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

Percentage Accurate: 89.2% → 94.7%

Time: 15.6s

Alternatives: 14

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+165}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+111}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{-1 - x} + \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.62e+165)
   (/ (+ x (/ y t)) (+ x 1.0))
   (if (<= z 3.2e+111)
     (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))
     (- (/ x (+ x 1.0)) (/ (+ (/ y (- -1.0 x)) (/ x (* z (+ x 1.0)))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.62e+165) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 3.2e+111) {
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((y / (-1.0 - x)) + (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.62d+165)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (z <= 3.2d+111) then
        tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    else
        tmp = (x / (x + 1.0d0)) - (((y / ((-1.0d0) - x)) + (x / (z * (x + 1.0d0)))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.62e+165) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 3.2e+111) {
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((y / (-1.0 - x)) + (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.62e+165:
		tmp = (x + (y / t)) / (x + 1.0)
	elif z <= 3.2e+111:
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	else:
		tmp = (x / (x + 1.0)) - (((y / (-1.0 - x)) + (x / (z * (x + 1.0)))) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.62e+165)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (z <= 3.2e+111)
		tmp = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(Float64(y / Float64(-1.0 - x)) + Float64(x / Float64(z * Float64(x + 1.0)))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.62e+165)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (z <= 3.2e+111)
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	else
		tmp = (x / (x + 1.0)) - (((y / (-1.0 - x)) + (x / (z * (x + 1.0)))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.62e+165], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+111], 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], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] + N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.61999999999999993e165

   1. Initial program 75.4%

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

      1. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in z around inf 99.9%

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

   if -1.61999999999999993e165 < z < 3.2000000000000001e111

   1. Initial program 98.2%

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

   if 3.2000000000000001e111 < z

   1. Initial program 68.4%

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

      1. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in t around -inf 90.1%

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

      1. +-commutative 90.1%

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

      2. mul-1-neg 90.1%

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

      3. unsub-neg 90.1%

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

      4. +-commutative 90.1%

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

   7. Simplified 90.1%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+165}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+111}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{-1 - x} + \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ \mathbf{if}\;\frac{x + \frac{t\_1}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{x + t\_1 \cdot \frac{\frac{1}{z - \frac{x}{t}}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{-1 - x} + \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x)))
   (if (<= (/ (+ x (/ t_1 (- (* z t) x))) (+ x 1.0)) 5e+307)
     (/ (+ x (* t_1 (/ (/ 1.0 (- z (/ x t))) t))) (+ x 1.0))
     (- (/ x (+ x 1.0)) (/ (+ (/ y (- -1.0 x)) (/ x (* z (+ x 1.0)))) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double tmp;
	if (((x + (t_1 / ((z * t) - x))) / (x + 1.0)) <= 5e+307) {
		tmp = (x + (t_1 * ((1.0 / (z - (x / t))) / t))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((y / (-1.0 - x)) + (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - x
    if (((x + (t_1 / ((z * t) - x))) / (x + 1.0d0)) <= 5d+307) then
        tmp = (x + (t_1 * ((1.0d0 / (z - (x / t))) / t))) / (x + 1.0d0)
    else
        tmp = (x / (x + 1.0d0)) - (((y / ((-1.0d0) - x)) + (x / (z * (x + 1.0d0)))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double tmp;
	if (((x + (t_1 / ((z * t) - x))) / (x + 1.0)) <= 5e+307) {
		tmp = (x + (t_1 * ((1.0 / (z - (x / t))) / t))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((y / (-1.0 - x)) + (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - x
	tmp = 0
	if ((x + (t_1 / ((z * t) - x))) / (x + 1.0)) <= 5e+307:
		tmp = (x + (t_1 * ((1.0 / (z - (x / t))) / t))) / (x + 1.0)
	else:
		tmp = (x / (x + 1.0)) - (((y / (-1.0 - x)) + (x / (z * (x + 1.0)))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - x)
	tmp = 0.0
	if (Float64(Float64(x + Float64(t_1 / Float64(Float64(z * t) - x))) / Float64(x + 1.0)) <= 5e+307)
		tmp = Float64(Float64(x + Float64(t_1 * Float64(Float64(1.0 / Float64(z - Float64(x / t))) / t))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(Float64(y / Float64(-1.0 - x)) + Float64(x / Float64(z * Float64(x + 1.0)))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - x;
	tmp = 0.0;
	if (((x + (t_1 / ((z * t) - x))) / (x + 1.0)) <= 5e+307)
		tmp = (x + (t_1 * ((1.0 / (z - (x / t))) / t))) / (x + 1.0);
	else
		tmp = (x / (x + 1.0)) - (((y / (-1.0 - x)) + (x / (z * (x + 1.0)))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[N[(N[(x + N[(t$95$1 / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 5e+307], N[(N[(x + N[(t$95$1 * N[(N[(1.0 / N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] + N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

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)) < 5e307

   1. Initial program 96.9%

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

      1. *-commutative 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf 96.9%

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

      1. mul-1-neg 96.9%

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

      2. unsub-neg 96.9%

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

   7. Simplified 96.9%

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

      1. div-inv 96.8%

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

      2. *-commutative 96.8%

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

   9. Applied egg-rr 96.8%

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

       1. inv-pow 96.8%

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

       2. unpow-prod-down 97.0%

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

       3. inv-pow 97.0%

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

   11. Applied egg-rr 97.0%

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

       1. associate-*l/ 97.1%

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

       2. *-lft-identity 97.1%

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

       3. unpow-1 97.1%

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

   13. Simplified 97.1%

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

   if 5e307 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 18.5%

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

      1. *-commutative 18.5%

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

   3. Simplified 18.5%

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

   5. Taylor expanded in t around -inf 82.7%

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

      1. +-commutative 82.7%

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

      2. mul-1-neg 82.7%

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

      3. unsub-neg 82.7%

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

      4. +-commutative 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{\frac{1}{z - \frac{x}{t}}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{-1 - x} + \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -750000 \lor \neg \left(t \leq -1.8 \cdot 10^{-64} \lor \neg \left(t \leq -2.8 \cdot 10^{-115}\right) \land t \leq 3.2 \cdot 10^{-138}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -750000.0)
         (not
          (or (<= t -1.8e-64) (and (not (<= t -2.8e-115)) (<= t 3.2e-138)))))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- (+ x 1.0) (* y (/ z x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -750000.0) || !((t <= -1.8e-64) || (!(t <= -2.8e-115) && (t <= 3.2e-138)))) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-750000.0d0)) .or. (.not. (t <= (-1.8d-64)) .or. (.not. (t <= (-2.8d-115))) .and. (t <= 3.2d-138))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = ((x + 1.0d0) - (y * (z / x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -750000.0) || !((t <= -1.8e-64) || (!(t <= -2.8e-115) && (t <= 3.2e-138)))) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -750000.0) or not ((t <= -1.8e-64) or (not (t <= -2.8e-115) and (t <= 3.2e-138))):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -750000.0) || !((t <= -1.8e-64) || (!(t <= -2.8e-115) && (t <= 3.2e-138))))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -750000.0) || ~(((t <= -1.8e-64) || (~((t <= -2.8e-115)) && (t <= 3.2e-138)))))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -750000.0], N[Not[Or[LessEqual[t, -1.8e-64], And[N[Not[LessEqual[t, -2.8e-115]], $MachinePrecision], LessEqual[t, 3.2e-138]]]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5e5 or -1.7999999999999999e-64 < t < -2.79999999999999987e-115 or 3.2000000000000001e-138 < t

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in z around inf 86.9%

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

   if -7.5e5 < t < -1.7999999999999999e-64 or -2.79999999999999987e-115 < t < 3.2000000000000001e-138

   1. Initial program 96.3%

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

      1. *-commutative 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0 80.2%

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

      1. associate-+r+ 80.2%

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

      2. mul-1-neg 80.2%

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

      3. unsub-neg 80.2%

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

      4. +-commutative 80.2%

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

      5. associate-/l* 83.7%

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

      6. +-commutative 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -750000 \lor \neg \left(t \leq -1.8 \cdot 10^{-64} \lor \neg \left(t \leq -2.8 \cdot 10^{-115}\right) \land t \leq 3.2 \cdot 10^{-138}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1300000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-118} \lor \neg \left(t \leq 3.1 \cdot 10^{-139}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1300000.0)
     t_1
     (if (<= t -9.5e-64)
       (/ (+ x (/ (- x (* y z)) x)) (+ x 1.0))
       (if (or (<= t -1.45e-118) (not (<= t 3.1e-139)))
         t_1
         (/ (- (+ x 1.0) (* y (/ z x))) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1300000.0) {
		tmp = t_1;
	} else if (t <= -9.5e-64) {
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	} else if ((t <= -1.45e-118) || !(t <= 3.1e-139)) {
		tmp = t_1;
	} else {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1300000.0d0)) then
        tmp = t_1
    else if (t <= (-9.5d-64)) then
        tmp = (x + ((x - (y * z)) / x)) / (x + 1.0d0)
    else if ((t <= (-1.45d-118)) .or. (.not. (t <= 3.1d-139))) then
        tmp = t_1
    else
        tmp = ((x + 1.0d0) - (y * (z / x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1300000.0) {
		tmp = t_1;
	} else if (t <= -9.5e-64) {
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	} else if ((t <= -1.45e-118) || !(t <= 3.1e-139)) {
		tmp = t_1;
	} else {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -1300000.0:
		tmp = t_1
	elif t <= -9.5e-64:
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0)
	elif (t <= -1.45e-118) or not (t <= 3.1e-139):
		tmp = t_1
	else:
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1300000.0)
		tmp = t_1;
	elseif (t <= -9.5e-64)
		tmp = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / x)) / Float64(x + 1.0));
	elseif ((t <= -1.45e-118) || !(t <= 3.1e-139))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1300000.0)
		tmp = t_1;
	elseif (t <= -9.5e-64)
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	elseif ((t <= -1.45e-118) || ~((t <= 3.1e-139)))
		tmp = t_1;
	else
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1300000.0], t$95$1, If[LessEqual[t, -9.5e-64], N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.45e-118], N[Not[LessEqual[t, 3.1e-139]], $MachinePrecision]], t$95$1, N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e6 or -9.50000000000000043e-64 < t < -1.4499999999999999e-118 or 3.0999999999999999e-139 < t

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in z around inf 86.9%

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

   if -1.3e6 < t < -9.50000000000000043e-64

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 79.6%

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

      1. neg-mul-1 79.6%

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

   7. Simplified 79.6%

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

   if -1.4499999999999999e-118 < t < 3.0999999999999999e-139

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around 0 80.4%

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

      1. associate-+r+ 80.4%

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

      2. mul-1-neg 80.4%

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

      3. unsub-neg 80.4%

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

      4. +-commutative 80.4%

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

      5. associate-/l* 84.6%

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

      6. +-commutative 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1300000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-118} \lor \neg \left(t \leq 3.1 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+165} \lor \neg \left(z \leq 8.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5e+165) (not (<= z 8.5e+96)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e+165) || !(z <= 8.5e+96)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.5d+165)) .or. (.not. (z <= 8.5d+96))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e+165) || !(z <= 8.5e+96)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.5e+165) or not (z <= 8.5e+96):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.5e+165) || !(z <= 8.5e+96))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.5e+165) || ~((z <= 8.5e+96)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.5e+165], N[Not[LessEqual[z, 8.5e+96]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999995e165 or 8.50000000000000025e96 < z

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in z around inf 92.5%

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

   if -1.49999999999999995e165 < z < 8.50000000000000025e96

   1. Initial program 98.2%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+165} \lor \neg \left(z \leq 8.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-96} \lor \neg \left(z \leq 1.85 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-96) (not (<= z 1.85e-123)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-96) || !(z <= 1.85e-123)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.2d-96)) .or. (.not. (z <= 1.85d-123))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-96) || !(z <= 1.85e-123)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-96) or not (z <= 1.85e-123):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-96) || !(z <= 1.85e-123))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.2e-96) || ~((z <= 1.85e-123)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e-96], N[Not[LessEqual[z, 1.85e-123]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.20000000000000016e-96 or 1.85000000000000008e-123 < z

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in z around inf 82.1%

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

   if -7.20000000000000016e-96 < z < 1.85000000000000008e-123

   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. Add Preprocessing

   5. Taylor expanded in y around 0 80.9%

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

      1. +-commutative 80.9%

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

   7. Simplified 80.9%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-96} \lor \neg \left(z \leq 1.85 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{-1}{x}\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ -1.0 x))))
   (if (<= x -4.6e-23)
     t_1
     (if (<= x 4.8e-79) (* y (/ 1.0 t)) (if (<= x 1.0) (* x (- 1.0 x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (-1.0 / x);
	double tmp;
	if (x <= -4.6e-23) {
		tmp = t_1;
	} else if (x <= 4.8e-79) {
		tmp = y * (1.0 / t);
	} else if (x <= 1.0) {
		tmp = x * (1.0 - x);
	} 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 + ((-1.0d0) / x)
    if (x <= (-4.6d-23)) then
        tmp = t_1
    else if (x <= 4.8d-79) then
        tmp = y * (1.0d0 / t)
    else if (x <= 1.0d0) then
        tmp = x * (1.0d0 - x)
    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 + (-1.0 / x);
	double tmp;
	if (x <= -4.6e-23) {
		tmp = t_1;
	} else if (x <= 4.8e-79) {
		tmp = y * (1.0 / t);
	} else if (x <= 1.0) {
		tmp = x * (1.0 - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + (-1.0 / x)
	tmp = 0
	if x <= -4.6e-23:
		tmp = t_1
	elif x <= 4.8e-79:
		tmp = y * (1.0 / t)
	elif x <= 1.0:
		tmp = x * (1.0 - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(-1.0 / x))
	tmp = 0.0
	if (x <= -4.6e-23)
		tmp = t_1;
	elseif (x <= 4.8e-79)
		tmp = Float64(y * Float64(1.0 / t));
	elseif (x <= 1.0)
		tmp = Float64(x * Float64(1.0 - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + (-1.0 / x);
	tmp = 0.0;
	if (x <= -4.6e-23)
		tmp = t_1;
	elseif (x <= 4.8e-79)
		tmp = y * (1.0 / t);
	elseif (x <= 1.0)
		tmp = x * (1.0 - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6e-23], t$95$1, If[LessEqual[x, 4.8e-79], N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6000000000000002e-23 or 1 < x

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in t around inf 88.2%

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

      1. +-commutative 88.2%

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

   7. Simplified 88.2%

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

   8. Taylor expanded in x around inf 87.0%

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

   if -4.6000000000000002e-23 < x < 4.80000000000000011e-79

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 59.9%

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

      2. associate-/r* 59.9%

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

      3. +-commutative 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in x around 0 53.7%

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

   if 4.80000000000000011e-79 < x < 1

   1. Initial program 78.5%

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

      1. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t around inf 59.4%

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

      1. +-commutative 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in x around 0 59.6%

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

      1. *-rgt-identity 59.6%

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

      2. neg-mul-1 59.6%

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

      3. sub-neg 59.6%

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

      4. *-rgt-identity 59.6%

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

   10. Simplified 59.6%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-23}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7800 \lor \neg \left(x \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7800.0) (not (<= x 5e-7)))
   (/ (+ x 1.0) (+ x 1.0))
   (/ (+ x (/ y t)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7800.0) || !(x <= 5e-7)) {
		tmp = (x + 1.0) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7800.0d0)) .or. (.not. (x <= 5d-7))) then
        tmp = (x + 1.0d0) / (x + 1.0d0)
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7800.0) || !(x <= 5e-7)) {
		tmp = (x + 1.0) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7800.0) or not (x <= 5e-7):
		tmp = (x + 1.0) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7800.0) || !(x <= 5e-7))
		tmp = Float64(Float64(x + 1.0) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7800.0) || ~((x <= 5e-7)))
		tmp = (x + 1.0) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7800.0], N[Not[LessEqual[x, 5e-7]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7800 or 4.99999999999999977e-7 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 89.3%

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

   if -7800 < x < 4.99999999999999977e-7

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around inf 72.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7800 \lor \neg \left(x \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.8e-16)
   (/ 1.0 (/ (+ x 1.0) x))
   (if (<= x 9.8e-76) (* y (/ z (- (* z t) x))) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e-16) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 9.8e-76) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.8d-16)) then
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    else if (x <= 9.8d-76) then
        tmp = y * (z / ((z * t) - x))
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e-16) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 9.8e-76) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.8e-16:
		tmp = 1.0 / ((x + 1.0) / x)
	elif x <= 9.8e-76:
		tmp = y * (z / ((z * t) - x))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.8e-16)
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	elseif (x <= 9.8e-76)
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.8e-16)
		tmp = 1.0 / ((x + 1.0) / x);
	elseif (x <= 9.8e-76)
		tmp = y * (z / ((z * t) - x));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.8e-16], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e-76], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8e-16

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

   3. Simplified 88.6%

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

      1. clear-num 88.6%

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

      2. inv-pow 88.6%

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

      3. fma-neg 88.6%

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

   6. Applied egg-rr 88.6%

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

      1. unpow-1 88.6%

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

      2. fma-neg 88.6%

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

      3. *-commutative 88.6%

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

      4. *-commutative 88.6%

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

   8. Simplified 88.6%

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

   9. Taylor expanded in x around inf 90.5%

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

   if -6.8e-16 < x < 9.79999999999999944e-76

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in y around inf 57.9%

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

      1. associate-/l* 59.5%

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

      2. associate-/r* 59.5%

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

      3. +-commutative 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in x around 0 59.5%

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

   if 9.79999999999999944e-76 < x

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

   7. Simplified 81.9%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.6e-25)
   (/ 1.0 (/ (+ x 1.0) x))
   (if (<= x 8.5e-77) (/ y (* t (+ x 1.0))) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.6e-25) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 8.5e-77) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.6d-25)) then
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    else if (x <= 8.5d-77) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.6e-25) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 8.5e-77) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.6e-25:
		tmp = 1.0 / ((x + 1.0) / x)
	elif x <= 8.5e-77:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.6e-25)
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	elseif (x <= 8.5e-77)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.6e-25)
		tmp = 1.0 / ((x + 1.0) / x);
	elseif (x <= 8.5e-77)
		tmp = y / (t * (x + 1.0));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.6e-25], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-77], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999998e-25

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

      1. clear-num 88.8%

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

      2. inv-pow 88.8%

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

      3. fma-neg 88.8%

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

   6. Applied egg-rr 88.8%

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

      1. unpow-1 88.8%

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

      2. fma-neg 88.8%

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

      3. *-commutative 88.8%

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

      4. *-commutative 88.8%

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

   8. Simplified 88.8%

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

   9. Taylor expanded in x around inf 89.1%

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

   if -4.5999999999999998e-25 < x < 8.4999999999999998e-77

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 59.9%

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

      2. associate-/r* 59.9%

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

      3. +-commutative 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in z around inf 53.8%

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

   if 8.4999999999999998e-77 < x

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

   7. Simplified 81.9%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-26} \lor \neg \left(x \leq 1.05 \cdot 10^{-76}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.45e-26) (not (<= x 1.05e-76)))
   (/ x (+ x 1.0))
   (* y (/ 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.45e-26) || !(x <= 1.05e-76)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y * (1.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.45d-26)) .or. (.not. (x <= 1.05d-76))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y * (1.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.45e-26) || !(x <= 1.05e-76)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y * (1.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.45e-26) or not (x <= 1.05e-76):
		tmp = x / (x + 1.0)
	else:
		tmp = y * (1.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.45e-26) || !(x <= 1.05e-76))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y * Float64(1.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.45e-26) || ~((x <= 1.05e-76)))
		tmp = x / (x + 1.0);
	else
		tmp = y * (1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.45e-26], N[Not[LessEqual[x, 1.05e-76]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4499999999999999e-26 or 1.04999999999999996e-76 < x

   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. Add Preprocessing

   5. Taylor expanded in t around inf 85.2%

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

      1. +-commutative 85.2%

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

   7. Simplified 85.2%

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

   if -1.4499999999999999e-26 < x < 1.04999999999999996e-76

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 59.9%

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

      2. associate-/r* 59.9%

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

      3. +-commutative 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in x around 0 53.7%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-26} \lor \neg \left(x \leq 1.05 \cdot 10^{-76}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.8e-28)
   (/ 1.0 (/ (+ x 1.0) x))
   (if (<= x 3.7e-78) (* y (/ 1.0 t)) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e-28) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 3.7e-78) {
		tmp = y * (1.0 / t);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-5.8d-28)) then
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    else if (x <= 3.7d-78) then
        tmp = y * (1.0d0 / t)
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e-28) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 3.7e-78) {
		tmp = y * (1.0 / t);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.8e-28:
		tmp = 1.0 / ((x + 1.0) / x)
	elif x <= 3.7e-78:
		tmp = y * (1.0 / t)
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.8e-28)
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	elseif (x <= 3.7e-78)
		tmp = Float64(y * Float64(1.0 / t));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.8e-28)
		tmp = 1.0 / ((x + 1.0) / x);
	elseif (x <= 3.7e-78)
		tmp = y * (1.0 / t);
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.8e-28], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e-78], N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.80000000000000026e-28

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

      1. clear-num 88.8%

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

      2. inv-pow 88.8%

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

      3. fma-neg 88.8%

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

   6. Applied egg-rr 88.8%

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

      1. unpow-1 88.8%

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

      2. fma-neg 88.8%

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

      3. *-commutative 88.8%

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

      4. *-commutative 88.8%

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

   8. Simplified 88.8%

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

   9. Taylor expanded in x around inf 89.1%

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

   if -5.80000000000000026e-28 < x < 3.70000000000000006e-78

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 59.9%

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

      2. associate-/r* 59.9%

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

      3. +-commutative 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in x around 0 53.7%

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

   if 3.70000000000000006e-78 < x

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

   7. Simplified 81.9%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.8e+188) (* x (- 1.0 x)) (* y (/ 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e+188) {
		tmp = x * (1.0 - x);
	} else {
		tmp = y * (1.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.8d+188)) then
        tmp = x * (1.0d0 - x)
    else
        tmp = y * (1.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e+188) {
		tmp = x * (1.0 - x);
	} else {
		tmp = y * (1.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.8e+188:
		tmp = x * (1.0 - x)
	else:
		tmp = y * (1.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.8e+188)
		tmp = Float64(x * Float64(1.0 - x));
	else
		tmp = Float64(y * Float64(1.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.8e+188)
		tmp = x * (1.0 - x);
	else
		tmp = y * (1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.8e+188], N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7999999999999998e188

   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. Add Preprocessing

   5. Taylor expanded in t around inf 90.0%

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

      1. +-commutative 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x around 0 50.3%

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

      1. *-rgt-identity 50.3%

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

      2. neg-mul-1 50.3%

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

      3. sub-neg 50.3%

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

      4. *-rgt-identity 50.3%

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

   10. Simplified 50.3%

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

   if -3.7999999999999998e188 < t

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around inf 35.4%

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

      1. associate-/l* 37.3%

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

      2. associate-/r* 39.4%

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

      3. +-commutative 39.4%

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

   7. Simplified 39.4%

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

   8. Taylor expanded in x around 0 30.3%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 12.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

   1. *-commutative 89.9%

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

3. Simplified 89.9%

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

5. Taylor expanded in t around inf 54.7%

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

   1. +-commutative 54.7%

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

7. Simplified 54.7%

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

8. Taylor expanded in x around 0 14.0%

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

   1. *-rgt-identity 14.0%

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

   2. neg-mul-1 14.0%

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

   3. sub-neg 14.0%

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

   4. *-rgt-identity 14.0%

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

10. Simplified 14.0%

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

11. Taylor expanded in x around 0 14.8%

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

12. Final simplification 14.8%

    \[\leadsto x \]
13. Add Preprocessing

Developer target: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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