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

Percentage Accurate: 89.0% → 95.4%

Time: 13.2s

Alternatives: 9

Speedup: 0.2×

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: 89.0% 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: 95.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-132}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+295}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t} + \frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* y z)) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 -5e-11)
     t_1
     (if (<= t_1 1e-132)
       (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
       (if (<= t_1 5e+295)
         t_1
         (+
          (/ (- (/ y (+ x 1.0)) (/ x (* z (+ x 1.0)))) t)
          (/ x (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e-11) {
		tmp = t_1;
	} else if (t_1 <= 1e-132) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_1 <= 5e+295) {
		tmp = t_1;
	} else {
		tmp = (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t) + (x / (x + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= (-5d-11)) then
        tmp = t_1
    else if (t_1 <= 1d-132) then
        tmp = (x - (((x / z) - y) / t)) / (x + 1.0d0)
    else if (t_1 <= 5d+295) then
        tmp = t_1
    else
        tmp = (((y / (x + 1.0d0)) - (x / (z * (x + 1.0d0)))) / t) + (x / (x + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e-11) {
		tmp = t_1;
	} else if (t_1 <= 1e-132) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_1 <= 5e+295) {
		tmp = t_1;
	} else {
		tmp = (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t) + (x / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -5e-11:
		tmp = t_1
	elif t_1 <= 1e-132:
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0)
	elif t_1 <= 5e+295:
		tmp = t_1
	else:
		tmp = (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t) + (x / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(y * z)) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -5e-11)
		tmp = t_1;
	elseif (t_1 <= 1e-132)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	elseif (t_1 <= 5e+295)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(y / Float64(x + 1.0)) - Float64(x / Float64(z * Float64(x + 1.0)))) / t) + Float64(x / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -5e-11)
		tmp = t_1;
	elseif (t_1 <= 1e-132)
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	elseif (t_1 <= 5e+295)
		tmp = t_1;
	else
		tmp = (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t) + (x / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-11], t$95$1, If[LessEqual[t$95$1, 1e-132], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+295], t$95$1, N[(N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -5.00000000000000018e-11 or 9.9999999999999999e-133 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 4.99999999999999991e295

   1. Initial program 98.4%

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

   if -5.00000000000000018e-11 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 9.9999999999999999e-133

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in t around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-out-- 100.0%

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

   6. Simplified 100.0%

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

   if 4.99999999999999991e295 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 24.7%

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

      1. *-commutative 24.7%

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

   3. Simplified 24.7%

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

   4. Taylor expanded in t around -inf 91.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{-132}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+295}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t} + \frac{x}{x + 1}\\ \end{array} \]

Alternative 2: 95.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-132}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+295}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* y z)) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 -5e-11)
     t_1
     (if (<= t_1 1e-132)
       (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
       (if (<= t_1 5e+295) t_1 (/ (+ x (/ y t)) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e-11) {
		tmp = t_1;
	} else if (t_1 <= 1e-132) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_1 <= 5e+295) {
		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 - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= (-5d-11)) then
        tmp = t_1
    else if (t_1 <= 1d-132) then
        tmp = (x - (((x / z) - y) / t)) / (x + 1.0d0)
    else if (t_1 <= 5d+295) 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 - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e-11) {
		tmp = t_1;
	} else if (t_1 <= 1e-132) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_1 <= 5e+295) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -5e-11:
		tmp = t_1
	elif t_1 <= 1e-132:
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0)
	elif t_1 <= 5e+295:
		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(x - Float64(y * z)) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -5e-11)
		tmp = t_1;
	elseif (t_1 <= 1e-132)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	elseif (t_1 <= 5e+295)
		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 - ((x - (y * z)) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -5e-11)
		tmp = t_1;
	elseif (t_1 <= 1e-132)
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	elseif (t_1 <= 5e+295)
		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[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-11], t$95$1, If[LessEqual[t$95$1, 1e-132], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+295], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -5.00000000000000018e-11 or 9.9999999999999999e-133 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 4.99999999999999991e295

   1. Initial program 98.4%

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

   if -5.00000000000000018e-11 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 9.9999999999999999e-133

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in t around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-out-- 100.0%

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

   6. Simplified 100.0%

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

   if 4.99999999999999991e295 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 24.7%

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

      1. *-commutative 24.7%

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

   3. Simplified 24.7%

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

   4. Taylor expanded in z around inf 91.4%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{-132}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+295}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1250000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{z \cdot t}{x \cdot \left(x + 1\right)} + 1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1250000.0)
     t_1
     (if (<= t -2.6e-84)
       (+ (/ (* z t) (* x (+ x 1.0))) 1.0)
       (if (<= t 5.8e-59) (/ (- x (/ y (/ x z))) (+ x 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1250000.0) {
		tmp = t_1;
	} else if (t <= -2.6e-84) {
		tmp = ((z * t) / (x * (x + 1.0))) + 1.0;
	} else if (t <= 5.8e-59) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	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 / t)) / (x + 1.0d0)
    if (t <= (-1250000.0d0)) then
        tmp = t_1
    else if (t <= (-2.6d-84)) then
        tmp = ((z * t) / (x * (x + 1.0d0))) + 1.0d0
    else if (t <= 5.8d-59) then
        tmp = (x - (y / (x / z))) / (x + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1250000.0) {
		tmp = t_1;
	} else if (t <= -2.6e-84) {
		tmp = ((z * t) / (x * (x + 1.0))) + 1.0;
	} else if (t <= 5.8e-59) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -1250000.0:
		tmp = t_1
	elif t <= -2.6e-84:
		tmp = ((z * t) / (x * (x + 1.0))) + 1.0
	elif t <= 5.8e-59:
		tmp = (x - (y / (x / z))) / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1250000.0)
		tmp = t_1;
	elseif (t <= -2.6e-84)
		tmp = Float64(Float64(Float64(z * t) / Float64(x * Float64(x + 1.0))) + 1.0);
	elseif (t <= 5.8e-59)
		tmp = Float64(Float64(x - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1250000.0)
		tmp = t_1;
	elseif (t <= -2.6e-84)
		tmp = ((z * t) / (x * (x + 1.0))) + 1.0;
	elseif (t <= 5.8e-59)
		tmp = (x - (y / (x / z))) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1250000.0], t$95$1, If[LessEqual[t, -2.6e-84], N[(N[(N[(z * t), $MachinePrecision] / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[t, 5.8e-59], N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25e6 or 5.80000000000000033e-59 < t

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in z around inf 86.1%

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

   if -1.25e6 < t < -2.6e-84

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 90.8%

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

   5. Taylor expanded in t around 0 85.1%

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

   if -2.6e-84 < t < 5.80000000000000033e-59

   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. Taylor expanded in y around inf 81.8%

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

   5. Taylor expanded in t around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

      3. associate-/l* 74.9%

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

      4. +-commutative 74.9%

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

   7. Simplified 74.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1250000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{z \cdot t}{x \cdot \left(x + 1\right)} + 1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 4: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3800 \lor \neg \left(z \leq 2.75 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3800.0) (not (<= z 2.75e-49)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3800.0) || !(z <= 2.75e-49)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3800.0d0)) .or. (.not. (z <= 2.75d-49))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3800.0) || !(z <= 2.75e-49)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3800.0) or not (z <= 2.75e-49):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3800.0) || !(z <= 2.75e-49))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3800.0) || ~((z <= 2.75e-49)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3800.0], N[Not[LessEqual[z, 2.75e-49]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3800 or 2.75000000000000016e-49 < z

   1. Initial program 80.6%

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

      1. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around inf 81.7%

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

   if -3800 < z < 2.75000000000000016e-49

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 81.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3800 \lor \neg \left(z \leq 2.75 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 5: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4600000 \lor \neg \left(t \leq 1.85 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4600000.0) (not (<= t 1.85e+34)))
   (/ (+ 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 <= -4600000.0) || !(t <= 1.85e+34)) {
		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 <= (-4600000.0d0)) .or. (.not. (t <= 1.85d+34))) 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 <= -4600000.0) || !(t <= 1.85e+34)) {
		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 <= -4600000.0) or not (t <= 1.85e+34):
		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 <= -4600000.0) || !(t <= 1.85e+34))
		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 <= -4600000.0) || ~((t <= 1.85e+34)))
		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, -4600000.0], N[Not[LessEqual[t, 1.85e+34]], $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 < -4.6e6 or 1.85000000000000004e34 < t

   1. Initial program 85.7%

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

      1. *-commutative 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in z around inf 89.4%

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

   if -4.6e6 < t < 1.85000000000000004e34

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around 0 81.9%

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

      1. associate-+r+ 81.9%

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

      2. mul-1-neg 81.9%

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

      3. unsub-neg 81.9%

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

      4. +-commutative 81.9%

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

      5. associate-/l* 85.3%

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

      6. +-commutative 85.3%

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

   6. Simplified 85.3%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4600000 \lor \neg \left(t \leq 1.85 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \]

Alternative 6: 76.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 105000000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.15e-73)
   1.0
   (if (<= x 105000000000.0) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e-73) {
		tmp = 1.0;
	} else if (x <= 105000000000.0) {
		tmp = (x + (y / t)) / (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 (x <= (-1.15d-73)) then
        tmp = 1.0d0
    else if (x <= 105000000000.0d0) then
        tmp = (x + (y / t)) / (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 (x <= -1.15e-73) {
		tmp = 1.0;
	} else if (x <= 105000000000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.15e-73:
		tmp = 1.0
	elif x <= 105000000000.0:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.15e-73)
		tmp = 1.0;
	elseif (x <= 105000000000.0)
		tmp = Float64(Float64(x + Float64(y / t)) / 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 (x <= -1.15e-73)
		tmp = 1.0;
	elseif (x <= 105000000000.0)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.15e-73], 1.0, If[LessEqual[x, 105000000000.0], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.14999999999999994e-73 or 1.05e11 < 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. Taylor expanded in y around inf 81.1%

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

   5. Taylor expanded in x around inf 84.3%

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

   if -1.14999999999999994e-73 < x < 1.05e11

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around inf 65.1%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 105000000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 67.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-94}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1e-74) 1.0 (if (<= x 1.6e-94) (/ y (* t (+ x 1.0))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1e-74) {
		tmp = 1.0;
	} else if (x <= 1.6e-94) {
		tmp = y / (t * (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 (x <= (-1d-74)) then
        tmp = 1.0d0
    else if (x <= 1.6d-94) then
        tmp = y / (t * (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 (x <= -1e-74) {
		tmp = 1.0;
	} else if (x <= 1.6e-94) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1e-74:
		tmp = 1.0
	elif x <= 1.6e-94:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1e-74)
		tmp = 1.0;
	elseif (x <= 1.6e-94)
		tmp = Float64(y / Float64(t * 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 (x <= -1e-74)
		tmp = 1.0;
	elseif (x <= 1.6e-94)
		tmp = y / (t * (x + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1e-74], 1.0, If[LessEqual[x, 1.6e-94], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999958e-75 or 1.59999999999999998e-94 < x

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around inf 78.6%

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

   5. Taylor expanded in x around inf 76.3%

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

   if -9.99999999999999958e-75 < x < 1.59999999999999998e-94

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around inf 69.4%

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

   5. Taylor expanded in y around inf 55.3%

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

      1. +-commutative 55.3%

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

   7. Simplified 55.3%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-94}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 61.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3900000000000 \lor \neg \left(t \leq 3.3 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3900000000000.0) (not (<= t 3.3e+61))) (/ x (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3900000000000.0) || !(t <= 3.3e+61)) {
		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 <= (-3900000000000.0d0)) .or. (.not. (t <= 3.3d+61))) 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 <= -3900000000000.0) || !(t <= 3.3e+61)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3900000000000.0) or not (t <= 3.3e+61):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3900000000000.0) || !(t <= 3.3e+61))
		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 <= -3900000000000.0) || ~((t <= 3.3e+61)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3900000000000.0], N[Not[LessEqual[t, 3.3e+61]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e12 or 3.2999999999999998e61 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 65.2%

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

      1. +-commutative 65.2%

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

   6. Simplified 65.2%

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

   if -3.9e12 < t < 3.2999999999999998e61

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around inf 75.8%

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

   5. Taylor expanded in x around inf 64.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3900000000000 \lor \neg \left(t \leq 3.3 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 52.6% 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 90.4%

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

   1. *-commutative 90.4%

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

3. Simplified 90.4%

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

4. Taylor expanded in y around inf 76.3%

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

5. Taylor expanded in x around inf 57.0%

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

6. Final simplification 57.0%

   \[\leadsto 1 \]

Developer target: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023318 
(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)))