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

Percentage Accurate: 89.1% → 94.1%

Time: 14.8s

Alternatives: 10

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: 89.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+173} \lor \neg \left(z \leq 1.15 \cdot 10^{+177}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e+173) (not (<= z 1.15e+177)))
   (/ (+ 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 <= -4.8e+173) || !(z <= 1.15e+177)) {
		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 <= (-4.8d+173)) .or. (.not. (z <= 1.15d+177))) 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 <= -4.8e+173) || !(z <= 1.15e+177)) {
		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 <= -4.8e+173) or not (z <= 1.15e+177):
		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 <= -4.8e+173) || !(z <= 1.15e+177))
		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 <= -4.8e+173) || ~((z <= 1.15e+177)))
		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, -4.8e+173], N[Not[LessEqual[z, 1.15e+177]], $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 < -4.7999999999999998e173 or 1.15e177 < z

   1. Initial program 57.0%

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

      1. *-commutative 57.0%

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

   3. Simplified 57.0%

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

   5. Taylor expanded in z around inf 96.5%

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

   if -4.7999999999999998e173 < z < 1.15e177

   1. Initial program 96.5%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+173} \lor \neg \left(z \leq 1.15 \cdot 10^{+177}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-110}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.5e-8)
   1.0
   (if (<= x -5.2e-93)
     (/ 1.0 (/ 1.0 x))
     (if (<= x -6.8e-110) 1.0 (if (<= x 9e-63) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e-8) {
		tmp = 1.0;
	} else if (x <= -5.2e-93) {
		tmp = 1.0 / (1.0 / x);
	} else if (x <= -6.8e-110) {
		tmp = 1.0;
	} else if (x <= 9e-63) {
		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 <= (-5.5d-8)) then
        tmp = 1.0d0
    else if (x <= (-5.2d-93)) then
        tmp = 1.0d0 / (1.0d0 / x)
    else if (x <= (-6.8d-110)) then
        tmp = 1.0d0
    else if (x <= 9d-63) 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 <= -5.5e-8) {
		tmp = 1.0;
	} else if (x <= -5.2e-93) {
		tmp = 1.0 / (1.0 / x);
	} else if (x <= -6.8e-110) {
		tmp = 1.0;
	} else if (x <= 9e-63) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.5e-8:
		tmp = 1.0
	elif x <= -5.2e-93:
		tmp = 1.0 / (1.0 / x)
	elif x <= -6.8e-110:
		tmp = 1.0
	elif x <= 9e-63:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.5e-8)
		tmp = 1.0;
	elseif (x <= -5.2e-93)
		tmp = Float64(1.0 / Float64(1.0 / x));
	elseif (x <= -6.8e-110)
		tmp = 1.0;
	elseif (x <= 9e-63)
		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 <= -5.5e-8)
		tmp = 1.0;
	elseif (x <= -5.2e-93)
		tmp = 1.0 / (1.0 / x);
	elseif (x <= -6.8e-110)
		tmp = 1.0;
	elseif (x <= 9e-63)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.5e-8], 1.0, If[LessEqual[x, -5.2e-93], N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.8e-110], 1.0, If[LessEqual[x, 9e-63], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5000000000000003e-8 or -5.1999999999999997e-93 < x < -6.8000000000000002e-110 or 8.9999999999999999e-63 < x

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in z around inf 67.0%

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

      1. +-commutative 67.0%

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

      2. div-inv 67.0%

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

      3. fma-define 67.0%

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

   7. Applied egg-rr 67.0%

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

   8. Taylor expanded in x around inf 83.0%

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

   if -5.5000000000000003e-8 < x < -5.1999999999999997e-93

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

      3. fma-neg 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

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

      2. fma-neg 99.6%

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

      3. *-commutative 99.6%

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

      4. *-commutative 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in x around inf 51.0%

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

   10. Taylor expanded in x around 0 47.0%

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

   if -6.8000000000000002e-110 < x < 8.9999999999999999e-63

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in z around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. div-inv 75.6%

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

      3. fma-define 75.7%

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

   7. Applied egg-rr 75.7%

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

   8. Taylor expanded in x around 0 61.3%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-110}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.5e-110)
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))
   (if (<= x 6.8e-41)
     (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0))
     (- 1.0 (* (/ y (+ x 1.0)) (/ z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.5e-110) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else if (x <= 6.8e-41) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x + 1.0)) * (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 (x <= (-3.5d-110)) then
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    else if (x <= 6.8d-41) then
        tmp = (x + ((y - (x / z)) / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y / (x + 1.0d0)) * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.5e-110) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else if (x <= 6.8e-41) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.5e-110:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	elif x <= 6.8e-41:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.5e-110)
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	elseif (x <= 6.8e-41)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y / Float64(x + 1.0)) * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.5e-110)
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	elseif (x <= 6.8e-41)
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.5e-110], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-41], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.49999999999999974e-110

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in y around 0 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   if -3.49999999999999974e-110 < x < 6.7999999999999997e-41

   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. Add Preprocessing

   5. Taylor expanded in t around inf 83.1%

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

   6. Taylor expanded in x around 0 83.1%

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

      1. sub-neg 83.1%

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

      2. distribute-lft-in 83.1%

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

      3. *-rgt-identity 83.1%

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

      4. distribute-rgt-neg-out 83.1%

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

      5. associate-*r/ 83.1%

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

      6. *-rgt-identity 83.1%

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

      7. associate-+r+ 83.1%

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

      8. +-commutative 83.1%

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

      9. unsub-neg 83.1%

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

      10. *-lft-identity 83.1%

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

      11. times-frac 83.2%

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

      12. associate-*l/ 83.1%

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

      13. *-lft-identity 83.1%

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

      14. div-sub 83.2%

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

   8. Simplified 83.2%

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

   if 6.7999999999999997e-41 < x

   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. Add Preprocessing

   5. Taylor expanded in t around 0 86.9%

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

      1. associate-+r+ 86.9%

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

      2. mul-1-neg 86.9%

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

      3. unsub-neg 86.9%

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

      4. +-commutative 86.9%

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

      5. associate-/l* 91.9%

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

      6. +-commutative 91.9%

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

   7. Simplified 91.9%

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

      1. div-sub 91.9%

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

      2. pow1 91.9%

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

      3. pow1 91.9%

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

      4. pow-div 91.9%

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

      5. metadata-eval 91.9%

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

      6. metadata-eval 91.9%

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

      7. associate-/r/ 91.8%

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

   9. Applied egg-rr 91.8%

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

   10. Taylor expanded in y around 0 86.8%

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

       1. +-commutative 86.8%

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

       2. *-commutative 86.8%

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

       3. times-frac 91.8%

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

   12. Simplified 91.8%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-112}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.4e-112)
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))
   (if (<= x 1.65e-41)
     (/ (+ x (/ (- y (/ x z)) 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 (x <= -3.4e-112) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else if (x <= 1.65e-41) {
		tmp = (x + ((y - (x / z)) / 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 (x <= (-3.4d-112)) then
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    else if (x <= 1.65d-41) then
        tmp = (x + ((y - (x / z)) / 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 (x <= -3.4e-112) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else if (x <= 1.65e-41) {
		tmp = (x + ((y - (x / z)) / 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 x <= -3.4e-112:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	elif x <= 1.65e-41:
		tmp = (x + ((y - (x / z)) / 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 (x <= -3.4e-112)
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	elseif (x <= 1.65e-41)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / 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 (x <= -3.4e-112)
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	elseif (x <= 1.65e-41)
		tmp = (x + ((y - (x / z)) / 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[LessEqual[x, -3.4e-112], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e-41], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / 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 3 regimes

2. if x < -3.3999999999999998e-112

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in y around 0 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   if -3.3999999999999998e-112 < x < 1.65000000000000012e-41

   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. Add Preprocessing

   5. Taylor expanded in t around inf 83.1%

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

   6. Taylor expanded in x around 0 83.1%

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

      1. sub-neg 83.1%

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

      2. distribute-lft-in 83.1%

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

      3. *-rgt-identity 83.1%

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

      4. distribute-rgt-neg-out 83.1%

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

      5. associate-*r/ 83.1%

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

      6. *-rgt-identity 83.1%

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

      7. associate-+r+ 83.1%

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

      8. +-commutative 83.1%

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

      9. unsub-neg 83.1%

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

      10. *-lft-identity 83.1%

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

      11. times-frac 83.2%

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

      12. associate-*l/ 83.1%

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

      13. *-lft-identity 83.1%

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

      14. div-sub 83.2%

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

   8. Simplified 83.2%

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

   if 1.65000000000000012e-41 < x

   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. Add Preprocessing

   5. Taylor expanded in t around 0 86.9%

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

      1. associate-+r+ 86.9%

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

      2. mul-1-neg 86.9%

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

      3. unsub-neg 86.9%

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

      4. +-commutative 86.9%

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

      5. associate-/l* 91.9%

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

      6. +-commutative 91.9%

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

   7. Simplified 91.9%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-112}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-106} \lor \neg \left(t \leq 4 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.4e-106) (not (<= t 4e-89)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* (/ y (+ x 1.0)) (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.4e-106) || !(t <= 4e-89)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.4d-106)) .or. (.not. (t <= 4d-89))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y / (x + 1.0d0)) * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.4e-106) || !(t <= 4e-89)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.4e-106) or not (t <= 4e-89):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.4e-106) || !(t <= 4e-89))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y / Float64(x + 1.0)) * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.4e-106) || ~((t <= 4e-89)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.4e-106], N[Not[LessEqual[t, 4e-89]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.39999999999999982e-106 or 4.00000000000000015e-89 < t

   1. Initial program 84.0%

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

      1. *-commutative 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in z around inf 88.0%

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

   if -3.39999999999999982e-106 < t < 4.00000000000000015e-89

   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 73.6%

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

      1. associate-+r+ 73.6%

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

      2. mul-1-neg 73.6%

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

      3. unsub-neg 73.6%

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

      4. +-commutative 73.6%

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

      5. associate-/l* 77.5%

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

      6. +-commutative 77.5%

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

   7. Simplified 77.5%

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

      1. div-sub 77.5%

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

      2. pow1 77.5%

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

      3. pow1 77.5%

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

      4. pow-div 77.5%

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

      5. metadata-eval 77.5%

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

      6. metadata-eval 77.5%

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

      7. associate-/r/ 75.5%

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

   9. Applied egg-rr 75.5%

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

   10. Taylor expanded in y around 0 73.5%

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

       1. +-commutative 73.5%

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

       2. *-commutative 73.5%

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

       3. times-frac 78.5%

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

   12. Simplified 78.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-106} \lor \neg \left(t \leq 4 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.05e+71) 1.0 (if (<= x 1.4e-62) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.05e+71) {
		tmp = 1.0;
	} else if (x <= 1.4e-62) {
		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 <= (-2.05d+71)) then
        tmp = 1.0d0
    else if (x <= 1.4d-62) 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 <= -2.05e+71) {
		tmp = 1.0;
	} else if (x <= 1.4e-62) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.05e+71:
		tmp = 1.0
	elif x <= 1.4e-62:
		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 <= -2.05e+71)
		tmp = 1.0;
	elseif (x <= 1.4e-62)
		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 <= -2.05e+71)
		tmp = 1.0;
	elseif (x <= 1.4e-62)
		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, -2.05e+71], 1.0, If[LessEqual[x, 1.4e-62], 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 < -2.0500000000000001e71 or 1.40000000000000001e-62 < x

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in z around inf 68.7%

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

      1. +-commutative 68.7%

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

      2. div-inv 68.7%

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

      3. fma-define 68.7%

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

   7. Applied egg-rr 68.7%

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

   8. Taylor expanded in x around inf 86.6%

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

   if -2.0500000000000001e71 < x < 1.40000000000000001e-62

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in z around inf 72.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-111}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.8e-111) 1.0 (if (<= x 8.9e-63) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e-111) {
		tmp = 1.0;
	} else if (x <= 8.9e-63) {
		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 <= (-4.8d-111)) then
        tmp = 1.0d0
    else if (x <= 8.9d-63) 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 <= -4.8e-111) {
		tmp = 1.0;
	} else if (x <= 8.9e-63) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.8e-111:
		tmp = 1.0
	elif x <= 8.9e-63:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.8e-111)
		tmp = 1.0;
	elseif (x <= 8.9e-63)
		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 <= -4.8e-111)
		tmp = 1.0;
	elseif (x <= 8.9e-63)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.8e-111], 1.0, If[LessEqual[x, 8.9e-63], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000001e-111 or 8.89999999999999988e-63 < x

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. div-inv 67.3%

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

      3. fma-define 67.3%

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

   7. Applied egg-rr 67.3%

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

   8. Taylor expanded in x around inf 75.9%

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

   if -4.8000000000000001e-111 < x < 8.89999999999999988e-63

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in z around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. div-inv 75.6%

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

      3. fma-define 75.7%

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

   7. Applied egg-rr 75.7%

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

   8. Taylor expanded in x around 0 61.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-111}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.8e-59) (/ x (+ x 1.0)) (if (<= x 1.02e-62) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-59) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.02e-62) {
		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 <= (-1.8d-59)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 1.02d-62) 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 <= -1.8e-59) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.02e-62) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8e-59:
		tmp = x / (x + 1.0)
	elif x <= 1.02e-62:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8e-59)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 1.02e-62)
		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 <= -1.8e-59)
		tmp = x / (x + 1.0);
	elseif (x <= 1.02e-62)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e-59], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e-62], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8e-59

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

   7. Simplified 81.9%

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

   if -1.8e-59 < x < 1.02000000000000005e-62

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in z around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. div-inv 72.9%

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

      3. fma-define 72.9%

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

   7. Applied egg-rr 72.9%

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

   8. Taylor expanded in x around 0 58.2%

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

   if 1.02000000000000005e-62 < x

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. div-inv 66.5%

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

      3. fma-define 66.5%

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

   7. Applied egg-rr 66.5%

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

   8. Taylor expanded in x around inf 82.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 2.6% 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 87.7%

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

   1. *-commutative 87.7%

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

3. Simplified 87.7%

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

   1. clear-num 87.7%

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

   2. inv-pow 87.7%

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

   3. fma-neg 87.7%

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

6. Applied egg-rr 87.7%

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

   1. unpow-1 87.7%

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

   2. fma-neg 87.7%

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

   3. *-commutative 87.7%

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

   4. *-commutative 87.7%

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

8. Simplified 87.7%

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

9. Taylor expanded in x around inf 49.1%

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

    1. frac-2neg 49.1%

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

    2. metadata-eval 49.1%

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

    3. div-inv 49.1%

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

    4. div-inv 49.0%

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

    5. +-commutative 49.0%

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

    6. distribute-lft-neg-in 49.0%

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

    7. +-commutative 49.0%

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

    8. add-sqr-sqrt 23.7%

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

    9. sqrt-unprod 13.1%

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

    10. sqr-neg 13.1%

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

    11. sqrt-unprod 1.3%

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

    12. add-sqr-sqrt 2.8%

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

    13. div-inv 2.8%

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

    14. frac-2neg 2.8%

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

    15. +-commutative 2.8%

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

    16. clear-num 2.8%

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

11. Applied egg-rr 2.8%

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

    1. associate-*r/ 2.8%

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

    2. mul-1-neg 2.8%

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

    3. +-commutative 2.8%

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

13. Simplified 2.8%

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

14. Taylor expanded in x around inf 2.8%

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

15. Final simplification 2.8%

    \[\leadsto -1 \]
16. Add Preprocessing

Alternative 10: 53.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.7%

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

   1. *-commutative 87.7%

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

3. Simplified 87.7%

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

5. Taylor expanded in z around inf 71.1%

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

   1. +-commutative 71.1%

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

   2. div-inv 71.1%

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

   3. fma-define 71.1%

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

7. Applied egg-rr 71.1%

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

8. Taylor expanded in x around inf 46.1%

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

9. Final simplification 46.1%

   \[\leadsto 1 \]
10. 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 2024034 
(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)))