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

Percentage Accurate: 89.3% → 94.7%

Time: 8.9s

Alternatives: 11

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: 89.3% 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: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ (- (* y z) x) (- x (* z t))) x) (- -1.0 x))))
   (if (<= t_1 5e+301) t_1 (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x);
	double tmp;
	if (t_1 <= 5e+301) {
		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 = ((((y * z) - x) / (x - (z * t))) - x) / ((-1.0d0) - x)
    if (t_1 <= 5d+301) 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 = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x);
	double tmp;
	if (t_1 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x)
	tmp = 0
	if t_1 <= 5e+301:
		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(Float64(y * z) - x) / Float64(x - Float64(z * t))) - x) / Float64(-1.0 - x))
	tmp = 0.0
	if (t_1 <= 5e+301)
		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 = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x);
	tmp = 0.0;
	if (t_1 <= 5e+301)
		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[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+301], 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))) < 5.0000000000000004e301

   1. Initial program 97.7%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 32.0%

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

      1. *-commutative 32.0%

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

   3. Simplified 32.0%

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

   5. Taylor expanded in z around inf 82.0%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x} \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+26} \lor \neg \left(z \leq 5.5 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e+26) (not (<= z 5.5e-27)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ (- x (* y z)) x)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+26) || !(z <= 5.5e-27)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + ((x - (y * z)) / 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 <= (-5.5d+26)) .or. (.not. (z <= 5.5d-27))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + ((x - (y * z)) / 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 <= -5.5e+26) || !(z <= 5.5e-27)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e+26) or not (z <= 5.5e-27):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e+26) || !(z <= 5.5e-27))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / x)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e+26) || ~((z <= 5.5e-27)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e+26], N[Not[LessEqual[z, 5.5e-27]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999997e26 or 5.5000000000000002e-27 < z

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in z around inf 89.7%

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

   if -5.4999999999999997e26 < z < 5.5000000000000002e-27

   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 t around 0 85.0%

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

      1. fma-neg 85.0%

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

      2. associate-*r/ 85.0%

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

      3. neg-mul-1 85.0%

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

      4. fma-neg 85.0%

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

      5. *-commutative 85.0%

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

   7. Simplified 85.0%

      \[\leadsto \frac{x + \color{blue}{\frac{-\left(z \cdot y - x\right)}{x}}}{x + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+26} \lor \neg \left(z \leq 5.5 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+26} \lor \neg \left(z \leq 5.6 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.8e+26) (not (<= z 5.6e-28)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ (- x (* y z)) x)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.8e+26) || !(z <= 5.6e-28)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + ((x - (y * z)) / 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 <= (-9.8d+26)) .or. (.not. (z <= 5.6d-28))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + ((x - (y * z)) / 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 <= -9.8e+26) || !(z <= 5.6e-28)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.8e+26) or not (z <= 5.6e-28):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.8e+26) || !(z <= 5.6e-28))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / x)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.8e+26) || ~((z <= 5.6e-28)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.8e+26], N[Not[LessEqual[z, 5.6e-28]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999947e26 or 5.5999999999999996e-28 < z

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in z around inf 89.7%

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

   if -9.79999999999999947e26 < z < 5.5999999999999996e-28

   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 t around 0 85.0%

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

      1. fma-neg 85.0%

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

      2. associate-*r/ 85.0%

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

      3. neg-mul-1 85.0%

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

      4. fma-neg 85.0%

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

      5. *-commutative 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in x around 0 85.0%

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

      1. neg-mul-1 85.0%

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

      2. unsub-neg 85.0%

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

   10. Simplified 85.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+26} \lor \neg \left(z \leq 5.6 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+26} \lor \neg \left(z \leq 9.6 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.9e+26) (not (<= z 9.6e-27)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* y (/ (/ z x) (- -1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.9e+26) || !(z <= 9.6e-27)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (y * ((z / x) / (-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 ((z <= (-5.9d+26)) .or. (.not. (z <= 9.6d-27))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + (y * ((z / x) / ((-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 ((z <= -5.9e+26) || !(z <= 9.6e-27)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.9e+26) or not (z <= 9.6e-27):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.9e+26) || !(z <= 9.6e-27))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(y * Float64(Float64(z / x) / Float64(-1.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.9e+26) || ~((z <= 9.6e-27)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.9e+26], N[Not[LessEqual[z, 9.6e-27]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(N[(z / x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9000000000000003e26 or 9.60000000000000008e-27 < z

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in z around inf 89.7%

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

   if -5.9000000000000003e26 < z < 9.60000000000000008e-27

   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 t around 0 85.0%

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

      1. fma-neg 85.0%

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

      2. associate-*r/ 85.0%

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

      3. neg-mul-1 85.0%

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

      4. fma-neg 85.0%

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

      5. *-commutative 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in x around 0 85.0%

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

      1. neg-mul-1 85.0%

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

      2. unsub-neg 85.0%

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

   10. Simplified 85.0%

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

   11. Taylor expanded in y around 0 85.0%

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

       1. rgt-mult-inverse 84.8%

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

       2. mul-1-neg 84.8%

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

       3. associate-/l* 84.8%

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

       4. distribute-rgt-neg-in 84.8%

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

       5. mul-1-neg 84.8%

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

       6. distribute-lft-in 84.8%

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

       7. distribute-rgt-in 84.8%

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

       8. lft-mult-inverse 85.0%

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

       9. mul-1-neg 85.0%

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

       10. distribute-frac-neg 85.0%

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

       11. +-commutative 85.0%

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

       12. distribute-lft-in 85.0%

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

       13. *-rgt-identity 85.0%

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

       14. fma-undefine 85.0%

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

       15. associate-*l/ 85.0%

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

       16. distribute-lft-neg-in 85.0%

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

       17. *-commutative 85.0%

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

       18. fma-undefine 85.0%

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

       19. *-rgt-identity 85.0%

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

   13. Simplified 85.0%

       \[\leadsto \color{blue}{1 + \left(-y \cdot \frac{\frac{z}{x}}{x + 1}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+26} \lor \neg \left(z \leq 9.6 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1080000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;\left(x + \frac{y}{t}\right) \cdot \frac{1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1080000000000.0)
   1.0
   (if (<= x 2.1e+22) (* (+ x (/ y t)) (/ 1.0 (+ x 1.0))) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1080000000000.0) {
		tmp = 1.0;
	} else if (x <= 2.1e+22) {
		tmp = (x + (y / t)) * (1.0 / (x + 1.0));
	} else {
		tmp = 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 (x <= (-1080000000000.0d0)) then
        tmp = 1.0d0
    else if (x <= 2.1d+22) then
        tmp = (x + (y / t)) * (1.0d0 / (x + 1.0d0))
    else
        tmp = 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 (x <= -1080000000000.0) {
		tmp = 1.0;
	} else if (x <= 2.1e+22) {
		tmp = (x + (y / t)) * (1.0 / (x + 1.0));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1080000000000.0:
		tmp = 1.0
	elif x <= 2.1e+22:
		tmp = (x + (y / t)) * (1.0 / (x + 1.0))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1080000000000.0)
		tmp = 1.0;
	elseif (x <= 2.1e+22)
		tmp = Float64(Float64(x + Float64(y / t)) * Float64(1.0 / Float64(x + 1.0)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1080000000000.0)
		tmp = 1.0;
	elseif (x <= 2.1e+22)
		tmp = (x + (y / t)) * (1.0 / (x + 1.0));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1080000000000.0], 1.0, If[LessEqual[x, 2.1e+22], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.08e12

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in z around inf 74.9%

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

   6. Taylor expanded in x around inf 97.0%

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

   if -1.08e12 < x < 2.0999999999999998e22

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in z around inf 65.7%

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

      1. div-inv 65.7%

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

   7. Applied egg-rr 65.7%

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

      1. *-commutative 65.7%

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

      2. +-commutative 65.7%

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

   9. Simplified 65.7%

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

   if 2.0999999999999998e22 < x

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in t around inf 91.2%

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

      1. +-commutative 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1080000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;\left(x + \frac{y}{t}\right) \cdot \frac{1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-15} \lor \neg \left(x \leq 1.65 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e-15) (not (<= x 1.65e-59)))
   (/ x (+ x 1.0))
   (* y (/ z (- (* z t) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e-15) || !(x <= 1.65e-59)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y * (z / ((z * t) - 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 <= (-7.2d-15)) .or. (.not. (x <= 1.65d-59))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y * (z / ((z * t) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e-15) || !(x <= 1.65e-59)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y * (z / ((z * t) - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e-15) or not (x <= 1.65e-59):
		tmp = x / (x + 1.0)
	else:
		tmp = y * (z / ((z * t) - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e-15) || !(x <= 1.65e-59))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e-15) || ~((x <= 1.65e-59)))
		tmp = x / (x + 1.0);
	else
		tmp = y * (z / ((z * t) - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e-15], N[Not[LessEqual[x, 1.65e-59]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2000000000000002e-15 or 1.64999999999999991e-59 < x

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around inf 86.5%

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

      1. +-commutative 86.5%

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

   7. Simplified 86.5%

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

   if -7.2000000000000002e-15 < x < 1.64999999999999991e-59

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in y around inf 64.9%

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

      1. associate-/l* 69.4%

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

      2. associate-/r* 69.4%

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

      3. +-commutative 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in x around 0 69.3%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-15} \lor \neg \left(x \leq 1.65 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -130000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+36}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -130000000.0)
   1.0
   (if (<= x 2.65e+36) (/ (+ x (/ y t)) (+ x 1.0)) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -130000000.0) {
		tmp = 1.0;
	} else if (x <= 2.65e+36) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 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 (x <= (-130000000.0d0)) then
        tmp = 1.0d0
    else if (x <= 2.65d+36) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 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 (x <= -130000000.0) {
		tmp = 1.0;
	} else if (x <= 2.65e+36) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -130000000.0:
		tmp = 1.0
	elif x <= 2.65e+36:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -130000000.0)
		tmp = 1.0;
	elseif (x <= 2.65e+36)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -130000000.0)
		tmp = 1.0;
	elseif (x <= 2.65e+36)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -130000000.0], 1.0, If[LessEqual[x, 2.65e+36], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e8

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in z around inf 74.9%

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

   6. Taylor expanded in x around inf 97.0%

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

   if -1.3e8 < x < 2.65e36

   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 65.9%

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

   if 2.65e36 < x

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in t around inf 91.1%

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

      1. +-commutative 91.1%

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

   7. Simplified 91.1%

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

Alternative 8: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -175:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -175.0)
   1.0
   (if (<= x 5.1e-59) (/ y (* t (+ x 1.0))) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -175.0) {
		tmp = 1.0;
	} else if (x <= 5.1e-59) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 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 (x <= (-175.0d0)) then
        tmp = 1.0d0
    else if (x <= 5.1d-59) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = 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 (x <= -175.0) {
		tmp = 1.0;
	} else if (x <= 5.1e-59) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -175.0:
		tmp = 1.0
	elif x <= 5.1e-59:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -175.0)
		tmp = 1.0;
	elseif (x <= 5.1e-59)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -175.0)
		tmp = 1.0;
	elseif (x <= 5.1e-59)
		tmp = y / (t * (x + 1.0));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -175.0], 1.0, If[LessEqual[x, 5.1e-59], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -175

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in z around inf 74.9%

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

   6. Taylor expanded in x around inf 97.0%

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

   if -175 < x < 5.0999999999999996e-59

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around inf 66.1%

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

   6. Taylor expanded in y around inf 55.3%

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

      1. +-commutative 55.3%

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

   8. Simplified 55.3%

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

   if 5.0999999999999996e-59 < x

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t around inf 81.3%

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

      1. +-commutative 81.3%

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

   7. Simplified 81.3%

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

Alternative 9: 68.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{-40} \lor \neg \left(x \leq 1.9 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.1e-40) (not (<= x 1.9e-57))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.1e-40) || !(x <= 1.9e-57)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / 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) :: tmp
    if ((x <= (-5.1d-40)) .or. (.not. (x <= 1.9d-57))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.1e-40) || !(x <= 1.9e-57)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.1e-40) or not (x <= 1.9e-57):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.1e-40) || !(x <= 1.9e-57))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.1e-40) || ~((x <= 1.9e-57)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.1e-40], N[Not[LessEqual[x, 1.9e-57]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.10000000000000037e-40 or 1.8999999999999999e-57 < x

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in t around inf 84.9%

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

      1. +-commutative 84.9%

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

   7. Simplified 84.9%

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

   if -5.10000000000000037e-40 < x < 1.8999999999999999e-57

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in z around inf 67.2%

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

   6. Taylor expanded in x around 0 56.6%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{-40} \lor \neg \left(x \leq 1.9 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-54}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.5e-54) 1.0 (if (<= x 1.2e-31) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.5e-54) {
		tmp = 1.0;
	} else if (x <= 1.2e-31) {
		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 <= (-7.5d-54)) then
        tmp = 1.0d0
    else if (x <= 1.2d-31) 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 <= -7.5e-54) {
		tmp = 1.0;
	} else if (x <= 1.2e-31) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.5e-54:
		tmp = 1.0
	elif x <= 1.2e-31:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.5e-54)
		tmp = 1.0;
	elseif (x <= 1.2e-31)
		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 <= -7.5e-54)
		tmp = 1.0;
	elseif (x <= 1.2e-31)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.5e-54], 1.0, If[LessEqual[x, 1.2e-31], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000005e-54 or 1.2e-31 < x

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around inf 70.7%

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

   6. Taylor expanded in x around inf 85.2%

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

   if -7.5000000000000005e-54 < x < 1.2e-31

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in z around inf 68.6%

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

   6. Taylor expanded in x around 0 56.2%

      \[\leadsto \color{blue}{\frac{y}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 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 89.2%

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

   1. *-commutative 89.2%

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

3. Simplified 89.2%

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

5. Taylor expanded in z around inf 69.8%

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

6. Taylor expanded in x around inf 55.7%

   \[\leadsto \color{blue}{1} \]
7. Add Preprocessing

Developer target: 99.4% 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 2024103 
(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)))