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

Percentage Accurate: 88.8% → 95.5%

Time: 13.1s

Alternatives: 13

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: 88.8% 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: 95.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+240}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+240)))
     (/ (+ x (/ y t)) (+ x 1.0))
     t_1)))

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 <= -((double) INFINITY)) || !(t_1 <= 5e+240)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+240)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	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 <= -math.inf) or not (t_1 <= 5e+240):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = t_1
	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 <= Float64(-Inf)) || !(t_1 <= 5e+240))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+240)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+240]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -inf.0 or 5.0000000000000003e240 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 38.1%

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

      1. *-commutative 38.1%

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

   3. Simplified 38.1%

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

   4. Taylor expanded in z around inf 88.3%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 5.0000000000000003e240

   1. Initial program 99.4%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty \lor \neg \left(\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+240}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 2: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-143}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y \cdot z}{x}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))
        (t_2 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -5.5e+24)
     t_2
     (if (<= z -1.5e-287)
       t_1
       (if (<= z 3.2e-143)
         (/ (+ x (- 1.0 (/ (* y z) x))) (+ x 1.0))
         (if (<= z 7.2e-44)
           t_1
           (if (<= z 2.5e+66)
             (/ (+ 1.0 (- x (/ y (/ x z)))) (+ x 1.0))
             t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -5.5e+24) {
		tmp = t_2;
	} else if (z <= -1.5e-287) {
		tmp = t_1;
	} else if (z <= 3.2e-143) {
		tmp = (x + (1.0 - ((y * z) / x))) / (x + 1.0);
	} else if (z <= 7.2e-44) {
		tmp = t_1;
	} else if (z <= 2.5e+66) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else {
		tmp = t_2;
	}
	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 = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    t_2 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-5.5d+24)) then
        tmp = t_2
    else if (z <= (-1.5d-287)) then
        tmp = t_1
    else if (z <= 3.2d-143) then
        tmp = (x + (1.0d0 - ((y * z) / x))) / (x + 1.0d0)
    else if (z <= 7.2d-44) then
        tmp = t_1
    else if (z <= 2.5d+66) then
        tmp = (1.0d0 + (x - (y / (x / z)))) / (x + 1.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -5.5e+24) {
		tmp = t_2;
	} else if (z <= -1.5e-287) {
		tmp = t_1;
	} else if (z <= 3.2e-143) {
		tmp = (x + (1.0 - ((y * z) / x))) / (x + 1.0);
	} else if (z <= 7.2e-44) {
		tmp = t_1;
	} else if (z <= 2.5e+66) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (x / ((z * t) - x))) / (x + 1.0)
	t_2 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -5.5e+24:
		tmp = t_2
	elif z <= -1.5e-287:
		tmp = t_1
	elif z <= 3.2e-143:
		tmp = (x + (1.0 - ((y * z) / x))) / (x + 1.0)
	elif z <= 7.2e-44:
		tmp = t_1
	elif z <= 2.5e+66:
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -5.5e+24)
		tmp = t_2;
	elseif (z <= -1.5e-287)
		tmp = t_1;
	elseif (z <= 3.2e-143)
		tmp = Float64(Float64(x + Float64(1.0 - Float64(Float64(y * z) / x))) / Float64(x + 1.0));
	elseif (z <= 7.2e-44)
		tmp = t_1;
	elseif (z <= 2.5e+66)
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	t_2 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -5.5e+24)
		tmp = t_2;
	elseif (z <= -1.5e-287)
		tmp = t_1;
	elseif (z <= 3.2e-143)
		tmp = (x + (1.0 - ((y * z) / x))) / (x + 1.0);
	elseif (z <= 7.2e-44)
		tmp = t_1;
	elseif (z <= 2.5e+66)
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+24], t$95$2, If[LessEqual[z, -1.5e-287], t$95$1, If[LessEqual[z, 3.2e-143], N[(N[(x + N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-44], t$95$1, If[LessEqual[z, 2.5e+66], N[(N[(1.0 + N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.5000000000000002e24 or 2.49999999999999996e66 < z

   1. Initial program 74.2%

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

      1. *-commutative 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in z around inf 87.6%

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

   if -5.5000000000000002e24 < z < -1.49999999999999996e-287 or 3.1999999999999998e-143 < z < 7.1999999999999998e-44

   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 84.8%

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

      1. +-commutative 84.8%

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

   6. Simplified 84.8%

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

   if -1.49999999999999996e-287 < z < 3.1999999999999998e-143

   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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

      2. *-commutative 99.9%

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

      3. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 84.7%

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

      1. associate-+r+ 84.7%

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

      2. mul-1-neg 84.7%

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

      3. unsub-neg 84.7%

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

   10. Simplified 84.7%

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

   if 7.1999999999999998e-44 < z < 2.49999999999999996e66

   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 t around 0 85.2%

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

      1. +-commutative 85.2%

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

      2. mul-1-neg 85.2%

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

      3. unsub-neg 85.2%

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

      4. associate-/l* 85.2%

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

      5. +-commutative 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-143}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y \cdot z}{x}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4200:\\ \;\;\;\;\frac{z}{x} \cdot \frac{-y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.2e-6)
   (/ x (+ x 1.0))
   (if (<= x 3.6e-236)
     (/ y (* t (+ x 1.0)))
     (if (<= x 6.8e-82)
       (- x (/ (/ x t) z))
       (if (<= x 1.6e-69)
         1.0
         (if (<= x 9.2e-28)
           x
           (if (<= x 4200.0) (* (/ z x) (/ (- y) x)) 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e-6) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.6e-236) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= 6.8e-82) {
		tmp = x - ((x / t) / z);
	} else if (x <= 1.6e-69) {
		tmp = 1.0;
	} else if (x <= 9.2e-28) {
		tmp = x;
	} else if (x <= 4200.0) {
		tmp = (z / x) * (-y / 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 <= (-6.2d-6)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 3.6d-236) then
        tmp = y / (t * (x + 1.0d0))
    else if (x <= 6.8d-82) then
        tmp = x - ((x / t) / z)
    else if (x <= 1.6d-69) then
        tmp = 1.0d0
    else if (x <= 9.2d-28) then
        tmp = x
    else if (x <= 4200.0d0) then
        tmp = (z / x) * (-y / 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 <= -6.2e-6) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.6e-236) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= 6.8e-82) {
		tmp = x - ((x / t) / z);
	} else if (x <= 1.6e-69) {
		tmp = 1.0;
	} else if (x <= 9.2e-28) {
		tmp = x;
	} else if (x <= 4200.0) {
		tmp = (z / x) * (-y / x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.2e-6:
		tmp = x / (x + 1.0)
	elif x <= 3.6e-236:
		tmp = y / (t * (x + 1.0))
	elif x <= 6.8e-82:
		tmp = x - ((x / t) / z)
	elif x <= 1.6e-69:
		tmp = 1.0
	elif x <= 9.2e-28:
		tmp = x
	elif x <= 4200.0:
		tmp = (z / x) * (-y / x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.2e-6)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 3.6e-236)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	elseif (x <= 6.8e-82)
		tmp = Float64(x - Float64(Float64(x / t) / z));
	elseif (x <= 1.6e-69)
		tmp = 1.0;
	elseif (x <= 9.2e-28)
		tmp = x;
	elseif (x <= 4200.0)
		tmp = Float64(Float64(z / x) * Float64(Float64(-y) / x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.2e-6)
		tmp = x / (x + 1.0);
	elseif (x <= 3.6e-236)
		tmp = y / (t * (x + 1.0));
	elseif (x <= 6.8e-82)
		tmp = x - ((x / t) / z);
	elseif (x <= 1.6e-69)
		tmp = 1.0;
	elseif (x <= 9.2e-28)
		tmp = x;
	elseif (x <= 4200.0)
		tmp = (z / x) * (-y / x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.2e-6], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-236], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-82], N[(x - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-69], 1.0, If[LessEqual[x, 9.2e-28], x, If[LessEqual[x, 4200.0], N[(N[(z / x), $MachinePrecision] * N[((-y) / x), $MachinePrecision]), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -6.1999999999999999e-6

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 87.5%

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

      1. +-commutative 87.5%

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

   6. Simplified 87.5%

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

   if -6.1999999999999999e-6 < x < 3.60000000000000008e-236

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around inf 55.3%

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

      1. associate-/l* 59.2%

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

      2. *-commutative 59.2%

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

      3. +-commutative 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in t around inf 54.7%

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

   if 3.60000000000000008e-236 < x < 6.7999999999999995e-82

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 75.2%

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

   5. Taylor expanded in y around 0 46.9%

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

   6. Taylor expanded in x around 0 46.8%

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

      1. *-commutative 46.8%

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

      2. sub-neg 46.8%

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

      3. distribute-rgt-in 46.8%

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

      4. distribute-lft-neg-in 46.8%

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

      5. unsub-neg 46.8%

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

      6. *-lft-identity 46.8%

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

      7. associate-*l/ 46.9%

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

      8. *-lft-identity 46.9%

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

      9. associate-/r* 46.9%

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

   8. Simplified 46.9%

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

   if 6.7999999999999995e-82 < x < 1.59999999999999999e-69 or 4200 < x

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in z around inf 68.9%

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

   5. Taylor expanded in x around inf 87.8%

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

   if 1.59999999999999999e-69 < x < 9.19999999999999942e-28

   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. Step-by-step derivation

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

   5. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

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

      2. *-commutative 99.6%

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

      3. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around inf 52.4%

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

   9. Taylor expanded in x around 0 52.6%

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

   if 9.19999999999999942e-28 < x < 4200

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around -inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. unsub-neg 59.8%

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

      3. distribute-rgt-out-- 59.8%

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

      4. unpow2 59.8%

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

      5. times-frac 59.8%

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

   6. Simplified 59.8%

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

   7. Taylor expanded in y around inf 59.8%

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

   8. Taylor expanded in z around inf 40.2%

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

      1. unpow2 40.2%

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

      2. associate-*r/ 40.2%

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

      3. *-commutative 40.2%

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

      4. neg-mul-1 40.2%

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

      5. distribute-rgt-neg-in 40.2%

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

      6. times-frac 40.2%

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

   10. Simplified 40.2%

       \[\leadsto \color{blue}{\frac{z}{x} \cdot \frac{-y}{x}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4200:\\ \;\;\;\;\frac{z}{x} \cdot \frac{-y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-99}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-69}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* t (+ x 1.0)))))
   (if (<= x -6.2e-6)
     (/ x (+ x 1.0))
     (if (<= x 3.6e-236)
       t_1
       (if (<= x 1.76e-99)
         (- x (/ (/ x t) z))
         (if (<= x 3e-69)
           1.0
           (if (<= x 1.05e-25) x (if (<= x 1.3) t_1 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t * (x + 1.0));
	double tmp;
	if (x <= -6.2e-6) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.6e-236) {
		tmp = t_1;
	} else if (x <= 1.76e-99) {
		tmp = x - ((x / t) / z);
	} else if (x <= 3e-69) {
		tmp = 1.0;
	} else if (x <= 1.05e-25) {
		tmp = x;
	} else if (x <= 1.3) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y / (t * (x + 1.0d0))
    if (x <= (-6.2d-6)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 3.6d-236) then
        tmp = t_1
    else if (x <= 1.76d-99) then
        tmp = x - ((x / t) / z)
    else if (x <= 3d-69) then
        tmp = 1.0d0
    else if (x <= 1.05d-25) then
        tmp = x
    else if (x <= 1.3d0) then
        tmp = t_1
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (t * (x + 1.0));
	double tmp;
	if (x <= -6.2e-6) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.6e-236) {
		tmp = t_1;
	} else if (x <= 1.76e-99) {
		tmp = x - ((x / t) / z);
	} else if (x <= 3e-69) {
		tmp = 1.0;
	} else if (x <= 1.05e-25) {
		tmp = x;
	} else if (x <= 1.3) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t * (x + 1.0))
	tmp = 0
	if x <= -6.2e-6:
		tmp = x / (x + 1.0)
	elif x <= 3.6e-236:
		tmp = t_1
	elif x <= 1.76e-99:
		tmp = x - ((x / t) / z)
	elif x <= 3e-69:
		tmp = 1.0
	elif x <= 1.05e-25:
		tmp = x
	elif x <= 1.3:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t * Float64(x + 1.0)))
	tmp = 0.0
	if (x <= -6.2e-6)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 3.6e-236)
		tmp = t_1;
	elseif (x <= 1.76e-99)
		tmp = Float64(x - Float64(Float64(x / t) / z));
	elseif (x <= 3e-69)
		tmp = 1.0;
	elseif (x <= 1.05e-25)
		tmp = x;
	elseif (x <= 1.3)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t * (x + 1.0));
	tmp = 0.0;
	if (x <= -6.2e-6)
		tmp = x / (x + 1.0);
	elseif (x <= 3.6e-236)
		tmp = t_1;
	elseif (x <= 1.76e-99)
		tmp = x - ((x / t) / z);
	elseif (x <= 3e-69)
		tmp = 1.0;
	elseif (x <= 1.05e-25)
		tmp = x;
	elseif (x <= 1.3)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e-6], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-236], t$95$1, If[LessEqual[x, 1.76e-99], N[(x - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-69], 1.0, If[LessEqual[x, 1.05e-25], x, If[LessEqual[x, 1.3], t$95$1, 1.0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.1999999999999999e-6

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 87.5%

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

      1. +-commutative 87.5%

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

   6. Simplified 87.5%

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

   if -6.1999999999999999e-6 < x < 3.60000000000000008e-236 or 1.05000000000000001e-25 < x < 1.30000000000000004

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around inf 54.8%

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

      1. associate-/l* 59.4%

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

      2. *-commutative 59.4%

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

      3. +-commutative 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in t around inf 54.2%

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

   if 3.60000000000000008e-236 < x < 1.75999999999999991e-99

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 75.2%

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

   5. Taylor expanded in y around 0 46.9%

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

   6. Taylor expanded in x around 0 46.8%

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

      1. *-commutative 46.8%

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

      2. sub-neg 46.8%

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

      3. distribute-rgt-in 46.8%

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

      4. distribute-lft-neg-in 46.8%

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

      5. unsub-neg 46.8%

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

      6. *-lft-identity 46.8%

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

      7. associate-*l/ 46.9%

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

      8. *-lft-identity 46.9%

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

      9. associate-/r* 46.9%

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

   8. Simplified 46.9%

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

   if 1.75999999999999991e-99 < x < 2.99999999999999989e-69 or 1.30000000000000004 < x

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in z around inf 67.8%

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

   5. Taylor expanded in x around inf 86.6%

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

   if 2.99999999999999989e-69 < x < 1.05000000000000001e-25

   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. Step-by-step derivation

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 46.9%

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

   9. Taylor expanded in x around 0 47.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-99}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-69}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 66.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-134}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-102}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-41}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (* (/ z x) (/ y x)))))
   (if (<= x -8.5e-72)
     t_1
     (if (<= x 3.6e-236)
       (/ y t)
       (if (<= x 4.5e-134)
         (- x (/ (/ x t) z))
         (if (<= x 3.3e-102)
           (* z (/ y (- (* z t) x)))
           (if (<= x 7.2e-41) 1.0 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((z / x) * (y / x));
	double tmp;
	if (x <= -8.5e-72) {
		tmp = t_1;
	} else if (x <= 3.6e-236) {
		tmp = y / t;
	} else if (x <= 4.5e-134) {
		tmp = x - ((x / t) / z);
	} else if (x <= 3.3e-102) {
		tmp = z * (y / ((z * t) - x));
	} else if (x <= 7.2e-41) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - ((z / x) * (y / x))
    if (x <= (-8.5d-72)) then
        tmp = t_1
    else if (x <= 3.6d-236) then
        tmp = y / t
    else if (x <= 4.5d-134) then
        tmp = x - ((x / t) / z)
    else if (x <= 3.3d-102) then
        tmp = z * (y / ((z * t) - x))
    else if (x <= 7.2d-41) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((z / x) * (y / x));
	double tmp;
	if (x <= -8.5e-72) {
		tmp = t_1;
	} else if (x <= 3.6e-236) {
		tmp = y / t;
	} else if (x <= 4.5e-134) {
		tmp = x - ((x / t) / z);
	} else if (x <= 3.3e-102) {
		tmp = z * (y / ((z * t) - x));
	} else if (x <= 7.2e-41) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - ((z / x) * (y / x))
	tmp = 0
	if x <= -8.5e-72:
		tmp = t_1
	elif x <= 3.6e-236:
		tmp = y / t
	elif x <= 4.5e-134:
		tmp = x - ((x / t) / z)
	elif x <= 3.3e-102:
		tmp = z * (y / ((z * t) - x))
	elif x <= 7.2e-41:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)))
	tmp = 0.0
	if (x <= -8.5e-72)
		tmp = t_1;
	elseif (x <= 3.6e-236)
		tmp = Float64(y / t);
	elseif (x <= 4.5e-134)
		tmp = Float64(x - Float64(Float64(x / t) / z));
	elseif (x <= 3.3e-102)
		tmp = Float64(z * Float64(y / Float64(Float64(z * t) - x)));
	elseif (x <= 7.2e-41)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - ((z / x) * (y / x));
	tmp = 0.0;
	if (x <= -8.5e-72)
		tmp = t_1;
	elseif (x <= 3.6e-236)
		tmp = y / t;
	elseif (x <= 4.5e-134)
		tmp = x - ((x / t) / z);
	elseif (x <= 3.3e-102)
		tmp = z * (y / ((z * t) - x));
	elseif (x <= 7.2e-41)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e-72], t$95$1, If[LessEqual[x, 3.6e-236], N[(y / t), $MachinePrecision], If[LessEqual[x, 4.5e-134], N[(x - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-102], N[(z * N[(y / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-41], 1.0, t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.50000000000000008e-72 or 7.2e-41 < 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 x around -inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

      3. distribute-rgt-out-- 67.6%

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

      4. unpow2 67.6%

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

      5. times-frac 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in y around inf 79.6%

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

   if -8.50000000000000008e-72 < x < 3.60000000000000008e-236

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in y around inf 58.0%

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

      1. associate-/l* 62.5%

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

      2. *-commutative 62.5%

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

      3. +-commutative 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in x around 0 60.0%

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

   if 3.60000000000000008e-236 < x < 4.5000000000000005e-134

   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. Taylor expanded in t around inf 73.2%

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

   5. Taylor expanded in y around 0 53.4%

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

   6. Taylor expanded in x around 0 53.4%

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

      1. *-commutative 53.4%

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

      2. sub-neg 53.4%

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

      3. distribute-rgt-in 53.4%

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

      4. distribute-lft-neg-in 53.4%

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

      5. unsub-neg 53.4%

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

      6. *-lft-identity 53.4%

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

      7. associate-*l/ 53.4%

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

      8. *-lft-identity 53.4%

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

      9. associate-/r* 53.5%

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

   8. Simplified 53.5%

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

   if 4.5000000000000005e-134 < x < 3.3e-102

   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. Taylor expanded in y around inf 86.0%

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

      1. times-frac 86.0%

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

      2. +-commutative 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in x around 0 86.0%

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

   if 3.3e-102 < x < 7.2e-41

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 40.6%

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

   5. Taylor expanded in x around inf 46.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-72}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-134}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-102}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-41}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \end{array} \]

Alternative 6: 66.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-133}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-104}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.5e-6)
   (/ x (+ x 1.0))
   (if (<= x 1.15e-236)
     (/ y (* t (+ x 1.0)))
     (if (<= x 2.2e-133)
       (- x (/ (/ x t) z))
       (if (<= x 6.5e-104)
         (* z (/ y (- (* z t) x)))
         (if (<= x 1.4e-88) x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e-6) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.15e-236) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= 2.2e-133) {
		tmp = x - ((x / t) / z);
	} else if (x <= 6.5e-104) {
		tmp = z * (y / ((z * t) - x));
	} else if (x <= 1.4e-88) {
		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 <= (-4.5d-6)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 1.15d-236) then
        tmp = y / (t * (x + 1.0d0))
    else if (x <= 2.2d-133) then
        tmp = x - ((x / t) / z)
    else if (x <= 6.5d-104) then
        tmp = z * (y / ((z * t) - x))
    else if (x <= 1.4d-88) 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 <= -4.5e-6) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.15e-236) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= 2.2e-133) {
		tmp = x - ((x / t) / z);
	} else if (x <= 6.5e-104) {
		tmp = z * (y / ((z * t) - x));
	} else if (x <= 1.4e-88) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.5e-6:
		tmp = x / (x + 1.0)
	elif x <= 1.15e-236:
		tmp = y / (t * (x + 1.0))
	elif x <= 2.2e-133:
		tmp = x - ((x / t) / z)
	elif x <= 6.5e-104:
		tmp = z * (y / ((z * t) - x))
	elif x <= 1.4e-88:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.5e-6)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 1.15e-236)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	elseif (x <= 2.2e-133)
		tmp = Float64(x - Float64(Float64(x / t) / z));
	elseif (x <= 6.5e-104)
		tmp = Float64(z * Float64(y / Float64(Float64(z * t) - x)));
	elseif (x <= 1.4e-88)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.5e-6)
		tmp = x / (x + 1.0);
	elseif (x <= 1.15e-236)
		tmp = y / (t * (x + 1.0));
	elseif (x <= 2.2e-133)
		tmp = x - ((x / t) / z);
	elseif (x <= 6.5e-104)
		tmp = z * (y / ((z * t) - x));
	elseif (x <= 1.4e-88)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.5e-6], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-236], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-133], N[(x - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-104], N[(z * N[(y / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-88], x, 1.0]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.50000000000000011e-6

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 87.5%

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

      1. +-commutative 87.5%

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

   6. Simplified 87.5%

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

   if -4.50000000000000011e-6 < x < 1.15000000000000003e-236

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around inf 55.3%

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

      1. associate-/l* 59.2%

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

      2. *-commutative 59.2%

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

      3. +-commutative 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in t around inf 54.7%

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

   if 1.15000000000000003e-236 < x < 2.2000000000000001e-133

   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. Taylor expanded in t around inf 73.2%

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

   5. Taylor expanded in y around 0 53.4%

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

   6. Taylor expanded in x around 0 53.4%

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

      1. *-commutative 53.4%

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

      2. sub-neg 53.4%

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

      3. distribute-rgt-in 53.4%

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

      4. distribute-lft-neg-in 53.4%

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

      5. unsub-neg 53.4%

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

      6. *-lft-identity 53.4%

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

      7. associate-*l/ 53.4%

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

      8. *-lft-identity 53.4%

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

      9. associate-/r* 53.5%

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

   8. Simplified 53.5%

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

   if 2.2000000000000001e-133 < x < 6.49999999999999991e-104

   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. Taylor expanded in y around inf 86.0%

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

      1. times-frac 86.0%

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

      2. +-commutative 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in x around 0 86.0%

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

   if 6.49999999999999991e-104 < x < 1.39999999999999988e-88

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

      1. clear-num 0.0%

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

      2. inv-pow 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. unpow-1 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x around inf 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

   if 1.39999999999999988e-88 < x

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 64.9%

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

   5. Taylor expanded in x around inf 74.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-133}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-104}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 78.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-17} \lor \neg \left(z \leq 3.8 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e-17) (not (<= z 3.8e+60)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ 1.0 (- x (/ y (/ x z)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e-17) || !(z <= 3.8e+60)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.5d-17)) .or. (.not. (z <= 3.8d+60))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (1.0d0 + (x - (y / (x / z)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e-17) || !(z <= 3.8e+60)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e-17) or not (z <= 3.8e+60):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e-17) || !(z <= 3.8e+60))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e-17) || ~((z <= 3.8e+60)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e-17], N[Not[LessEqual[z, 3.8e+60]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000001e-17 or 3.80000000000000009e60 < z

   1. Initial program 76.7%

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

      1. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in z around inf 87.1%

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

   if -5.50000000000000001e-17 < z < 3.80000000000000009e60

   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 t around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. mul-1-neg 77.6%

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

      3. unsub-neg 77.6%

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

      4. associate-/l* 77.6%

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

      5. +-commutative 77.6%

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

   6. Simplified 77.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-17} \lor \neg \left(z \leq 3.8 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \]

Alternative 8: 65.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-68}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.6e-26)
   (/ x (+ x 1.0))
   (if (<= x 3.6e-236)
     (/ y t)
     (if (<= x 6.6e-74)
       (- x (/ (/ x t) z))
       (if (<= x 1.66e-68)
         1.0
         (if (<= x 1.05e-25) x (if (<= x 1.3) (/ y t) 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.6e-26) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.6e-236) {
		tmp = y / t;
	} else if (x <= 6.6e-74) {
		tmp = x - ((x / t) / z);
	} else if (x <= 1.66e-68) {
		tmp = 1.0;
	} else if (x <= 1.05e-25) {
		tmp = x;
	} else if (x <= 1.3) {
		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 <= (-3.6d-26)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 3.6d-236) then
        tmp = y / t
    else if (x <= 6.6d-74) then
        tmp = x - ((x / t) / z)
    else if (x <= 1.66d-68) then
        tmp = 1.0d0
    else if (x <= 1.05d-25) then
        tmp = x
    else if (x <= 1.3d0) 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 <= -3.6e-26) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.6e-236) {
		tmp = y / t;
	} else if (x <= 6.6e-74) {
		tmp = x - ((x / t) / z);
	} else if (x <= 1.66e-68) {
		tmp = 1.0;
	} else if (x <= 1.05e-25) {
		tmp = x;
	} else if (x <= 1.3) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.6e-26:
		tmp = x / (x + 1.0)
	elif x <= 3.6e-236:
		tmp = y / t
	elif x <= 6.6e-74:
		tmp = x - ((x / t) / z)
	elif x <= 1.66e-68:
		tmp = 1.0
	elif x <= 1.05e-25:
		tmp = x
	elif x <= 1.3:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.6e-26)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 3.6e-236)
		tmp = Float64(y / t);
	elseif (x <= 6.6e-74)
		tmp = Float64(x - Float64(Float64(x / t) / z));
	elseif (x <= 1.66e-68)
		tmp = 1.0;
	elseif (x <= 1.05e-25)
		tmp = x;
	elseif (x <= 1.3)
		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 <= -3.6e-26)
		tmp = x / (x + 1.0);
	elseif (x <= 3.6e-236)
		tmp = y / t;
	elseif (x <= 6.6e-74)
		tmp = x - ((x / t) / z);
	elseif (x <= 1.66e-68)
		tmp = 1.0;
	elseif (x <= 1.05e-25)
		tmp = x;
	elseif (x <= 1.3)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.6e-26], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-236], N[(y / t), $MachinePrecision], If[LessEqual[x, 6.6e-74], N[(x - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.66e-68], 1.0, If[LessEqual[x, 1.05e-25], x, If[LessEqual[x, 1.3], N[(y / t), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.6000000000000001e-26

   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 inf 83.9%

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

      1. +-commutative 83.9%

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

   6. Simplified 83.9%

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

   if -3.6000000000000001e-26 < x < 3.60000000000000008e-236 or 1.05000000000000001e-25 < x < 1.30000000000000004

   1. Initial program 85.7%

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

      1. *-commutative 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in y around inf 53.8%

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

      1. associate-/l* 58.7%

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

      2. *-commutative 58.7%

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

      3. +-commutative 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in x around 0 55.5%

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

   if 3.60000000000000008e-236 < x < 6.59999999999999992e-74

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 75.2%

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

   5. Taylor expanded in y around 0 46.9%

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

   6. Taylor expanded in x around 0 46.8%

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

      1. *-commutative 46.8%

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

      2. sub-neg 46.8%

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

      3. distribute-rgt-in 46.8%

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

      4. distribute-lft-neg-in 46.8%

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

      5. unsub-neg 46.8%

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

      6. *-lft-identity 46.8%

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

      7. associate-*l/ 46.9%

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

      8. *-lft-identity 46.9%

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

      9. associate-/r* 46.9%

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

   8. Simplified 46.9%

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

   if 6.59999999999999992e-74 < x < 1.6600000000000001e-68 or 1.30000000000000004 < x

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in z around inf 67.8%

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

   5. Taylor expanded in x around inf 86.6%

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

   if 1.6600000000000001e-68 < x < 1.05000000000000001e-25

   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. Step-by-step derivation

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 46.9%

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

   9. Taylor expanded in x around 0 47.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-68}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 75.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-167} \lor \neg \left(z \leq 6.6 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e-167) (not (<= z 6.6e-108)))
   (/ (+ x (/ y t)) (+ x 1.0))
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e-167) || !(z <= 6.6e-108)) {
		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 <= (-1.25d-167)) .or. (.not. (z <= 6.6d-108))) 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 <= -1.25e-167) || !(z <= 6.6e-108)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e-167) or not (z <= 6.6e-108):
		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 <= -1.25e-167) || !(z <= 6.6e-108))
		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 <= -1.25e-167) || ~((z <= 6.6e-108)))
		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, -1.25e-167], N[Not[LessEqual[z, 6.6e-108]], $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 < -1.25000000000000005e-167 or 6.6000000000000004e-108 < z

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in z around inf 78.3%

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

   if -1.25000000000000005e-167 < z < 6.6000000000000004e-108

   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 z around inf 38.9%

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

   5. Taylor expanded in x around inf 70.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-167} \lor \neg \left(z \leq 6.6 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 68.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-158}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4e-71)
   1.0
   (if (<= x 1.02e-158)
     (/ y t)
     (if (<= x 1e-133) x (if (<= x 8.2e-83) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e-71) {
		tmp = 1.0;
	} else if (x <= 1.02e-158) {
		tmp = y / t;
	} else if (x <= 1e-133) {
		tmp = x;
	} else if (x <= 8.2e-83) {
		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 <= (-4d-71)) then
        tmp = 1.0d0
    else if (x <= 1.02d-158) then
        tmp = y / t
    else if (x <= 1d-133) then
        tmp = x
    else if (x <= 8.2d-83) 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 <= -4e-71) {
		tmp = 1.0;
	} else if (x <= 1.02e-158) {
		tmp = y / t;
	} else if (x <= 1e-133) {
		tmp = x;
	} else if (x <= 8.2e-83) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4e-71:
		tmp = 1.0
	elif x <= 1.02e-158:
		tmp = y / t
	elif x <= 1e-133:
		tmp = x
	elif x <= 8.2e-83:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4e-71)
		tmp = 1.0;
	elseif (x <= 1.02e-158)
		tmp = Float64(y / t);
	elseif (x <= 1e-133)
		tmp = x;
	elseif (x <= 8.2e-83)
		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 <= -4e-71)
		tmp = 1.0;
	elseif (x <= 1.02e-158)
		tmp = y / t;
	elseif (x <= 1e-133)
		tmp = x;
	elseif (x <= 8.2e-83)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4e-71], 1.0, If[LessEqual[x, 1.02e-158], N[(y / t), $MachinePrecision], If[LessEqual[x, 1e-133], x, If[LessEqual[x, 8.2e-83], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9999999999999997e-71 or 8.1999999999999999e-83 < 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 z around inf 65.5%

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

   5. Taylor expanded in x around inf 75.7%

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

   if -3.9999999999999997e-71 < x < 1.0199999999999999e-158 or 1.0000000000000001e-133 < x < 8.1999999999999999e-83

   1. Initial program 87.8%

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

      1. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in y around inf 56.4%

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

      1. associate-/l* 59.9%

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

      2. *-commutative 59.9%

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

      3. +-commutative 59.9%

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

   6. Simplified 59.9%

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

   7. Taylor expanded in x around 0 55.9%

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

   if 1.0199999999999999e-158 < x < 1.0000000000000001e-133

   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. Step-by-step derivation

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 67.8%

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

   9. Taylor expanded in x around 0 67.8%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-158}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 68.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-79}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.4e-33)
   (/ x (+ x 1.0))
   (if (<= x 8e-156)
     (/ y t)
     (if (<= x 2.7e-133) x (if (<= x 7.4e-79) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-33) {
		tmp = x / (x + 1.0);
	} else if (x <= 8e-156) {
		tmp = y / t;
	} else if (x <= 2.7e-133) {
		tmp = x;
	} else if (x <= 7.4e-79) {
		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 <= (-2.4d-33)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 8d-156) then
        tmp = y / t
    else if (x <= 2.7d-133) then
        tmp = x
    else if (x <= 7.4d-79) 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 <= -2.4e-33) {
		tmp = x / (x + 1.0);
	} else if (x <= 8e-156) {
		tmp = y / t;
	} else if (x <= 2.7e-133) {
		tmp = x;
	} else if (x <= 7.4e-79) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.4e-33:
		tmp = x / (x + 1.0)
	elif x <= 8e-156:
		tmp = y / t
	elif x <= 2.7e-133:
		tmp = x
	elif x <= 7.4e-79:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.4e-33)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 8e-156)
		tmp = Float64(y / t);
	elseif (x <= 2.7e-133)
		tmp = x;
	elseif (x <= 7.4e-79)
		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 <= -2.4e-33)
		tmp = x / (x + 1.0);
	elseif (x <= 8e-156)
		tmp = y / t;
	elseif (x <= 2.7e-133)
		tmp = x;
	elseif (x <= 7.4e-79)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.4e-33], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-156], N[(y / t), $MachinePrecision], If[LessEqual[x, 2.7e-133], x, If[LessEqual[x, 7.4e-79], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e-33

   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 inf 83.9%

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

      1. +-commutative 83.9%

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

   6. Simplified 83.9%

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

   if -2.4e-33 < x < 8.00000000000000032e-156 or 2.6999999999999999e-133 < x < 7.40000000000000035e-79

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in y around inf 53.6%

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

      1. associate-/l* 56.9%

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

      2. *-commutative 56.9%

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

      3. +-commutative 56.9%

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

   6. Simplified 56.9%

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

   7. Taylor expanded in x around 0 53.1%

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

   if 8.00000000000000032e-156 < x < 2.6999999999999999e-133

   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. Step-by-step derivation

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 67.8%

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

   9. Taylor expanded in x around 0 67.8%

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

   if 7.40000000000000035e-79 < x

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 64.9%

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

   5. Taylor expanded in x around inf 74.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-79}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12: 55.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-248}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.05e-248) 1.0 (if (<= x 1.5e-84) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.05e-248) {
		tmp = 1.0;
	} else if (x <= 1.5e-84) {
		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 <= (-1.05d-248)) then
        tmp = 1.0d0
    else if (x <= 1.5d-84) 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 <= -1.05e-248) {
		tmp = 1.0;
	} else if (x <= 1.5e-84) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.05e-248:
		tmp = 1.0
	elif x <= 1.5e-84:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.05e-248)
		tmp = 1.0;
	elseif (x <= 1.5e-84)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.05e-248)
		tmp = 1.0;
	elseif (x <= 1.5e-84)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.05e-248], 1.0, If[LessEqual[x, 1.5e-84], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e-248 or 1.5000000000000001e-84 < x

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 64.5%

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

   5. Taylor expanded in x around inf 63.2%

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

   if -1.05e-248 < x < 1.5000000000000001e-84

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

      1. clear-num 92.6%

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

      2. inv-pow 92.6%

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

   5. Applied egg-rr 92.6%

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

      1. unpow-1 92.6%

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

      2. *-commutative 92.6%

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

      3. *-commutative 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in x around inf 29.6%

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

   9. Taylor expanded in x around 0 29.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-248}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 54.3% 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 89.6%

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

   1. *-commutative 89.6%

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

3. Simplified 89.6%

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

4. Taylor expanded in z around inf 66.8%

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

5. Taylor expanded in x around inf 51.9%

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

6. Final simplification 51.9%

   \[\leadsto 1 \]

Developer target: 99.4% 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 2023199 
(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)))