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

Percentage Accurate: 89.6% → 94.9%

Time: 13.1s

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: 89.6% 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: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ t_2 := z \cdot t - x\\ \mathbf{if}\;\frac{x + \frac{t_1}{t_2}}{x + 1} \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t_2}{t_1}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x)) (t_2 (- (* z t) x)))
   (if (<= (/ (+ x (/ t_1 t_2)) (+ x 1.0)) 2e+298)
     (/ (+ 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 = (y * z) - x;
	double t_2 = (z * t) - x;
	double tmp;
	if (((x + (t_1 / t_2)) / (x + 1.0)) <= 2e+298) {
		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 = (y * z) - x
    t_2 = (z * t) - x
    if (((x + (t_1 / t_2)) / (x + 1.0d0)) <= 2d+298) 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 = (y * z) - x;
	double t_2 = (z * t) - x;
	double tmp;
	if (((x + (t_1 / t_2)) / (x + 1.0)) <= 2e+298) {
		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 = (y * z) - x
	t_2 = (z * t) - x
	tmp = 0
	if ((x + (t_1 / t_2)) / (x + 1.0)) <= 2e+298:
		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(Float64(y * z) - x)
	t_2 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (Float64(Float64(x + Float64(t_1 / t_2)) / Float64(x + 1.0)) <= 2e+298)
		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 = (y * z) - x;
	t_2 = (z * t) - x;
	tmp = 0.0;
	if (((x + (t_1 / t_2)) / (x + 1.0)) <= 2e+298)
		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[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[N[(N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 2e+298], 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 1)) < 1.9999999999999999e298

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

   3. Simplified 96.6%

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

      1. clear-num 96.6%

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

      2. inv-pow 96.6%

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

      3. fma-neg 96.6%

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

   6. Applied egg-rr 96.6%

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

      1. unpow-1 96.6%

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

      2. *-commutative 96.6%

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

      3. fma-neg 96.6%

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

      4. *-commutative 96.6%

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

   8. Simplified 96.6%

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

   if 1.9999999999999999e298 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 21.1%

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

      1. *-commutative 21.1%

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

   3. Simplified 21.1%

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

   5. Taylor expanded in z around inf 80.4%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{y \cdot z - x}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 2e+298) 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) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 2e+298) {
		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) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= 2d+298) 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) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 2e+298) {
		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) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= 2e+298:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 2e+298)
		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) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 2e+298)
		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[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+298], 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 1)) < 1.9999999999999999e298

   1. Initial program 96.6%

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

   if 1.9999999999999999e298 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 21.1%

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

      1. *-commutative 21.1%

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

   3. Simplified 21.1%

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

   5. Taylor expanded in z around inf 80.4%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-53} \lor \neg \left(t \leq 3.1 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.8e-53) (not (<= t 3.1e-46)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- (+ x 1.0) (/ y (/ x z))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e-53) || !(t <= 3.1e-46)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y / (x / z))) / (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 ((t <= (-3.8d-53)) .or. (.not. (t <= 3.1d-46))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = ((x + 1.0d0) - (y / (x / z))) / (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 ((t <= -3.8e-53) || !(t <= 3.1e-46)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.8e-53) or not (t <= 3.1e-46):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.8e-53) || !(t <= 3.1e-46))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.8e-53) || ~((t <= 3.1e-46)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.8e-53], N[Not[LessEqual[t, 3.1e-46]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7999999999999998e-53 or 3.1000000000000001e-46 < 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 93.7%

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

   if -3.7999999999999998e-53 < t < 3.1000000000000001e-46

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around 0 82.6%

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

      1. associate-+r+ 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

      4. +-commutative 82.6%

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

      5. associate-/l* 86.4%

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

      6. +-commutative 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-53} \lor \neg \left(t \leq 3.1 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-56} \lor \neg \left(t \leq 2.6 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z}{x + 1} \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e-56) (not (<= t 2.6e-48)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* (/ z (+ x 1.0)) (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-56) || !(t <= 2.6e-48)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) * (y / 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 ((t <= (-8.5d-56)) .or. (.not. (t <= 2.6d-48))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((z / (x + 1.0d0)) * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-56) || !(t <= 2.6e-48)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e-56) or not (t <= 2.6e-48):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((z / (x + 1.0)) * (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e-56) || !(t <= 2.6e-48))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(z / Float64(x + 1.0)) * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e-56) || ~((t <= 2.6e-48)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((z / (x + 1.0)) * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e-56], N[Not[LessEqual[t, 2.6e-48]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.49999999999999932e-56 or 2.59999999999999987e-48 < 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 93.7%

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

   if -8.49999999999999932e-56 < t < 2.59999999999999987e-48

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around 0 82.6%

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

      1. associate-+r+ 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

      4. +-commutative 82.6%

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

      5. associate-/l* 86.4%

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

      6. +-commutative 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. sub-neg 82.6%

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

      3. times-frac 82.8%

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

      4. +-commutative 82.8%

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

   10. Simplified 82.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-56} \lor \neg \left(t \leq 2.6 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z}{x + 1} \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-54} \lor \neg \left(t \leq 4 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x + 1}}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.16e-54) (not (<= t 4e-44)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (/ z (+ x 1.0)) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.16e-54) || !(t <= 4e-44)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	}
	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 ((t <= (-1.16d-54)) .or. (.not. (t <= 4d-44))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((z / (x + 1.0d0)) / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.16e-54) || !(t <= 4e-44)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.16e-54) or not (t <= 4e-44):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.16e-54) || !(t <= 4e-44))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(z / Float64(x + 1.0)) / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.16e-54) || ~((t <= 4e-44)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.16e-54], N[Not[LessEqual[t, 4e-44]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.16e-54 or 3.99999999999999981e-44 < 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 93.7%

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

   if -1.16e-54 < t < 3.99999999999999981e-44

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around 0 82.6%

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

      1. associate-+r+ 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

      4. +-commutative 82.6%

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

      5. associate-/l* 86.4%

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

      6. +-commutative 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. sub-neg 82.6%

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

      3. times-frac 82.8%

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

      4. +-commutative 82.8%

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

   10. Simplified 82.8%

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

       1. *-commutative 82.8%

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

       2. clear-num 82.7%

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

       3. un-div-inv 83.2%

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

   12. Applied egg-rr 83.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-54} \lor \neg \left(t \leq 4 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x + 1}}{\frac{x}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-57} \lor \neg \left(t \leq 10^{-46}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.6e-57) (not (<= t 1e-46)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (* y z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e-57) || !(t <= 1e-46)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * z) / 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 ((t <= (-6.6d-57)) .or. (.not. (t <= 1d-46))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y * z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e-57) || !(t <= 1e-46)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * z) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.6e-57) or not (t <= 1e-46):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y * z) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.6e-57) || !(t <= 1e-46))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.6e-57) || ~((t <= 1e-46)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y * z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.6e-57], N[Not[LessEqual[t, 1e-46]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5999999999999997e-57 or 1.00000000000000002e-46 < 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 93.7%

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

   if -6.5999999999999997e-57 < t < 1.00000000000000002e-46

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around 0 82.6%

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

      1. associate-+r+ 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

      4. +-commutative 82.6%

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

      5. associate-/l* 86.4%

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

      6. +-commutative 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. sub-neg 82.6%

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

      3. times-frac 82.8%

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

      4. +-commutative 82.8%

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

   10. Simplified 82.8%

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

   11. Taylor expanded in x around 0 71.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-57} \lor \neg \left(t \leq 10^{-46}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-50}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{-93}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5e-50)
   1.0
   (if (<= x -3.4e-118) x (if (<= x 3.75e-93) (/ y t) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5e-50) {
		tmp = 1.0;
	} else if (x <= -3.4e-118) {
		tmp = x;
	} else if (x <= 3.75e-93) {
		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 <= (-5d-50)) then
        tmp = 1.0d0
    else if (x <= (-3.4d-118)) then
        tmp = x
    else if (x <= 3.75d-93) 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 <= -5e-50) {
		tmp = 1.0;
	} else if (x <= -3.4e-118) {
		tmp = x;
	} else if (x <= 3.75e-93) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5e-50:
		tmp = 1.0
	elif x <= -3.4e-118:
		tmp = x
	elif x <= 3.75e-93:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5e-50)
		tmp = 1.0;
	elseif (x <= -3.4e-118)
		tmp = x;
	elseif (x <= 3.75e-93)
		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 <= -5e-50)
		tmp = 1.0;
	elseif (x <= -3.4e-118)
		tmp = x;
	elseif (x <= 3.75e-93)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5e-50], 1.0, If[LessEqual[x, -3.4e-118], x, If[LessEqual[x, 3.75e-93], N[(y / t), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.99999999999999968e-50 or 3.75000000000000017e-93 < x

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

   3. Simplified 91.2%

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

      1. clear-num 91.2%

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

      2. inv-pow 91.2%

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

      3. fma-neg 91.2%

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

   6. Applied egg-rr 91.2%

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

      1. unpow-1 91.2%

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

      2. *-commutative 91.2%

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

      3. fma-neg 91.2%

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

      4. *-commutative 91.2%

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

   8. Simplified 91.2%

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

   9. Taylor expanded in z around inf 70.2%

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

   10. Taylor expanded in x around inf 80.1%

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

   if -4.99999999999999968e-50 < x < -3.39999999999999991e-118

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in t around inf 55.4%

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

      1. +-commutative 55.4%

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

   7. Simplified 55.4%

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

   8. Taylor expanded in x around 0 55.4%

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

   if -3.39999999999999991e-118 < x < 3.75000000000000017e-93

   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. Step-by-step derivation

      1. clear-num 89.1%

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

      2. inv-pow 89.1%

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

      3. fma-neg 89.1%

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

   6. Applied egg-rr 89.1%

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

      1. unpow-1 89.1%

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

      2. *-commutative 89.1%

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

      3. fma-neg 89.1%

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

      4. *-commutative 89.1%

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

   8. Simplified 89.1%

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

   9. Taylor expanded in x around 0 56.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-50}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{-93}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-90} \lor \neg \left(t \leq 2.7 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.1e-90) (not (<= t 2.7e+34)))
   (/ x (+ x 1.0))
   (- 1.0 (/ (* y z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e-90) || !(t <= 2.7e+34)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * z) / 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 ((t <= (-1.1d-90)) .or. (.not. (t <= 2.7d+34))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y * z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e-90) || !(t <= 2.7e+34)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * z) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.1e-90) or not (t <= 2.7e+34):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0 - ((y * z) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.1e-90) || !(t <= 2.7e+34))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.1e-90) || ~((t <= 2.7e+34)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0 - ((y * z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.1e-90], N[Not[LessEqual[t, 2.7e+34]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.09999999999999993e-90 or 2.7e34 < t

   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 77.0%

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

      1. +-commutative 77.0%

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

   7. Simplified 77.0%

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

   if -1.09999999999999993e-90 < t < 2.7e34

   1. Initial program 94.6%

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

      1. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around 0 79.1%

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

      1. associate-+r+ 79.1%

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

      2. mul-1-neg 79.1%

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

      3. unsub-neg 79.1%

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

      4. +-commutative 79.1%

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

      5. associate-/l* 82.6%

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

      6. +-commutative 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in y around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. sub-neg 79.0%

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

      3. times-frac 79.2%

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

      4. +-commutative 79.2%

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

   10. Simplified 79.2%

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

   11. Taylor expanded in x around 0 68.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-90} \lor \neg \left(t \leq 2.7 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-5} \lor \neg \left(t \leq 2.6 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.05e-5) (not (<= t 2.6e+29))) (/ x (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e-5) || !(t <= 2.6e+29)) {
		tmp = x / (x + 1.0);
	} 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 ((t <= (-1.05d-5)) .or. (.not. (t <= 2.6d+29))) then
        tmp = x / (x + 1.0d0)
    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 ((t <= -1.05e-5) || !(t <= 2.6e+29)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.05e-5) or not (t <= 2.6e+29):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.05e-5) || !(t <= 2.6e+29))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.05e-5) || ~((t <= 2.6e+29)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.05e-5], N[Not[LessEqual[t, 2.6e+29]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999994e-5 or 2.6e29 < t

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in t around inf 79.1%

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

      1. +-commutative 79.1%

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

   7. Simplified 79.1%

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

   if -1.04999999999999994e-5 < t < 2.6e29

   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. Step-by-step derivation

      1. clear-num 95.1%

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

      2. inv-pow 95.1%

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

      3. fma-neg 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. unpow-1 95.1%

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

      2. *-commutative 95.1%

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

      3. fma-neg 95.1%

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

      4. *-commutative 95.1%

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

   8. Simplified 95.1%

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

   9. Taylor expanded in z around inf 49.2%

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

   10. Taylor expanded in x around inf 60.0%

       \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-5} \lor \neg \left(t \leq 2.6 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{-50}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.1e-50) 1.0 (if (<= x 1.4e-61) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.1e-50) {
		tmp = 1.0;
	} else if (x <= 1.4e-61) {
		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 <= (-5.1d-50)) then
        tmp = 1.0d0
    else if (x <= 1.4d-61) 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 <= -5.1e-50) {
		tmp = 1.0;
	} else if (x <= 1.4e-61) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.1e-50:
		tmp = 1.0
	elif x <= 1.4e-61:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.1e-50)
		tmp = 1.0;
	elseif (x <= 1.4e-61)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.1e-50)
		tmp = 1.0;
	elseif (x <= 1.4e-61)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.1e-50], 1.0, If[LessEqual[x, 1.4e-61], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.10000000000000045e-50 or 1.4000000000000001e-61 < x

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

      1. clear-num 90.9%

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

      2. inv-pow 90.9%

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

      3. fma-neg 90.9%

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

   6. Applied egg-rr 90.9%

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

      1. unpow-1 90.9%

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

      2. *-commutative 90.9%

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

      3. fma-neg 90.9%

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

      4. *-commutative 90.9%

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

   8. Simplified 90.9%

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

   9. Taylor expanded in z around inf 70.2%

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

   10. Taylor expanded in x around inf 82.3%

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

   if -5.10000000000000045e-50 < x < 1.4000000000000001e-61

   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 34.3%

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

      1. +-commutative 34.3%

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

   7. Simplified 34.3%

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

   8. Taylor expanded in x around 0 34.3%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{-50}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.9% 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 90.7%

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

   1. *-commutative 90.7%

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

3. Simplified 90.7%

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

   1. clear-num 90.7%

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

   2. inv-pow 90.7%

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

   3. fma-neg 90.7%

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

6. Applied egg-rr 90.7%

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

   1. unpow-1 90.7%

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

   2. *-commutative 90.7%

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

   3. fma-neg 90.7%

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

   4. *-commutative 90.7%

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

8. Simplified 90.7%

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

9. Taylor expanded in z around inf 73.3%

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

10. Taylor expanded in x around inf 55.8%

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

11. Final simplification 55.8%

    \[\leadsto 1 \]
12. Add Preprocessing

Developer target: 99.6% 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 2024024 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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