e-121)
		tmp = y / t;
	elseif (x <= 1.75e-84)
		tmp = x;
	elseif (x <= 100000000.0)
		tmp = y / t;
	else
		tmp = 1.0 - (1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.2], 1.0, If[LessEqual[x, 1.95e-121], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.75e-84], x, If[LessEqual[x, 100000000.0], N[(y / t), $MachinePrecision], N[(1.0 - N[(1.0 / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.20000000000000001

   1. Initial program 91.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 91.3%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 75.7%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around inf 87.1%

      \[\leadsto \color{blue}{1} \]

   if -0.20000000000000001 < x < 1.95e-121 or 1.7500000000000001e-84 < x < 1e8

   1. Initial program 90.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.5%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 72.5%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around 0 52.7%

      \[\leadsto \color{blue}{\frac{y}{t}} \]

   if 1.95e-121 < x < 1.7500000000000001e-84

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 52.1%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 52.1%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 52.1%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   8. Taylor expanded in x around 0 52.1%

      \[\leadsto \color{blue}{x} \]

   if 1e8 < x

   1. Initial program 85.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 85.5%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 85.6%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 85.6%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 85.6%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   8. Taylor expanded in x around inf 85.6%

      \[\leadsto \color{blue}{1 - \frac{1}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-121}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-16} \lor \neg \left(z \leq 7.8 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{x - z \cdot t}{x}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.6e-16) (not (<= z 7.8e-33)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ 1.0 (/ (- x (* z t)) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e-16) || !(z <= 7.8e-33)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 / ((x - (z * t)) / x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.6d-16)) .or. (.not. (z <= 7.8d-33))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (1.0d0 / ((x - (z * t)) / x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e-16) || !(z <= 7.8e-33)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 / ((x - (z * t)) / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.6e-16) or not (z <= 7.8e-33):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (1.0 / ((x - (z * t)) / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.6e-16) || !(z <= 7.8e-33))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(x - Float64(z * t)) / x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.6e-16) || ~((z <= 7.8e-33)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (1.0 / ((x - (z * t)) / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.6e-16], N[Not[LessEqual[z, 7.8e-33]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 / N[(N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999998e-16 or 7.79999999999999948e-33 < z

   1. Initial program 83.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 83.4%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 85.4%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   if -4.5999999999999998e-16 < z < 7.79999999999999948e-33

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{z \cdot t - x}{y \cdot z - x}}}}{x + 1} \]

      2. inv-pow 99.9%

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

      3. fma-neg 99.9%

         \[\leadsto \frac{x + {\left(\frac{z \cdot t - x}{\color{blue}{\mathsf{fma}\left(y, z, -x\right)}}\right)}^{-1}}{x + 1} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \frac{x + \color{blue}{{\left(\frac{z \cdot t - x}{\mathsf{fma}\left(y, z, -x\right)}\right)}^{-1}}}{x + 1} \]
   7. Step-by-step derivation

      1. unpow-1 99.9%

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

      2. div-sub 99.9%

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

      3. *-commutative 99.9%

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

      4. div-sub 99.9%

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

      5. fma-neg 99.9%

         \[\leadsto \frac{x + \frac{1}{\frac{t \cdot z - x}{\color{blue}{y \cdot z - x}}}}{x + 1} \]

      6. *-commutative 99.9%

         \[\leadsto \frac{x + \frac{1}{\frac{t \cdot z - x}{\color{blue}{z \cdot y} - x}}}{x + 1} \]

   8. Simplified 99.9%

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t \cdot z - x}{z \cdot y - x}}}}{x + 1} \]

   9. Taylor expanded in y around 0 81.6%

      \[\leadsto \frac{x + \frac{1}{\color{blue}{-1 \cdot \frac{t \cdot z - x}{x}}}}{x + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-16} \lor \neg \left(z \leq 7.8 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{x - z \cdot t}{x}}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.2)
   1.0
   (if (<= x 4.2e-120)
     (/ y t)
     (if (<= x 2.1e-84) x (if (<= x 100000000.0) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.2) {
		tmp = 1.0;
	} else if (x <= 4.2e-120) {
		tmp = y / t;
	} else if (x <= 2.1e-84) {
		tmp = x;
	} else if (x <= 100000000.0) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-0.2d0)) then
        tmp = 1.0d0
    else if (x <= 4.2d-120) then
        tmp = y / t
    else if (x <= 2.1d-84) then
        tmp = x
    else if (x <= 100000000.0d0) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.2) {
		tmp = 1.0;
	} else if (x <= 4.2e-120) {
		tmp = y / t;
	} else if (x <= 2.1e-84) {
		tmp = x;
	} else if (x <= 100000000.0) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.2:
		tmp = 1.0
	elif x <= 4.2e-120:
		tmp = y / t
	elif x <= 2.1e-84:
		tmp = x
	elif x <= 100000000.0:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.2)
		tmp = 1.0;
	elseif (x <= 4.2e-120)
		tmp = Float64(y / t);
	elseif (x <= 2.1e-84)
		tmp = x;
	elseif (x <= 100000000.0)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.2)
		tmp = 1.0;
	elseif (x <= 4.2e-120)
		tmp = y / t;
	elseif (x <= 2.1e-84)
		tmp = x;
	elseif (x <= 100000000.0)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.2], 1.0, If[LessEqual[x, 4.2e-120], N[(y / t), $MachinePrecision], If[LessEqual[x, 2.1e-84], x, If[LessEqual[x, 100000000.0], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.20000000000000001 or 1e8 < x

   1. Initial program 88.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 88.2%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 76.9%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around inf 86.2%

      \[\leadsto \color{blue}{1} \]

   if -0.20000000000000001 < x < 4.2000000000000001e-120 or 2.09999999999999998e-84 < x < 1e8

   1. Initial program 90.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.5%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 72.5%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around 0 52.7%

      \[\leadsto \color{blue}{\frac{y}{t}} \]

   if 4.2000000000000001e-120 < x < 2.09999999999999998e-84

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 52.1%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 52.1%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 52.1%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   8. Taylor expanded in x around 0 52.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-16} \lor \neg \left(z \leq 2.45 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.2e-16) (not (<= z 2.45e-31)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-16) || !(z <= 2.45e-31)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.2d-16)) .or. (.not. (z <= 2.45d-31))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-16) || !(z <= 2.45e-31)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.2e-16) or not (z <= 2.45e-31):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.2e-16) || !(z <= 2.45e-31))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.2e-16) || ~((z <= 2.45e-31)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.2e-16], N[Not[LessEqual[z, 2.45e-31]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e-16 or 2.45000000000000012e-31 < z

   1. Initial program 83.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 83.4%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 85.4%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   if -4.2000000000000002e-16 < z < 2.45000000000000012e-31

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.5%

      \[\leadsto \color{blue}{\frac{x - \frac{x}{t \cdot z - x}}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 81.5%

         \[\leadsto \frac{x - \frac{x}{t \cdot z - x}}{\color{blue}{x + 1}} \]

   7. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{x - \frac{x}{t \cdot z - x}}{x + 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-16} \lor \neg \left(z \leq 2.45 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+46}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.8e+62)
   1.0
   (if (<= x 2e+46) (/ (+ x (/ y t)) (+ x 1.0)) (- 1.0 (/ 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e+62) {
		tmp = 1.0;
	} else if (x <= 2e+46) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (1.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-5.8d+62)) then
        tmp = 1.0d0
    else if (x <= 2d+46) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - (1.0d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e+62) {
		tmp = 1.0;
	} else if (x <= 2e+46) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.8e+62:
		tmp = 1.0
	elif x <= 2e+46:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - (1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.8e+62)
		tmp = 1.0;
	elseif (x <= 2e+46)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.8e+62)
		tmp = 1.0;
	elseif (x <= 2e+46)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - (1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.8e+62], 1.0, If[LessEqual[x, 2e+46], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.79999999999999968e62

   1. Initial program 88.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 88.5%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 88.5%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 75.9%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around inf 95.4%

      \[\leadsto \color{blue}{1} \]

   if -5.79999999999999968e62 < x < 2e46

   1. Initial program 91.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 91.6%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 73.5%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   if 2e46 < x

   1. Initial program 86.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 86.3%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 91.6%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 91.6%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   8. Taylor expanded in x around inf 91.6%

      \[\leadsto \color{blue}{1 - \frac{1}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+46}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.2) 1.0 (if (<= x 4.1e-85) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.2) {
		tmp = 1.0;
	} else if (x <= 4.1e-85) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-0.2d0)) then
        tmp = 1.0d0
    else if (x <= 4.1d-85) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.2) {
		tmp = 1.0;
	} else if (x <= 4.1e-85) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.2:
		tmp = 1.0
	elif x <= 4.1e-85:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.2)
		tmp = 1.0;
	elseif (x <= 4.1e-85)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.2)
		tmp = 1.0;
	elseif (x <= 4.1e-85)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.2], 1.0, If[LessEqual[x, 4.1e-85], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.20000000000000001 or 4.09999999999999994e-85 < x

   1. Initial program 87.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.4%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 75.3%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

   6. Taylor expanded in x around inf 78.3%

      \[\leadsto \color{blue}{1} \]

   if -0.20000000000000001 < x < 4.09999999999999994e-85

   1. Initial program 92.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 92.9%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 27.6%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 27.6%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 27.6%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   8. Taylor expanded in x around 0 26.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.3% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 89.9%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
2. Step-by-step derivation

   1. *-commutative 89.9%

      \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

3. Simplified 89.9%

   \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 74.3%

   \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]

6. Taylor expanded in x around inf 50.2%

   \[\leadsto \color{blue}{1} \]

7. Final simplification 50.2%

   \[\leadsto 1 \]
8. Add Preprocessing

Developer target: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(y / Float64(t - Float64(x / z))) - Float64(x / Float64(Float64(t * z) - x)))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024075 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))