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

Percentage Accurate: 88.5% → 95.6%

Time: 15.5s

Alternatives: 14

Speedup: 0.3×

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: 88.5% 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: 95.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{\mathsf{fma}\left(t, z, -x\right)}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+200}:\\ \;\;\;\;{\left(\frac{x + 1}{x + \frac{\mathsf{fma}\left(y, z, -x\right)}{t_1}}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -5e+41)
     (* (/ y (+ x 1.0)) (/ z (fma t z (- x))))
     (if (<= t_2 5e+200)
       (pow (/ (+ x 1.0) (+ x (/ (fma y z (- x)) t_1))) -1.0)
       (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+41) {
		tmp = (y / (x + 1.0)) * (z / fma(t, z, -x));
	} else if (t_2 <= 5e+200) {
		tmp = pow(((x + 1.0) / (x + (fma(y, z, -x) / t_1))), -1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -5e+41)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / fma(t, z, Float64(-x))));
	elseif (t_2 <= 5e+200)
		tmp = Float64(Float64(x + 1.0) / Float64(x + Float64(fma(y, z, Float64(-x)) / t_1))) ^ -1.0;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+41], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / N[(t * z + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+200], N[Power[N[(N[(x + 1.0), $MachinePrecision] / N[(x + N[(N[(y * z + (-x)), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -5.00000000000000022e41

   1. Initial program 65.7%

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

      1. *-commutative 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in y around inf 65.3%

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

      1. times-frac 93.5%

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

      2. +-commutative 93.5%

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

      3. fma-neg 93.5%

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

   7. Simplified 93.5%

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

   if -5.00000000000000022e41 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 5.00000000000000019e200

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

      1. clear-num 99.2%

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

      2. inv-pow 99.2%

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

      3. fma-neg 99.2%

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

   6. Applied egg-rr 99.2%

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

   if 5.00000000000000019e200 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 18.8%

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

      1. *-commutative 18.8%

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

   3. Simplified 18.8%

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

   5. Taylor expanded in z around inf 87.2%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{\mathsf{fma}\left(t, z, -x\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+200}:\\ \;\;\;\;{\left(\frac{x + 1}{x + \frac{\mathsf{fma}\left(y, z, -x\right)}{z \cdot t - x}}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{\mathsf{fma}\left(t, z, -x\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 -2e+80)
     (* (/ y (+ x 1.0)) (/ z (fma t z (- x))))
     (if (<= t_1 5e+200) t_1 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e+80) {
		tmp = (y / (x + 1.0)) * (z / fma(t, z, -x));
	} else if (t_1 <= 5e+200) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -2e+80)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / fma(t, z, Float64(-x))));
	elseif (t_1 <= 5e+200)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+80], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / N[(t * z + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+200], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -2e80

   1. Initial program 62.1%

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

      1. *-commutative 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in y around inf 61.7%

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

      1. times-frac 92.9%

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

      2. +-commutative 92.9%

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

      3. fma-neg 92.9%

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

   7. Simplified 92.9%

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

   if -2e80 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 5.00000000000000019e200

   1. Initial program 99.2%

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

   if 5.00000000000000019e200 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 18.8%

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

      1. *-commutative 18.8%

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

   3. Simplified 18.8%

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

   5. Taylor expanded in z around inf 87.2%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{\mathsf{fma}\left(t, z, -x\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+200}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+96}:\\ \;\;\;\;\frac{y}{\frac{t_1 \cdot \left(x + 1\right)}{z}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+200}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -5e+96)
     (/ y (/ (* t_1 (+ x 1.0)) z))
     (if (<= t_2 5e+200) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+96) {
		tmp = y / ((t_1 * (x + 1.0)) / z);
	} else if (t_2 <= 5e+200) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-5d+96)) then
        tmp = y / ((t_1 * (x + 1.0d0)) / z)
    else if (t_2 <= 5d+200) then
        tmp = t_2
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+96) {
		tmp = y / ((t_1 * (x + 1.0)) / z);
	} else if (t_2 <= 5e+200) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -5e+96:
		tmp = y / ((t_1 * (x + 1.0)) / z)
	elif t_2 <= 5e+200:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -5e+96)
		tmp = Float64(y / Float64(Float64(t_1 * Float64(x + 1.0)) / z));
	elseif (t_2 <= 5e+200)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -5e+96)
		tmp = y / ((t_1 * (x + 1.0)) / z);
	elseif (t_2 <= 5e+200)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+96], N[(y / N[(N[(t$95$1 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+200], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -5.0000000000000004e96

   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. Step-by-step derivation

      1. clear-num 60.9%

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

      2. inv-pow 60.9%

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

      3. fma-neg 60.9%

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

   6. Applied egg-rr 60.9%

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

   7. Taylor expanded in y around inf 60.3%

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

      1. associate-/l* 81.7%

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

      2. *-commutative 81.7%

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

      3. +-commutative 81.7%

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

   9. Simplified 81.7%

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

   if -5.0000000000000004e96 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 5.00000000000000019e200

   1. Initial program 99.2%

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

   if 5.00000000000000019e200 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 18.8%

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

      1. *-commutative 18.8%

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

   3. Simplified 18.8%

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

   5. Taylor expanded in z around inf 87.2%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+96}:\\ \;\;\;\;\frac{y}{\frac{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+200}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 112000000000:\\ \;\;\;\;1 - \frac{y}{\left(x + 1\right) \cdot \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -4.7e-9)
     t_1
     (if (<= t -3.15e-52)
       1.0
       (if (<= t -7.4e-61)
         (/ y (* t (+ x 1.0)))
         (if (<= t 112000000000.0)
           (- 1.0 (/ y (* (+ x 1.0) (/ x z))))
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -4.7e-9) {
		tmp = t_1;
	} else if (t <= -3.15e-52) {
		tmp = 1.0;
	} else if (t <= -7.4e-61) {
		tmp = y / (t * (x + 1.0));
	} else if (t <= 112000000000.0) {
		tmp = 1.0 - (y / ((x + 1.0) * (x / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-4.7d-9)) then
        tmp = t_1
    else if (t <= (-3.15d-52)) then
        tmp = 1.0d0
    else if (t <= (-7.4d-61)) then
        tmp = y / (t * (x + 1.0d0))
    else if (t <= 112000000000.0d0) then
        tmp = 1.0d0 - (y / ((x + 1.0d0) * (x / z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -4.7e-9) {
		tmp = t_1;
	} else if (t <= -3.15e-52) {
		tmp = 1.0;
	} else if (t <= -7.4e-61) {
		tmp = y / (t * (x + 1.0));
	} else if (t <= 112000000000.0) {
		tmp = 1.0 - (y / ((x + 1.0) * (x / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -4.7e-9:
		tmp = t_1
	elif t <= -3.15e-52:
		tmp = 1.0
	elif t <= -7.4e-61:
		tmp = y / (t * (x + 1.0))
	elif t <= 112000000000.0:
		tmp = 1.0 - (y / ((x + 1.0) * (x / z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -4.7e-9)
		tmp = t_1;
	elseif (t <= -3.15e-52)
		tmp = 1.0;
	elseif (t <= -7.4e-61)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	elseif (t <= 112000000000.0)
		tmp = Float64(1.0 - Float64(y / Float64(Float64(x + 1.0) * Float64(x / z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -4.7e-9)
		tmp = t_1;
	elseif (t <= -3.15e-52)
		tmp = 1.0;
	elseif (t <= -7.4e-61)
		tmp = y / (t * (x + 1.0));
	elseif (t <= 112000000000.0)
		tmp = 1.0 - (y / ((x + 1.0) * (x / z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.7e-9], t$95$1, If[LessEqual[t, -3.15e-52], 1.0, If[LessEqual[t, -7.4e-61], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 112000000000.0], N[(1.0 - N[(y / N[(N[(x + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.6999999999999999e-9 or 1.12e11 < 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 89.5%

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

   if -4.6999999999999999e-9 < t < -3.1500000000000002e-52

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 68.4%

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

   6. Taylor expanded in x around inf 100.0%

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

   if -3.1500000000000002e-52 < t < -7.3999999999999999e-61

   1. Initial program 76.0%

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

      1. *-commutative 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in y around inf 76.0%

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

   6. Taylor expanded in z around inf 93.1%

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

   if -7.3999999999999999e-61 < t < 1.12e11

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 72.7%

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

      1. associate-+r+ 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-/l* 77.7%

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

      6. +-commutative 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in y around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. +-commutative 72.6%

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

      3. *-commutative 72.6%

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

      4. times-frac 78.5%

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

      5. sub-neg 78.5%

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

      6. associate-*r/ 77.7%

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

      7. associate-/l* 78.5%

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

      8. associate-/l/ 78.5%

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

   10. Simplified 78.5%

       \[\leadsto \color{blue}{1 - \frac{y}{\frac{x}{z} \cdot \left(x + 1\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-9}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 112000000000:\\ \;\;\;\;1 - \frac{y}{\left(x + 1\right) \cdot \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{y}{\frac{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}{z}}\\ \mathbf{elif}\;t \leq 115000000000:\\ \;\;\;\;1 - \frac{y}{\left(x + 1\right) \cdot \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.15e-8)
     t_1
     (if (<= t -1.7e-52)
       1.0
       (if (<= t -7.4e-61)
         (/ y (/ (* (- (* z t) x) (+ x 1.0)) z))
         (if (<= t 115000000000.0)
           (- 1.0 (/ y (* (+ x 1.0) (/ x z))))
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.15e-8) {
		tmp = t_1;
	} else if (t <= -1.7e-52) {
		tmp = 1.0;
	} else if (t <= -7.4e-61) {
		tmp = y / ((((z * t) - x) * (x + 1.0)) / z);
	} else if (t <= 115000000000.0) {
		tmp = 1.0 - (y / ((x + 1.0) * (x / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.15d-8)) then
        tmp = t_1
    else if (t <= (-1.7d-52)) then
        tmp = 1.0d0
    else if (t <= (-7.4d-61)) then
        tmp = y / ((((z * t) - x) * (x + 1.0d0)) / z)
    else if (t <= 115000000000.0d0) then
        tmp = 1.0d0 - (y / ((x + 1.0d0) * (x / z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.15e-8) {
		tmp = t_1;
	} else if (t <= -1.7e-52) {
		tmp = 1.0;
	} else if (t <= -7.4e-61) {
		tmp = y / ((((z * t) - x) * (x + 1.0)) / z);
	} else if (t <= 115000000000.0) {
		tmp = 1.0 - (y / ((x + 1.0) * (x / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -1.15e-8:
		tmp = t_1
	elif t <= -1.7e-52:
		tmp = 1.0
	elif t <= -7.4e-61:
		tmp = y / ((((z * t) - x) * (x + 1.0)) / z)
	elif t <= 115000000000.0:
		tmp = 1.0 - (y / ((x + 1.0) * (x / z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1.15e-8)
		tmp = t_1;
	elseif (t <= -1.7e-52)
		tmp = 1.0;
	elseif (t <= -7.4e-61)
		tmp = Float64(y / Float64(Float64(Float64(Float64(z * t) - x) * Float64(x + 1.0)) / z));
	elseif (t <= 115000000000.0)
		tmp = Float64(1.0 - Float64(y / Float64(Float64(x + 1.0) * Float64(x / z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1.15e-8)
		tmp = t_1;
	elseif (t <= -1.7e-52)
		tmp = 1.0;
	elseif (t <= -7.4e-61)
		tmp = y / ((((z * t) - x) * (x + 1.0)) / z);
	elseif (t <= 115000000000.0)
		tmp = 1.0 - (y / ((x + 1.0) * (x / z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e-8], t$95$1, If[LessEqual[t, -1.7e-52], 1.0, If[LessEqual[t, -7.4e-61], N[(y / N[(N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 115000000000.0], N[(1.0 - N[(y / N[(N[(x + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15e-8 or 1.15e11 < 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 89.5%

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

   if -1.15e-8 < t < -1.70000000000000009e-52

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 68.4%

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

   6. Taylor expanded in x around inf 100.0%

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

   if -1.70000000000000009e-52 < t < -7.3999999999999999e-61

   1. Initial program 76.0%

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

      1. *-commutative 76.0%

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

   3. Simplified 76.0%

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

      1. clear-num 76.4%

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

      2. inv-pow 76.4%

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

      3. fma-neg 76.4%

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

   6. Applied egg-rr 76.4%

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

   7. Taylor expanded in y around inf 76.0%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -7.3999999999999999e-61 < t < 1.15e11

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 72.7%

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

      1. associate-+r+ 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-/l* 77.7%

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

      6. +-commutative 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in y around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. +-commutative 72.6%

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

      3. *-commutative 72.6%

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

      4. times-frac 78.5%

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

      5. sub-neg 78.5%

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

      6. associate-*r/ 77.7%

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

      7. associate-/l* 78.5%

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

      8. associate-/l/ 78.5%

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

   10. Simplified 78.5%

       \[\leadsto \color{blue}{1 - \frac{y}{\frac{x}{z} \cdot \left(x + 1\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-8}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{y}{\frac{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}{z}}\\ \mathbf{elif}\;t \leq 115000000000:\\ \;\;\;\;1 - \frac{y}{\left(x + 1\right) \cdot \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+49} \lor \neg \left(z \leq 3.5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e+49) (not (<= z 3.5e-9)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+49) || !(z <= 3.5e-9)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.8d+49)) .or. (.not. (z <= 3.5d-9))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+49) || !(z <= 3.5e-9)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e+49) or not (z <= 3.5e-9):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e+49) || !(z <= 3.5e-9))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.8e+49) || ~((z <= 3.5e-9)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e+49], N[Not[LessEqual[z, 3.5e-9]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e49 or 3.4999999999999999e-9 < z

   1. Initial program 73.9%

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

      1. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around inf 85.5%

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

   if -5.8e49 < z < 3.4999999999999999e-9

   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 y around 0 80.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+49} \lor \neg \left(z \leq 3.5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{-143} \lor \neg \left(z \leq 3.8 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.95e-143) (not (<= z 3.8e-75)))
   (/ (+ x (/ y t)) (+ x 1.0))
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.95e-143) || !(z <= 3.8e-75)) {
		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 ((z <= (-2.95d-143)) .or. (.not. (z <= 3.8d-75))) 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 ((z <= -2.95e-143) || !(z <= 3.8e-75)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.95e-143) or not (z <= 3.8e-75):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.95e-143) || !(z <= 3.8e-75))
		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 ((z <= -2.95e-143) || ~((z <= 3.8e-75)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.95e-143], N[Not[LessEqual[z, 3.8e-75]], $MachinePrecision]], 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 z < -2.95e-143 or 3.79999999999999994e-75 < z

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in z around inf 82.7%

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

   if -2.95e-143 < z < 3.79999999999999994e-75

   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 z around inf 46.9%

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

   6. Taylor expanded in x around inf 68.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{-143} \lor \neg \left(z \leq 3.8 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-144} \lor \neg \left(z \leq 4.1 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(z - \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.5e-144) (not (<= z 4.1e-75)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* y (- z (/ z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.5e-144) || !(z <= 4.1e-75)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (y * (z - (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 <= (-2.5d-144)) .or. (.not. (z <= 4.1d-75))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + (y * (z - (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 <= -2.5e-144) || !(z <= 4.1e-75)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (y * (z - (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.5e-144) or not (z <= 4.1e-75):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (y * (z - (z / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.5e-144) || !(z <= 4.1e-75))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(y * Float64(z - Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.5e-144) || ~((z <= 4.1e-75)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (y * (z - (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.5e-144], N[Not[LessEqual[z, 4.1e-75]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(z - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999999e-144 or 4.10000000000000002e-75 < z

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in z around inf 82.7%

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

   if -2.4999999999999999e-144 < z < 4.10000000000000002e-75

   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 79.6%

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

      1. associate-+r+ 79.6%

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

      2. mul-1-neg 79.6%

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

      3. unsub-neg 79.6%

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

      4. +-commutative 79.6%

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

      5. associate-/l* 79.6%

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

      6. +-commutative 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in x around 0 71.7%

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

      1. associate--l+ 71.7%

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

      2. associate-*r/ 71.7%

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

      3. associate-*r* 71.7%

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

      4. neg-mul-1 71.7%

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

      5. associate-*r* 71.7%

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

      6. neg-mul-1 71.7%

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

      7. distribute-lft-out-- 71.7%

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

   10. Simplified 71.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-144} \lor \neg \left(z \leq 4.1 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(z - \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.4e-82)
   1.0
   (if (<= x -4.5e-149)
     (* x (+ 1.0 (/ -1.0 (* z t))))
     (if (<= x 7e-89) (/ y t) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.4e-82) {
		tmp = 1.0;
	} else if (x <= -4.5e-149) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 7e-89) {
		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 <= (-5.4d-82)) then
        tmp = 1.0d0
    else if (x <= (-4.5d-149)) then
        tmp = x * (1.0d0 + ((-1.0d0) / (z * t)))
    else if (x <= 7d-89) 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 <= -5.4e-82) {
		tmp = 1.0;
	} else if (x <= -4.5e-149) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 7e-89) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.4e-82:
		tmp = 1.0
	elif x <= -4.5e-149:
		tmp = x * (1.0 + (-1.0 / (z * t)))
	elif x <= 7e-89:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.4e-82)
		tmp = 1.0;
	elseif (x <= -4.5e-149)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	elseif (x <= 7e-89)
		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 <= -5.4e-82)
		tmp = 1.0;
	elseif (x <= -4.5e-149)
		tmp = x * (1.0 + (-1.0 / (z * t)));
	elseif (x <= 7e-89)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.4e-82], 1.0, If[LessEqual[x, -4.5e-149], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-89], N[(y / t), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4000000000000003e-82 or 6.9999999999999994e-89 < x

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 69.2%

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

   6. Taylor expanded in x around inf 77.9%

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

   if -5.4000000000000003e-82 < x < -4.4999999999999998e-149

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t around -inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-lft-out-- 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around 0 55.0%

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

      1. +-commutative 55.0%

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

   10. Simplified 55.0%

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

   11. Taylor expanded in x around 0 55.0%

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

   if -4.4999999999999998e-149 < x < 6.9999999999999994e-89

   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 z around inf 75.3%

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

   6. Taylor expanded in x around 0 55.9%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-149}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8e-82)
   1.0
   (if (<= x -1.9e-149) (- x (/ (/ x t) z)) (if (<= x 2.75e-89) (/ y t) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8e-82) {
		tmp = 1.0;
	} else if (x <= -1.9e-149) {
		tmp = x - ((x / t) / z);
	} else if (x <= 2.75e-89) {
		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 <= (-8d-82)) then
        tmp = 1.0d0
    else if (x <= (-1.9d-149)) then
        tmp = x - ((x / t) / z)
    else if (x <= 2.75d-89) 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 <= -8e-82) {
		tmp = 1.0;
	} else if (x <= -1.9e-149) {
		tmp = x - ((x / t) / z);
	} else if (x <= 2.75e-89) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8e-82:
		tmp = 1.0
	elif x <= -1.9e-149:
		tmp = x - ((x / t) / z)
	elif x <= 2.75e-89:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8e-82)
		tmp = 1.0;
	elseif (x <= -1.9e-149)
		tmp = Float64(x - Float64(Float64(x / t) / z));
	elseif (x <= 2.75e-89)
		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 <= -8e-82)
		tmp = 1.0;
	elseif (x <= -1.9e-149)
		tmp = x - ((x / t) / z);
	elseif (x <= 2.75e-89)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8e-82], 1.0, If[LessEqual[x, -1.9e-149], N[(x - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.75e-89], N[(y / t), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -8e-82 or 2.75000000000000006e-89 < x

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 69.2%

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

   6. Taylor expanded in x around inf 77.9%

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

   if -8e-82 < x < -1.90000000000000003e-149

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t around -inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-lft-out-- 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around 0 55.0%

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

      1. +-commutative 55.0%

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

   10. Simplified 55.0%

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

   11. Taylor expanded in x around 0 55.0%

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

       1. sub-neg 55.0%

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

       2. distribute-rgt-in 55.0%

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

       3. *-lft-identity 55.0%

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

       4. cancel-sign-sub-inv 55.0%

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

       5. associate-*l/ 55.0%

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

       6. times-frac 55.1%

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

       7. associate-*l/ 55.0%

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

       8. *-lft-identity 55.0%

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

   13. Simplified 55.0%

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

   14. Taylor expanded in x around 0 55.0%

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

       1. associate-/r* 53.9%

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

   16. Simplified 53.9%

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

   if -1.90000000000000003e-149 < x < 2.75000000000000006e-89

   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 z around inf 75.3%

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

   6. Taylor expanded in x around 0 55.9%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-149}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-149}:\\ \;\;\;\;x - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.05e-81)
   1.0
   (if (<= x -7.5e-149) (- x (/ (/ x z) t)) (if (<= x 1.4e-87) (/ y t) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.05e-81) {
		tmp = 1.0;
	} else if (x <= -7.5e-149) {
		tmp = x - ((x / z) / t);
	} else if (x <= 1.4e-87) {
		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 <= (-1.05d-81)) then
        tmp = 1.0d0
    else if (x <= (-7.5d-149)) then
        tmp = x - ((x / z) / t)
    else if (x <= 1.4d-87) 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 <= -1.05e-81) {
		tmp = 1.0;
	} else if (x <= -7.5e-149) {
		tmp = x - ((x / z) / t);
	} else if (x <= 1.4e-87) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.05e-81:
		tmp = 1.0
	elif x <= -7.5e-149:
		tmp = x - ((x / z) / t)
	elif x <= 1.4e-87:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.05e-81)
		tmp = 1.0;
	elseif (x <= -7.5e-149)
		tmp = Float64(x - Float64(Float64(x / z) / t));
	elseif (x <= 1.4e-87)
		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 <= -1.05e-81)
		tmp = 1.0;
	elseif (x <= -7.5e-149)
		tmp = x - ((x / z) / t);
	elseif (x <= 1.4e-87)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.05e-81], 1.0, If[LessEqual[x, -7.5e-149], N[(x - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-87], N[(y / t), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e-81 or 1.4e-87 < x

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 69.2%

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

   6. Taylor expanded in x around inf 77.9%

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

   if -1.05e-81 < x < -7.49999999999999995e-149

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t around -inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-lft-out-- 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around 0 55.0%

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

      1. +-commutative 55.0%

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

   10. Simplified 55.0%

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

   11. Taylor expanded in x around 0 55.0%

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

       1. sub-neg 55.0%

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

       2. distribute-rgt-in 55.0%

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

       3. *-lft-identity 55.0%

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

       4. cancel-sign-sub-inv 55.0%

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

       5. associate-*l/ 55.0%

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

       6. times-frac 55.1%

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

       7. associate-*l/ 55.0%

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

       8. *-lft-identity 55.0%

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

   13. Simplified 55.0%

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

   if -7.49999999999999995e-149 < x < 1.4e-87

   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 z around inf 75.3%

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

   6. Taylor expanded in x around 0 55.9%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-149}:\\ \;\;\;\;x - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.2e-82)
   1.0
   (if (<= x -7.4e-149) x (if (<= x 2.55e-89) (/ y t) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.2e-82) {
		tmp = 1.0;
	} else if (x <= -7.4e-149) {
		tmp = x;
	} else if (x <= 2.55e-89) {
		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 <= (-9.2d-82)) then
        tmp = 1.0d0
    else if (x <= (-7.4d-149)) then
        tmp = x
    else if (x <= 2.55d-89) 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 <= -9.2e-82) {
		tmp = 1.0;
	} else if (x <= -7.4e-149) {
		tmp = x;
	} else if (x <= 2.55e-89) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.2e-82:
		tmp = 1.0
	elif x <= -7.4e-149:
		tmp = x
	elif x <= 2.55e-89:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.2e-82)
		tmp = 1.0;
	elseif (x <= -7.4e-149)
		tmp = x;
	elseif (x <= 2.55e-89)
		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 <= -9.2e-82)
		tmp = 1.0;
	elseif (x <= -7.4e-149)
		tmp = x;
	elseif (x <= 2.55e-89)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.2e-82], 1.0, If[LessEqual[x, -7.4e-149], x, If[LessEqual[x, 2.55e-89], N[(y / t), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.19999999999999988e-82 or 2.55000000000000002e-89 < x

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 69.2%

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

   6. Taylor expanded in x around inf 77.9%

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

   if -9.19999999999999988e-82 < x < -7.3999999999999998e-149

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t around -inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-lft-out-- 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around 0 55.0%

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

      1. +-commutative 55.0%

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

   10. Simplified 55.0%

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

   11. Taylor expanded in x around 0 55.0%

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

       1. sub-neg 55.0%

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

       2. distribute-rgt-in 55.0%

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

       3. *-lft-identity 55.0%

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

       4. cancel-sign-sub-inv 55.0%

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

       5. associate-*l/ 55.0%

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

       6. times-frac 55.1%

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

       7. associate-*l/ 55.0%

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

       8. *-lft-identity 55.0%

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

   13. Simplified 55.0%

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

   14. Taylor expanded in z around inf 47.5%

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

   if -7.3999999999999998e-149 < x < 2.55000000000000002e-89

   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 z around inf 75.3%

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

   6. Taylor expanded in x around 0 55.9%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.8e-82) 1.0 (if (<= x 5.5e-54) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e-82) {
		tmp = 1.0;
	} else if (x <= 5.5e-54) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.8d-82)) then
        tmp = 1.0d0
    else if (x <= 5.5d-54) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e-82) {
		tmp = 1.0;
	} else if (x <= 5.5e-54) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.8e-82:
		tmp = 1.0
	elif x <= 5.5e-54:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.8e-82)
		tmp = 1.0;
	elseif (x <= 5.5e-54)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.8e-82)
		tmp = 1.0;
	elseif (x <= 5.5e-54)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.8e-82], 1.0, If[LessEqual[x, 5.5e-54], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.80000000000000017e-82 or 5.50000000000000046e-54 < x

   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 z around inf 69.1%

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

   6. Taylor expanded in x around inf 79.2%

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

   if -4.80000000000000017e-82 < x < 5.50000000000000046e-54

   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 t around -inf 81.0%

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

      1. mul-1-neg 81.0%

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

      2. distribute-lft-out-- 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in y around 0 35.4%

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

      1. +-commutative 35.4%

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

   10. Simplified 35.4%

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

   11. Taylor expanded in x around 0 35.4%

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

       1. sub-neg 35.4%

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

       2. distribute-rgt-in 35.4%

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

       3. *-lft-identity 35.4%

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

       4. cancel-sign-sub-inv 35.4%

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

       5. associate-*l/ 35.4%

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

       6. times-frac 35.5%

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

       7. associate-*l/ 35.5%

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

       8. *-lft-identity 35.5%

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

   13. Simplified 35.5%

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

   14. Taylor expanded in z around inf 28.0%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.8% 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 87.9%

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

   1. *-commutative 87.9%

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

3. Simplified 87.9%

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

5. Taylor expanded in z around inf 70.8%

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

6. Taylor expanded in x around inf 53.0%

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

7. Final simplification 53.0%

   \[\leadsto 1 \]
8. 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 2024019 
(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)))