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

Percentage Accurate: 89.2% → 96.5%

Time: 11.7s

Alternatives: 10

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: 89.2% 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: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \left(t - \frac{x}{z}\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+274}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 -5e+37)
     (/ y (* (+ x 1.0) (- t (/ x z))))
     (if (<= t_1 2e+274) 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 <= -5e+37) {
		tmp = y / ((x + 1.0) * (t - (x / z)));
	} else if (t_1 <= 2e+274) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= (-5d+37)) then
        tmp = y / ((x + 1.0d0) * (t - (x / z)))
    else if (t_1 <= 2d+274) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+37) {
		tmp = y / ((x + 1.0) * (t - (x / z)));
	} else if (t_1 <= 2e+274) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -5e+37:
		tmp = y / ((x + 1.0) * (t - (x / z)))
	elif t_1 <= 2e+274:
		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 <= -5e+37)
		tmp = Float64(y / Float64(Float64(x + 1.0) * Float64(t - Float64(x / z))));
	elseif (t_1 <= 2e+274)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -5e+37)
		tmp = y / ((x + 1.0) * (t - (x / z)));
	elseif (t_1 <= 2e+274)
		tmp = t_1;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+37], N[(y / N[(N[(x + 1.0), $MachinePrecision] * N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+274], 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)) < -4.99999999999999989e37

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

   3. Simplified 80.9%

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

      1. clear-num 80.8%

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

      2. inv-pow 80.8%

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

   5. Applied egg-rr 80.8%

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

      1. unpow-1 80.8%

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

      2. *-commutative 80.8%

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

      3. *-commutative 80.8%

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

   7. Simplified 80.8%

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

   8. Taylor expanded in y around inf 80.8%

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

   9. Taylor expanded in y around inf 80.6%

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

       1. associate-/r* 80.9%

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

       2. associate-/l* 99.7%

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

       3. +-commutative 99.7%

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

       4. associate-/l/ 99.7%

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

       5. div-sub 99.7%

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

       6. associate-/l* 99.8%

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

       7. *-inverses 99.8%

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

       8. /-rgt-identity 99.8%

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

   11. Simplified 99.8%

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

   if -4.99999999999999989e37 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.99999999999999984e274

   1. Initial program 99.9%

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

   if 1.99999999999999984e274 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 11.2%

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

      1. *-commutative 11.2%

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

   3. Simplified 11.2%

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

   4. Taylor expanded in z around inf 77.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \left(t - \frac{x}{z}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+274}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{t}\\ t_2 := z \cdot t - x\\ t_3 := \frac{x + \frac{1}{\frac{t_2}{y \cdot z}}}{x + 1}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{t_1 - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-188}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{x - \frac{x}{t_2}}{x + 1}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ y t)))
        (t_2 (- (* z t) x))
        (t_3 (/ (+ x (/ 1.0 (/ t_2 (* y z)))) (+ x 1.0))))
   (if (<= z -1.3e+55)
     (/ (- t_1 (/ x (* z t))) (+ x 1.0))
     (if (<= z -1.02e-188)
       t_3
       (if (<= z 8.8e-30)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= z 2e+169) t_3 (/ t_1 (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y / t);
	double t_2 = (z * t) - x;
	double t_3 = (x + (1.0 / (t_2 / (y * z)))) / (x + 1.0);
	double tmp;
	if (z <= -1.3e+55) {
		tmp = (t_1 - (x / (z * t))) / (x + 1.0);
	} else if (z <= -1.02e-188) {
		tmp = t_3;
	} else if (z <= 8.8e-30) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (z <= 2e+169) {
		tmp = t_3;
	} else {
		tmp = t_1 / (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) :: t_3
    real(8) :: tmp
    t_1 = x + (y / t)
    t_2 = (z * t) - x
    t_3 = (x + (1.0d0 / (t_2 / (y * z)))) / (x + 1.0d0)
    if (z <= (-1.3d+55)) then
        tmp = (t_1 - (x / (z * t))) / (x + 1.0d0)
    else if (z <= (-1.02d-188)) then
        tmp = t_3
    else if (z <= 8.8d-30) then
        tmp = (x - (x / t_2)) / (x + 1.0d0)
    else if (z <= 2d+169) then
        tmp = t_3
    else
        tmp = t_1 / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y / t);
	double t_2 = (z * t) - x;
	double t_3 = (x + (1.0 / (t_2 / (y * z)))) / (x + 1.0);
	double tmp;
	if (z <= -1.3e+55) {
		tmp = (t_1 - (x / (z * t))) / (x + 1.0);
	} else if (z <= -1.02e-188) {
		tmp = t_3;
	} else if (z <= 8.8e-30) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (z <= 2e+169) {
		tmp = t_3;
	} else {
		tmp = t_1 / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y / t)
	t_2 = (z * t) - x
	t_3 = (x + (1.0 / (t_2 / (y * z)))) / (x + 1.0)
	tmp = 0
	if z <= -1.3e+55:
		tmp = (t_1 - (x / (z * t))) / (x + 1.0)
	elif z <= -1.02e-188:
		tmp = t_3
	elif z <= 8.8e-30:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif z <= 2e+169:
		tmp = t_3
	else:
		tmp = t_1 / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y / t))
	t_2 = Float64(Float64(z * t) - x)
	t_3 = Float64(Float64(x + Float64(1.0 / Float64(t_2 / Float64(y * z)))) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -1.3e+55)
		tmp = Float64(Float64(t_1 - Float64(x / Float64(z * t))) / Float64(x + 1.0));
	elseif (z <= -1.02e-188)
		tmp = t_3;
	elseif (z <= 8.8e-30)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (z <= 2e+169)
		tmp = t_3;
	else
		tmp = Float64(t_1 / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y / t);
	t_2 = (z * t) - x;
	t_3 = (x + (1.0 / (t_2 / (y * z)))) / (x + 1.0);
	tmp = 0.0;
	if (z <= -1.3e+55)
		tmp = (t_1 - (x / (z * t))) / (x + 1.0);
	elseif (z <= -1.02e-188)
		tmp = t_3;
	elseif (z <= 8.8e-30)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (z <= 2e+169)
		tmp = t_3;
	else
		tmp = t_1 / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(1.0 / N[(t$95$2 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+55], N[(N[(t$95$1 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e-188], t$95$3, If[LessEqual[z, 8.8e-30], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+169], t$95$3, N[(t$95$1 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e55

   1. Initial program 75.4%

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

      1. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in t around inf 87.7%

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

   if -1.3e55 < z < -1.02e-188 or 8.79999999999999933e-30 < z < 1.99999999999999987e169

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

   3. Simplified 98.9%

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

      1. clear-num 98.9%

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

      2. inv-pow 98.9%

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

   5. Applied egg-rr 98.9%

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

      1. unpow-1 98.9%

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

      2. *-commutative 98.9%

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

      3. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in y around inf 93.5%

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

   if -1.02e-188 < z < 8.79999999999999933e-30

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 82.4%

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

      1. +-commutative 82.4%

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

   6. Simplified 82.4%

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

   if 1.99999999999999987e169 < z

   1. Initial program 61.7%

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

      1. *-commutative 61.7%

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

   3. Simplified 61.7%

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

   4. Taylor expanded in z around inf 87.2%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{\left(x + \frac{y}{t}\right) - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-188}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{y \cdot z}}}{x + 1}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+169}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{y \cdot z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 82.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-60} \lor \neg \left(t \leq 45000000000000\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.85e-60) (not (<= t 45000000000000.0)))
   (/ (+ 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 <= -1.85e-60) || !(t <= 45000000000000.0)) {
		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 <= (-1.85d-60)) .or. (.not. (t <= 45000000000000.0d0))) 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 <= -1.85e-60) || !(t <= 45000000000000.0)) {
		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 <= -1.85e-60) or not (t <= 45000000000000.0):
		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 <= -1.85e-60) || !(t <= 45000000000000.0))
		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 <= -1.85e-60) || ~((t <= 45000000000000.0)))
		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, -1.85e-60], N[Not[LessEqual[t, 45000000000000.0]], $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 < -1.85000000000000012e-60 or 4.5e13 < t

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around inf 88.0%

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

   if -1.85000000000000012e-60 < t < 4.5e13

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in t around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. mul-1-neg 71.6%

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

      3. unsub-neg 71.6%

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

      4. associate-/l* 77.1%

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

      5. +-commutative 77.1%

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

   6. Simplified 77.1%

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

   7. Taylor expanded in y around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. unsub-neg 71.5%

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

      3. times-frac 77.8%

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

   9. Simplified 77.8%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-60} \lor \neg \left(t \leq 45000000000000\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \end{array} \]

Alternative 4: 77.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+18} \lor \neg \left(x \leq 1.4 \cdot 10^{+56}\right):\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.3e+18) (not (<= x 1.4e+56)))
   (- 1.0 (* (/ z x) (/ y x)))
   (/ (+ x (/ y t)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e+18) || !(x <= 1.4e+56)) {
		tmp = 1.0 - ((z / x) * (y / x));
	} 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) :: tmp
    if ((x <= (-4.3d+18)) .or. (.not. (x <= 1.4d+56))) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    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 tmp;
	if ((x <= -4.3e+18) || !(x <= 1.4e+56)) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.3e+18) or not (x <= 1.4e+56):
		tmp = 1.0 - ((z / x) * (y / x))
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.3e+18) || !(x <= 1.4e+56))
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	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)
	tmp = 0.0;
	if ((x <= -4.3e+18) || ~((x <= 1.4e+56)))
		tmp = 1.0 - ((z / x) * (y / x));
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.3e+18], N[Not[LessEqual[x, 1.4e+56]], $MachinePrecision]], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e18 or 1.40000000000000004e56 < x

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around -inf 77.9%

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

      1. mul-1-neg 77.9%

         \[\leadsto 1 + \color{blue}{\left(-\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)} \]

      2. unsub-neg 77.9%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out-- 77.9%

         \[\leadsto 1 - \frac{\color{blue}{z \cdot \left(y - t\right)}}{{x}^{2}} \]

      4. unpow2 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in y around inf 87.6%

      \[\leadsto 1 - \color{blue}{\frac{y \cdot z}{{x}^{2}}} \]
   8. Step-by-step derivation

      1. unpow2 87.6%

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

      2. times-frac 96.0%

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

   9. Simplified 96.0%

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

   if -4.3e18 < x < 1.40000000000000004e56

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in z around inf 63.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+18} \lor \neg \left(x \leq 1.4 \cdot 10^{+56}\right):\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 5: 67.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.25e-5)
   1.0
   (if (<= x 7e-63) (/ y (* t (+ x 1.0))) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.25e-5) {
		tmp = 1.0;
	} else if (x <= 7e-63) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.25d-5)) then
        tmp = 1.0d0
    else if (x <= 7d-63) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.25e-5) {
		tmp = 1.0;
	} else if (x <= 7e-63) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.25e-5:
		tmp = 1.0
	elif x <= 7e-63:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.25e-5)
		tmp = 1.0;
	elseif (x <= 7e-63)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.25e-5)
		tmp = 1.0;
	elseif (x <= 7e-63)
		tmp = y / (t * (x + 1.0));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.25e-5], 1.0, If[LessEqual[x, 7e-63], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25000000000000006e-5

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

      1. clear-num 89.9%

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

      2. inv-pow 89.9%

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

   5. Applied egg-rr 89.9%

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

      1. unpow-1 89.9%

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

      2. *-commutative 89.9%

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

      3. *-commutative 89.9%

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

   7. Simplified 89.9%

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

   8. Taylor expanded in y around inf 88.6%

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

   9. Taylor expanded in x around inf 86.8%

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

   if -1.25000000000000006e-5 < x < 7.00000000000000006e-63

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 69.7%

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

   5. Taylor expanded in y around inf 49.3%

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

   if 7.00000000000000006e-63 < x

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in t around inf 81.2%

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

      1. +-commutative 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 6: 67.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.5e-5)
   1.0
   (if (<= x 8.5e-70) (/ (/ y (+ x 1.0)) t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.5e-5) {
		tmp = 1.0;
	} else if (x <= 8.5e-70) {
		tmp = (y / (x + 1.0)) / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.5d-5)) then
        tmp = 1.0d0
    else if (x <= 8.5d-70) then
        tmp = (y / (x + 1.0d0)) / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.5e-5) {
		tmp = 1.0;
	} else if (x <= 8.5e-70) {
		tmp = (y / (x + 1.0)) / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.5e-5:
		tmp = 1.0
	elif x <= 8.5e-70:
		tmp = (y / (x + 1.0)) / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.5e-5)
		tmp = 1.0;
	elseif (x <= 8.5e-70)
		tmp = Float64(Float64(y / Float64(x + 1.0)) / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.5e-5)
		tmp = 1.0;
	elseif (x <= 8.5e-70)
		tmp = (y / (x + 1.0)) / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.5e-5], 1.0, If[LessEqual[x, 8.5e-70], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.50000000000000004e-5

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

      1. clear-num 89.9%

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

      2. inv-pow 89.9%

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

   5. Applied egg-rr 89.9%

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

      1. unpow-1 89.9%

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

      2. *-commutative 89.9%

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

      3. *-commutative 89.9%

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

   7. Simplified 89.9%

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

   8. Taylor expanded in y around inf 88.6%

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

   9. Taylor expanded in x around inf 86.8%

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

   if -1.50000000000000004e-5 < x < 8.5000000000000002e-70

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 69.7%

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

   5. Taylor expanded in t around 0 57.1%

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

   6. Taylor expanded in y around inf 49.3%

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

      1. associate-/r* 49.3%

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

      2. +-commutative 49.3%

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

   8. Simplified 49.3%

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

   if 8.5000000000000002e-70 < x

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in t around inf 81.2%

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

      1. +-commutative 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 7: 68.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0042:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.0042)
   (- 1.0 (* (/ z x) (/ y x)))
   (if (<= x 2e-77) (/ (/ y (+ x 1.0)) t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.0042) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 2e-77) {
		tmp = (y / (x + 1.0)) / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-0.0042d0)) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    else if (x <= 2d-77) then
        tmp = (y / (x + 1.0d0)) / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.0042) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 2e-77) {
		tmp = (y / (x + 1.0)) / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.0042:
		tmp = 1.0 - ((z / x) * (y / x))
	elif x <= 2e-77:
		tmp = (y / (x + 1.0)) / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.0042)
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	elseif (x <= 2e-77)
		tmp = Float64(Float64(y / Float64(x + 1.0)) / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.0042)
		tmp = 1.0 - ((z / x) * (y / x));
	elseif (x <= 2e-77)
		tmp = (y / (x + 1.0)) / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.0042], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-77], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00419999999999999974

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around -inf 77.3%

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

      1. mul-1-neg 77.3%

         \[\leadsto 1 + \color{blue}{\left(-\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)} \]

      2. unsub-neg 77.3%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out-- 77.3%

         \[\leadsto 1 - \frac{\color{blue}{z \cdot \left(y - t\right)}}{{x}^{2}} \]

      4. unpow2 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in y around inf 85.9%

      \[\leadsto 1 - \color{blue}{\frac{y \cdot z}{{x}^{2}}} \]
   8. Step-by-step derivation

      1. unpow2 85.9%

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

      2. times-frac 93.5%

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

   9. Simplified 93.5%

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

   if -0.00419999999999999974 < x < 1.9999999999999999e-77

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 69.7%

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

   5. Taylor expanded in t around 0 57.1%

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

   6. Taylor expanded in y around inf 49.3%

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

      1. associate-/r* 49.3%

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

      2. +-commutative 49.3%

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

   8. Simplified 49.3%

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

   if 1.9999999999999999e-77 < x

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in t around inf 81.2%

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

      1. +-commutative 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0042:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 8: 67.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.25e-5) 1.0 (if (<= x 7.5e-67) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.25e-5) {
		tmp = 1.0;
	} else if (x <= 7.5e-67) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.25d-5)) then
        tmp = 1.0d0
    else if (x <= 7.5d-67) then
        tmp = y / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.25e-5) {
		tmp = 1.0;
	} else if (x <= 7.5e-67) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.25e-5:
		tmp = 1.0
	elif x <= 7.5e-67:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.25e-5)
		tmp = 1.0;
	elseif (x <= 7.5e-67)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.25e-5)
		tmp = 1.0;
	elseif (x <= 7.5e-67)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.25e-5], 1.0, If[LessEqual[x, 7.5e-67], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25000000000000006e-5

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

      1. clear-num 89.9%

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

      2. inv-pow 89.9%

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

   5. Applied egg-rr 89.9%

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

      1. unpow-1 89.9%

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

      2. *-commutative 89.9%

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

      3. *-commutative 89.9%

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

   7. Simplified 89.9%

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

   8. Taylor expanded in y around inf 88.6%

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

   9. Taylor expanded in x around inf 86.8%

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

   if -1.25000000000000006e-5 < x < 7.5000000000000005e-67

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 69.7%

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

   5. Taylor expanded in y around inf 49.3%

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

   6. Taylor expanded in x around 0 49.1%

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

   if 7.5000000000000005e-67 < x

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in t around inf 81.2%

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

      1. +-commutative 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 9: 67.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.25e-5) 1.0 (if (<= x 7.1e-40) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.25e-5) {
		tmp = 1.0;
	} else if (x <= 7.1e-40) {
		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 <= (-1.25d-5)) then
        tmp = 1.0d0
    else if (x <= 7.1d-40) 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 <= -1.25e-5) {
		tmp = 1.0;
	} else if (x <= 7.1e-40) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.25e-5:
		tmp = 1.0
	elif x <= 7.1e-40:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.25e-5)
		tmp = 1.0;
	elseif (x <= 7.1e-40)
		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 <= -1.25e-5)
		tmp = 1.0;
	elseif (x <= 7.1e-40)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.25e-5], 1.0, If[LessEqual[x, 7.1e-40], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000006e-5 or 7.10000000000000023e-40 < x

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

   5. Applied egg-rr 89.2%

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

      1. unpow-1 89.2%

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

      2. *-commutative 89.2%

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

      3. *-commutative 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in y around inf 86.2%

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

   9. Taylor expanded in x around inf 86.4%

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

   if -1.25000000000000006e-5 < x < 7.10000000000000023e-40

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in t around inf 70.1%

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

   5. Taylor expanded in y around inf 48.3%

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

   6. Taylor expanded in x around 0 48.1%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

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 89.7%

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

   1. *-commutative 89.7%

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

3. Simplified 89.7%

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

   1. clear-num 89.6%

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

   2. inv-pow 89.6%

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

5. Applied egg-rr 89.6%

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

   1. unpow-1 89.6%

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

   2. *-commutative 89.6%

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

   3. *-commutative 89.6%

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

7. Simplified 89.6%

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

8. Taylor expanded in y around inf 76.4%

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

9. Taylor expanded in x around inf 53.7%

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

10. Final simplification 53.7%

    \[\leadsto 1 \]

Developer target: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023185 
(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)))