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

Percentage Accurate: 88.7% → 95.1%

Time: 15.5s

Alternatives: 11

Speedup: 0.6×

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: 88.7% 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: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+136}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+42}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{t\_1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot \left(\frac{x}{y \cdot t\_1} + \frac{z}{x - z \cdot t}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (<= z -2.15e+136)
     (/ (+ x (/ y t)) (+ x 1.0))
     (if (<= z 5e+42)
       (/ (+ x (/ (- (* z y) x) t_1)) (+ x 1.0))
       (/ (- x (* y (+ (/ x (* y t_1)) (/ z (- x (* z t)))))) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (z <= -2.15e+136) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 5e+42) {
		tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0);
	} else {
		tmp = (x - (y * ((x / (y * t_1)) + (z / (x - (z * t)))))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * t) - x
    if (z <= (-2.15d+136)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (z <= 5d+42) then
        tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0d0)
    else
        tmp = (x - (y * ((x / (y * t_1)) + (z / (x - (z * t)))))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (z <= -2.15e+136) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 5e+42) {
		tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0);
	} else {
		tmp = (x - (y * ((x / (y * t_1)) + (z / (x - (z * t)))))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if z <= -2.15e+136:
		tmp = (x + (y / t)) / (x + 1.0)
	elif z <= 5e+42:
		tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0)
	else:
		tmp = (x - (y * ((x / (y * t_1)) + (z / (x - (z * t)))))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (z <= -2.15e+136)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (z <= 5e+42)
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - x) / t_1)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(y * Float64(Float64(x / Float64(y * t_1)) + Float64(z / Float64(x - Float64(z * t)))))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if (z <= -2.15e+136)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (z <= 5e+42)
		tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0);
	else
		tmp = (x - (y * ((x / (y * t_1)) + (z / (x - (z * t)))))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -2.15e+136], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+42], N[(N[(x + N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * N[(N[(x / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1499999999999999e136

   1. Initial program 68.3%

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

      1. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 97.4%

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

   if -2.1499999999999999e136 < z < 5.00000000000000007e42

   1. Initial program 98.7%

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

   if 5.00000000000000007e42 < z

   1. Initial program 64.2%

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

      1. *-commutative 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in y around inf 94.2%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+136}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+42}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot \left(\frac{x}{y \cdot \left(z \cdot t - x\right)} + \frac{z}{x - z \cdot t}\right)}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+85}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\right) + \frac{x}{t \cdot \left(z \cdot \left(-1 - x\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.6e+130)
   (/ (+ x (/ y t)) (+ x 1.0))
   (if (<= z 1.26e+85)
     (/ (+ x (/ (- (* z y) x) (- (* z t) x))) (+ x 1.0))
     (+
      (+ (/ x (+ x 1.0)) (/ y (* t (+ x 1.0))))
      (/ x (* t (* z (- -1.0 x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.6e+130) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 1.26e+85) {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) + (x / (t * (z * (-1.0 - x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.6d+130)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (z <= 1.26d+85) then
        tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0d0)
    else
        tmp = ((x / (x + 1.0d0)) + (y / (t * (x + 1.0d0)))) + (x / (t * (z * ((-1.0d0) - x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.6e+130) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 1.26e+85) {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) + (x / (t * (z * (-1.0 - x))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.6e+130:
		tmp = (x + (y / t)) / (x + 1.0)
	elif z <= 1.26e+85:
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0)
	else:
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) + (x / (t * (z * (-1.0 - x))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.6e+130)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (z <= 1.26e+85)
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(x + 1.0)))) + Float64(x / Float64(t * Float64(z * Float64(-1.0 - x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.6e+130)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (z <= 1.26e+85)
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	else
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) + (x / (t * (z * (-1.0 - x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.6e+130], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e+85], N[(N[(x + N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(t * N[(z * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5999999999999997e130

   1. Initial program 68.3%

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

      1. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 97.4%

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

   if -5.5999999999999997e130 < z < 1.26000000000000003e85

   1. Initial program 98.2%

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

   if 1.26000000000000003e85 < z

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in t around inf 83.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+85}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\right) + \frac{x}{t \cdot \left(z \cdot \left(-1 - x\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+132}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} + \frac{y}{-1 - x}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+132)
   (/ (+ x (/ y t)) (+ x 1.0))
   (if (<= z 5.4e+90)
     (/ (+ x (/ (- (* z y) x) (- (* z t) x))) (+ x 1.0))
     (- (/ x (+ x 1.0)) (/ (+ (/ x (* z (+ x 1.0))) (/ y (- -1.0 x))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+132) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 5.4e+90) {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) + (y / (-1.0 - x))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.8d+132)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (z <= 5.4d+90) then
        tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0d0)
    else
        tmp = (x / (x + 1.0d0)) - (((x / (z * (x + 1.0d0))) + (y / ((-1.0d0) - x))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+132) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 5.4e+90) {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) + (y / (-1.0 - x))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+132:
		tmp = (x + (y / t)) / (x + 1.0)
	elif z <= 5.4e+90:
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0)
	else:
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) + (y / (-1.0 - x))) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+132)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (z <= 5.4e+90)
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(Float64(x / Float64(z * Float64(x + 1.0))) + Float64(y / Float64(-1.0 - x))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+132)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (z <= 5.4e+90)
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	else
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) + (y / (-1.0 - x))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+132], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+90], N[(N[(x + N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999999e132

   1. Initial program 68.3%

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

      1. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 97.4%

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

   if -2.7999999999999999e132 < z < 5.4e90

   1. Initial program 98.2%

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

   if 5.4e90 < z

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. mul-1-neg 83.1%

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

      3. unsub-neg 83.1%

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

      4. +-commutative 83.1%

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

      5. distribute-lft-out-- 83.1%

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

      6. +-commutative 83.1%

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

      7. +-commutative 83.1%

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

   7. Simplified 83.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+132}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} + \frac{y}{-1 - x}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+131} \lor \neg \left(z \leq 8.6 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+131) (not (<= z 8.6e+90)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ (- (* z y) x) (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+131) || !(z <= 8.6e+90)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - 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 <= (-2.2d+131)) .or. (.not. (z <= 8.6d+90))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (((z * y) - 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 <= -2.2e+131) || !(z <= 8.6e+90)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+131) or not (z <= 8.6e+90):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+131) || !(z <= 8.6e+90))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - 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 <= -2.2e+131) || ~((z <= 8.6e+90)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+131], N[Not[LessEqual[z, 8.6e+90]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / 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 < -2.1999999999999999e131 or 8.5999999999999994e90 < z

   1. Initial program 64.2%

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

      1. *-commutative 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in z around inf 89.5%

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

   if -2.1999999999999999e131 < z < 8.5999999999999994e90

   1. Initial program 98.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+131} \lor \neg \left(z \leq 8.6 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-270}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-68}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7e-61)
   1.0
   (if (<= x 1.8e-270)
     (/ y t)
     (if (<= x 5e-124) x (if (<= x 2.05e-68) (/ y t) (/ x (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e-61) {
		tmp = 1.0;
	} else if (x <= 1.8e-270) {
		tmp = y / t;
	} else if (x <= 5e-124) {
		tmp = x;
	} else if (x <= 2.05e-68) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-7d-61)) then
        tmp = 1.0d0
    else if (x <= 1.8d-270) then
        tmp = y / t
    else if (x <= 5d-124) then
        tmp = x
    else if (x <= 2.05d-68) then
        tmp = y / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e-61) {
		tmp = 1.0;
	} else if (x <= 1.8e-270) {
		tmp = y / t;
	} else if (x <= 5e-124) {
		tmp = x;
	} else if (x <= 2.05e-68) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7e-61:
		tmp = 1.0
	elif x <= 1.8e-270:
		tmp = y / t
	elif x <= 5e-124:
		tmp = x
	elif x <= 2.05e-68:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7e-61)
		tmp = 1.0;
	elseif (x <= 1.8e-270)
		tmp = Float64(y / t);
	elseif (x <= 5e-124)
		tmp = x;
	elseif (x <= 2.05e-68)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7e-61)
		tmp = 1.0;
	elseif (x <= 1.8e-270)
		tmp = y / t;
	elseif (x <= 5e-124)
		tmp = x;
	elseif (x <= 2.05e-68)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7e-61], 1.0, If[LessEqual[x, 1.8e-270], N[(y / t), $MachinePrecision], If[LessEqual[x, 5e-124], x, If[LessEqual[x, 2.05e-68], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.0000000000000006e-61

   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. Add Preprocessing

   5. Taylor expanded in y around inf 98.8%

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

   6. Taylor expanded in z around inf 72.5%

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

   7. Taylor expanded in x around inf 80.1%

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

   if -7.0000000000000006e-61 < x < 1.7999999999999999e-270 or 5.0000000000000003e-124 < x < 2.05000000000000011e-68

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around inf 76.9%

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

   6. Taylor expanded in z around inf 75.5%

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

   7. Taylor expanded in x around 0 64.1%

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

   if 1.7999999999999999e-270 < x < 5.0000000000000003e-124

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 38.7%

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

      1. +-commutative 38.7%

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

   7. Simplified 38.7%

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

   8. Taylor expanded in x around 0 38.7%

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

   if 2.05000000000000011e-68 < x

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in t around inf 81.8%

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

      1. +-commutative 81.8%

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

   7. Simplified 81.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-270}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-68}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-58}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-270}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.1e-58)
   1.0
   (if (<= x 1.8e-270)
     (/ y t)
     (if (<= x 2.2e-124) x (if (<= x 2.1e-66) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.1e-58) {
		tmp = 1.0;
	} else if (x <= 1.8e-270) {
		tmp = y / t;
	} else if (x <= 2.2e-124) {
		tmp = x;
	} else if (x <= 2.1e-66) {
		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 <= (-1.1d-58)) then
        tmp = 1.0d0
    else if (x <= 1.8d-270) then
        tmp = y / t
    else if (x <= 2.2d-124) then
        tmp = x
    else if (x <= 2.1d-66) 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 <= -1.1e-58) {
		tmp = 1.0;
	} else if (x <= 1.8e-270) {
		tmp = y / t;
	} else if (x <= 2.2e-124) {
		tmp = x;
	} else if (x <= 2.1e-66) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.1e-58:
		tmp = 1.0
	elif x <= 1.8e-270:
		tmp = y / t
	elif x <= 2.2e-124:
		tmp = x
	elif x <= 2.1e-66:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.1e-58)
		tmp = 1.0;
	elseif (x <= 1.8e-270)
		tmp = Float64(y / t);
	elseif (x <= 2.2e-124)
		tmp = x;
	elseif (x <= 2.1e-66)
		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 <= -1.1e-58)
		tmp = 1.0;
	elseif (x <= 1.8e-270)
		tmp = y / t;
	elseif (x <= 2.2e-124)
		tmp = x;
	elseif (x <= 2.1e-66)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.1e-58], 1.0, If[LessEqual[x, 1.8e-270], N[(y / t), $MachinePrecision], If[LessEqual[x, 2.2e-124], x, If[LessEqual[x, 2.1e-66], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.10000000000000003e-58 or 2.1e-66 < x

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around inf 99.3%

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

   6. Taylor expanded in z around inf 74.3%

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

   7. Taylor expanded in x around inf 80.7%

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

   if -1.10000000000000003e-58 < x < 1.7999999999999999e-270 or 2.1999999999999999e-124 < x < 2.1e-66

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around inf 76.9%

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

   6. Taylor expanded in z around inf 75.5%

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

   7. Taylor expanded in x around 0 64.1%

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

   if 1.7999999999999999e-270 < x < 2.1999999999999999e-124

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 38.7%

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

      1. +-commutative 38.7%

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

   7. Simplified 38.7%

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

   8. Taylor expanded in x around 0 38.7%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-58}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-270}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-254}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-51}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.8e-61)
   1.0
   (if (<= x 9.6e-254)
     (/ y t)
     (if (<= x 1.35e-51) (- 1.0 (* y (/ z x))) (/ x (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-61) {
		tmp = 1.0;
	} else if (x <= 9.6e-254) {
		tmp = y / t;
	} else if (x <= 1.35e-51) {
		tmp = 1.0 - (y * (z / x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.8d-61)) then
        tmp = 1.0d0
    else if (x <= 9.6d-254) then
        tmp = y / t
    else if (x <= 1.35d-51) then
        tmp = 1.0d0 - (y * (z / x))
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-61) {
		tmp = 1.0;
	} else if (x <= 9.6e-254) {
		tmp = y / t;
	} else if (x <= 1.35e-51) {
		tmp = 1.0 - (y * (z / x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8e-61:
		tmp = 1.0
	elif x <= 9.6e-254:
		tmp = y / t
	elif x <= 1.35e-51:
		tmp = 1.0 - (y * (z / x))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8e-61)
		tmp = 1.0;
	elseif (x <= 9.6e-254)
		tmp = Float64(y / t);
	elseif (x <= 1.35e-51)
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.8e-61)
		tmp = 1.0;
	elseif (x <= 9.6e-254)
		tmp = y / t;
	elseif (x <= 1.35e-51)
		tmp = 1.0 - (y * (z / x));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e-61], 1.0, If[LessEqual[x, 9.6e-254], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.35e-51], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.80000000000000007e-61

   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. Add Preprocessing

   5. Taylor expanded in y around inf 98.8%

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

   6. Taylor expanded in z around inf 72.5%

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

   7. Taylor expanded in x around inf 80.1%

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

   if -1.80000000000000007e-61 < x < 9.60000000000000007e-254

   1. Initial program 80.0%

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

      1. *-commutative 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in y around inf 74.0%

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

   6. Taylor expanded in z around inf 80.0%

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

   7. Taylor expanded in x around 0 64.4%

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

   if 9.60000000000000007e-254 < x < 1.3499999999999999e-51

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around 0 49.8%

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

      1. associate-+r+ 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

      4. +-commutative 49.8%

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

      5. associate-/l* 49.9%

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

      6. +-commutative 49.9%

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

   7. Simplified 49.9%

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

      1. div-sub 49.9%

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

      2. pow1 49.9%

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

      3. pow1 49.9%

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

      4. pow-div 49.9%

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

      5. metadata-eval 49.9%

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

      6. metadata-eval 49.9%

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

   9. Applied egg-rr 49.9%

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

   10. Taylor expanded in x around 0 49.8%

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

       1. associate-*r/ 49.9%

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

   12. Simplified 49.9%

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

   if 1.3499999999999999e-51 < x

   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. Add Preprocessing

   5. Taylor expanded in t around inf 85.0%

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

      1. +-commutative 85.0%

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

   7. Simplified 85.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-254}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-51}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-92} \lor \neg \left(t \leq 8.6 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.6e-92) (not (<= t 8.6e-132)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* (/ y x) (/ z (- -1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.6e-92) || !(t <= 8.6e-132)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.6d-92)) .or. (.not. (t <= 8.6d-132))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((y / x) * (z / ((-1.0d0) - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.6e-92) || !(t <= 8.6e-132)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.6e-92) or not (t <= 8.6e-132):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.6e-92) || !(t <= 8.6e-132))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(y / x) * Float64(z / Float64(-1.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.6e-92) || ~((t <= 8.6e-132)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.6e-92], N[Not[LessEqual[t, 8.6e-132]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y / x), $MachinePrecision] * N[(z / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.60000000000000016e-92 or 8.5999999999999994e-132 < t

   1. Initial program 84.2%

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

      1. *-commutative 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in z around inf 84.8%

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

   if -3.60000000000000016e-92 < t < 8.5999999999999994e-132

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in t around 0 77.1%

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

      1. associate-+r+ 77.1%

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

      2. mul-1-neg 77.1%

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

      3. unsub-neg 77.1%

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

      4. +-commutative 77.1%

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

      5. associate-/l* 82.9%

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

      6. +-commutative 82.9%

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

   7. Simplified 82.9%

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

      1. div-sub 82.9%

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

      2. pow1 82.9%

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

      3. pow1 82.9%

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

      4. pow-div 82.9%

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

      5. metadata-eval 82.9%

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

      6. metadata-eval 82.9%

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

   9. Applied egg-rr 82.9%

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

       1. associate-*r/ 77.1%

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

       2. add-sqr-sqrt 41.5%

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

       3. sqrt-unprod 62.5%

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

       4. sqr-neg 62.5%

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

       5. sqrt-unprod 30.4%

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

       6. add-sqr-sqrt 54.7%

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

       7. associate-/r* 54.6%

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

       8. times-frac 58.3%

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

       9. add-sqr-sqrt 34.0%

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

       10. sqrt-unprod 64.1%

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

       11. sqr-neg 64.1%

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

       12. sqrt-unprod 38.4%

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

       13. add-sqr-sqrt 78.7%

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

   11. Applied egg-rr 78.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-92} \lor \neg \left(t \leq 8.6 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-89} \lor \neg \left(t \leq 5 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.4e-89) (not (<= t 5e-50)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (/ (* y (/ z x)) (- -1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.4e-89) || !(t <= 5e-50)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.4d-89)) .or. (.not. (t <= 5d-50))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((y * (z / x)) / ((-1.0d0) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.4e-89) || !(t <= 5e-50)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.4e-89) or not (t <= 5e-50):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.4e-89) || !(t <= 5e-50))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(y * Float64(z / x)) / Float64(-1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.4e-89) || ~((t <= 5e-50)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.4e-89], N[Not[LessEqual[t, 5e-50]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.40000000000000016e-89 or 4.99999999999999968e-50 < t

   1. Initial program 83.0%

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

      1. *-commutative 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in z around inf 87.9%

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

   if -2.40000000000000016e-89 < t < 4.99999999999999968e-50

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around 0 74.4%

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

      1. associate-+r+ 74.4%

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

      2. mul-1-neg 74.4%

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

      3. unsub-neg 74.4%

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

      4. +-commutative 74.4%

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

      5. associate-/l* 79.2%

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

      6. +-commutative 79.2%

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

   7. Simplified 79.2%

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

      1. div-sub 79.2%

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

      2. pow1 79.2%

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

      3. pow1 79.2%

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

      4. pow-div 79.2%

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

      5. metadata-eval 79.2%

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

      6. metadata-eval 79.2%

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

   9. Applied egg-rr 79.2%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-89} \lor \neg \left(t \leq 5 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-15} \lor \neg \left(z \leq 8 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.3e-15) (not (<= z 8e-29)))
   (/ (+ 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 ((z <= -2.3e-15) || !(z <= 8e-29)) {
		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 ((z <= (-2.3d-15)) .or. (.not. (z <= 8d-29))) 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 ((z <= -2.3e-15) || !(z <= 8e-29)) {
		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 (z <= -2.3e-15) or not (z <= 8e-29):
		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 ((z <= -2.3e-15) || !(z <= 8e-29))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.3e-15) || ~((z <= 8e-29)))
		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[z, -2.3e-15], N[Not[LessEqual[z, 8e-29]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999999e-15 or 7.99999999999999955e-29 < z

   1. Initial program 75.5%

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

      1. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in z around inf 84.7%

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

   if -2.2999999999999999e-15 < z < 7.99999999999999955e-29

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 79.5%

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

      1. associate-+r+ 79.5%

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

      2. mul-1-neg 79.5%

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

      3. unsub-neg 79.5%

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

      4. +-commutative 79.5%

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

      5. associate-/l* 79.6%

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

      6. +-commutative 79.6%

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

   7. Simplified 79.6%

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

      1. div-sub 79.6%

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

      2. pow1 79.6%

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

      3. pow1 79.6%

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

      4. pow-div 79.6%

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

      5. metadata-eval 79.6%

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

      6. metadata-eval 79.6%

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

   9. Applied egg-rr 79.6%

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

   10. Taylor expanded in x around 0 76.6%

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

       1. associate-*r/ 76.7%

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

   12. Simplified 76.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-15} \lor \neg \left(z \leq 8 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.5% 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 87.3%

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

   1. *-commutative 87.3%

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

3. Simplified 87.3%

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

5. Taylor expanded in y around inf 92.3%

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

6. Taylor expanded in z around inf 73.6%

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

7. Taylor expanded in x around inf 53.9%

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

8. Final simplification 53.9%

   \[\leadsto 1 \]
9. Add Preprocessing

Developer target: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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