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

Percentage Accurate: 89.6% → 97.3%

Time: 11.3s

Alternatives: 8

Speedup: 0.2×

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: 89.6% 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: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x - \frac{x - y \cdot z}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -50000000000000:\\ \;\;\;\;y \cdot \frac{z}{t\_1 \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t\_2 \leq 10^{-68}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+299}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (- x (/ (- x (* y z)) t_1)) (+ x 1.0))))
   (if (<= t_2 -50000000000000.0)
     (* y (/ z (* t_1 (+ x 1.0))))
     (if (<= t_2 1e-68)
       (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
       (if (<= t_2 1e+299)
         t_2
         (+
          (/ x (+ x 1.0))
          (/ (- (/ y (+ x 1.0)) (/ x (* z (+ x 1.0)))) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -50000000000000.0) {
		tmp = y * (z / (t_1 * (x + 1.0)));
	} else if (t_2 <= 1e-68) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_2 <= 1e+299) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (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) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-50000000000000.0d0)) then
        tmp = y * (z / (t_1 * (x + 1.0d0)))
    else if (t_2 <= 1d-68) then
        tmp = (x - (((x / z) - y) / t)) / (x + 1.0d0)
    else if (t_2 <= 1d+299) then
        tmp = t_2
    else
        tmp = (x / (x + 1.0d0)) + (((y / (x + 1.0d0)) - (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 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -50000000000000.0) {
		tmp = y * (z / (t_1 * (x + 1.0)));
	} else if (t_2 <= 1e-68) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_2 <= 1e+299) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -50000000000000.0:
		tmp = y * (z / (t_1 * (x + 1.0)))
	elif t_2 <= 1e-68:
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0)
	elif t_2 <= 1e+299:
		tmp = t_2
	else:
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(y * z)) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -50000000000000.0)
		tmp = Float64(y * Float64(z / Float64(t_1 * Float64(x + 1.0))));
	elseif (t_2 <= 1e-68)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	elseif (t_2 <= 1e+299)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(Float64(y / Float64(x + 1.0)) - Float64(x / Float64(z * Float64(x + 1.0)))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -50000000000000.0)
		tmp = y * (z / (t_1 * (x + 1.0)));
	elseif (t_2 <= 1e-68)
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	elseif (t_2 <= 1e+299)
		tmp = t_2;
	else
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -50000000000000.0], N[(y * N[(z / N[(t$95$1 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-68], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+299], t$95$2, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -5e13

   1. Initial program 78.0%

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

      1. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in y around inf 77.5%

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

      1. associate-/l* 90.2%

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

      2. +-commutative 90.2%

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

   7. Simplified 90.2%

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

   if -5e13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.00000000000000007e-68

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-lft-out-- 99.9%

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

   7. Simplified 99.9%

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

   if 1.00000000000000007e-68 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.0000000000000001e299

   1. Initial program 99.9%

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

   if 1.0000000000000001e299 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 23.0%

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

      1. *-commutative 23.0%

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

   3. Simplified 23.0%

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

   5. Taylor expanded in t around -inf 82.9%

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

      1. +-commutative 82.9%

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

      2. mul-1-neg 82.9%

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

      3. unsub-neg 82.9%

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

      4. +-commutative 82.9%

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

      5. sub-neg 82.9%

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

      6. mul-1-neg 82.9%

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

      7. distribute-neg-frac2 82.9%

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

      8. distribute-neg-in 82.9%

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

      9. metadata-eval 82.9%

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

      10. unsub-neg 82.9%

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

      11. mul-1-neg 82.9%

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

      12. remove-double-neg 82.9%

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

      13. +-commutative 82.9%

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

   7. Simplified 82.9%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq -50000000000000:\\ \;\;\;\;y \cdot \frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{-68}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{+299}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x - \frac{x - y \cdot z}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -50000000000000:\\ \;\;\;\;y \cdot \frac{z}{t\_1 \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t\_2 \leq 10^{-68}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+299}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y}{t}\right) \cdot \frac{1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (- x (/ (- x (* y z)) t_1)) (+ x 1.0))))
   (if (<= t_2 -50000000000000.0)
     (* y (/ z (* t_1 (+ x 1.0))))
     (if (<= t_2 1e-68)
       (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
       (if (<= t_2 1e+299) t_2 (* (+ x (/ y t)) (/ 1.0 (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -50000000000000.0) {
		tmp = y * (z / (t_1 * (x + 1.0)));
	} else if (t_2 <= 1e-68) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_2 <= 1e+299) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) * (1.0 / (x + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-50000000000000.0d0)) then
        tmp = y * (z / (t_1 * (x + 1.0d0)))
    else if (t_2 <= 1d-68) then
        tmp = (x - (((x / z) - y) / t)) / (x + 1.0d0)
    else if (t_2 <= 1d+299) then
        tmp = t_2
    else
        tmp = (x + (y / t)) * (1.0d0 / (x + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -50000000000000.0) {
		tmp = y * (z / (t_1 * (x + 1.0)));
	} else if (t_2 <= 1e-68) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_2 <= 1e+299) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) * (1.0 / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -50000000000000.0:
		tmp = y * (z / (t_1 * (x + 1.0)))
	elif t_2 <= 1e-68:
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0)
	elif t_2 <= 1e+299:
		tmp = t_2
	else:
		tmp = (x + (y / t)) * (1.0 / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(y * z)) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -50000000000000.0)
		tmp = Float64(y * Float64(z / Float64(t_1 * Float64(x + 1.0))));
	elseif (t_2 <= 1e-68)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	elseif (t_2 <= 1e+299)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) * Float64(1.0 / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -50000000000000.0)
		tmp = y * (z / (t_1 * (x + 1.0)));
	elseif (t_2 <= 1e-68)
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	elseif (t_2 <= 1e+299)
		tmp = t_2;
	else
		tmp = (x + (y / t)) * (1.0 / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -50000000000000.0], N[(y * N[(z / N[(t$95$1 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-68], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+299], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -5e13

   1. Initial program 78.0%

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

      1. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in y around inf 77.5%

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

      1. associate-/l* 90.2%

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

      2. +-commutative 90.2%

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

   7. Simplified 90.2%

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

   if -5e13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.00000000000000007e-68

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-lft-out-- 99.9%

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

   7. Simplified 99.9%

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

   if 1.00000000000000007e-68 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.0000000000000001e299

   1. Initial program 99.9%

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

   if 1.0000000000000001e299 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 23.0%

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

      1. *-commutative 23.0%

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

   3. Simplified 23.0%

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

   5. Taylor expanded in z around inf 82.7%

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

      1. div-inv 82.7%

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

   7. Applied egg-rr 82.7%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq -50000000000000:\\ \;\;\;\;y \cdot \frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{-68}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{+299}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y}{t}\right) \cdot \frac{1}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-86}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -1.35e-65)
     t_1
     (if (<= x 2.7e-86)
       (/ y t)
       (if (<= x 8e-37) t_1 (if (<= x 1.45e-18) (/ y t) 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -1.35e-65) {
		tmp = t_1;
	} else if (x <= 2.7e-86) {
		tmp = y / t;
	} else if (x <= 8e-37) {
		tmp = t_1;
	} else if (x <= 1.45e-18) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (x <= (-1.35d-65)) then
        tmp = t_1
    else if (x <= 2.7d-86) then
        tmp = y / t
    else if (x <= 8d-37) then
        tmp = t_1
    else if (x <= 1.45d-18) 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 t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -1.35e-65) {
		tmp = t_1;
	} else if (x <= 2.7e-86) {
		tmp = y / t;
	} else if (x <= 8e-37) {
		tmp = t_1;
	} else if (x <= 1.45e-18) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -1.35e-65:
		tmp = t_1
	elif x <= 2.7e-86:
		tmp = y / t
	elif x <= 8e-37:
		tmp = t_1
	elif x <= 1.45e-18:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -1.35e-65)
		tmp = t_1;
	elseif (x <= 2.7e-86)
		tmp = Float64(y / t);
	elseif (x <= 8e-37)
		tmp = t_1;
	elseif (x <= 1.45e-18)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -1.35e-65)
		tmp = t_1;
	elseif (x <= 2.7e-86)
		tmp = y / t;
	elseif (x <= 8e-37)
		tmp = t_1;
	elseif (x <= 1.45e-18)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e-65], t$95$1, If[LessEqual[x, 2.7e-86], N[(y / t), $MachinePrecision], If[LessEqual[x, 8e-37], t$95$1, If[LessEqual[x, 1.45e-18], N[(y / t), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3499999999999999e-65 or 2.69999999999999992e-86 < x < 8.00000000000000053e-37

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around inf 75.7%

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

      1. +-commutative 75.7%

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

   7. Simplified 75.7%

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

   if -1.3499999999999999e-65 < x < 2.69999999999999992e-86 or 8.00000000000000053e-37 < x < 1.45e-18

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in z around inf 77.4%

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

      1. div-inv 77.4%

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

   7. Applied egg-rr 77.4%

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

   8. Taylor expanded in x around 0 61.5%

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

   if 1.45e-18 < x

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in z around inf 64.8%

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

      1. div-inv 64.7%

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

   7. Applied egg-rr 64.7%

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

   8. Taylor expanded in x around inf 88.4%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-86}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -7 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -7e-65)
     t_1
     (if (<= x 7.2e-83)
       (/ (/ y t) (+ x 1.0))
       (if (<= x 5e-36) t_1 (if (<= x 7.5e-19) (/ y t) 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -7e-65) {
		tmp = t_1;
	} else if (x <= 7.2e-83) {
		tmp = (y / t) / (x + 1.0);
	} else if (x <= 5e-36) {
		tmp = t_1;
	} else if (x <= 7.5e-19) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (x <= (-7d-65)) then
        tmp = t_1
    else if (x <= 7.2d-83) then
        tmp = (y / t) / (x + 1.0d0)
    else if (x <= 5d-36) then
        tmp = t_1
    else if (x <= 7.5d-19) 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 t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -7e-65) {
		tmp = t_1;
	} else if (x <= 7.2e-83) {
		tmp = (y / t) / (x + 1.0);
	} else if (x <= 5e-36) {
		tmp = t_1;
	} else if (x <= 7.5e-19) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -7e-65:
		tmp = t_1
	elif x <= 7.2e-83:
		tmp = (y / t) / (x + 1.0)
	elif x <= 5e-36:
		tmp = t_1
	elif x <= 7.5e-19:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -7e-65)
		tmp = t_1;
	elseif (x <= 7.2e-83)
		tmp = Float64(Float64(y / t) / Float64(x + 1.0));
	elseif (x <= 5e-36)
		tmp = t_1;
	elseif (x <= 7.5e-19)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -7e-65)
		tmp = t_1;
	elseif (x <= 7.2e-83)
		tmp = (y / t) / (x + 1.0);
	elseif (x <= 5e-36)
		tmp = t_1;
	elseif (x <= 7.5e-19)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-65], t$95$1, If[LessEqual[x, 7.2e-83], N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-36], t$95$1, If[LessEqual[x, 7.5e-19], N[(y / t), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.00000000000000009e-65 or 7.20000000000000025e-83 < x < 5.00000000000000004e-36

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around inf 75.7%

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

      1. +-commutative 75.7%

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

   7. Simplified 75.7%

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

   if -7.00000000000000009e-65 < x < 7.20000000000000025e-83

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in y around inf 58.9%

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

      1. associate-/l* 60.1%

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

      2. +-commutative 60.1%

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

   7. Simplified 60.1%

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

   8. Taylor expanded in z around inf 60.9%

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

      1. associate-/r* 60.9%

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

      2. +-commutative 60.9%

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

   10. Simplified 60.9%

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

       1. associate-*r/ 60.9%

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

       2. un-div-inv 61.3%

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

   12. Applied egg-rr 61.3%

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

   if 5.00000000000000004e-36 < x < 7.49999999999999957e-19

   1. Initial program 66.7%

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

      1. *-commutative 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in z around inf 69.8%

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

      1. div-inv 69.8%

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

   7. Applied egg-rr 69.8%

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

   8. Taylor expanded in x around 0 69.8%

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

   if 7.49999999999999957e-19 < x

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in z around inf 64.8%

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

      1. div-inv 64.7%

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

   7. Applied egg-rr 64.7%

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

   8. Taylor expanded in x around inf 88.4%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-56} \lor \neg \left(t \leq 1.2 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{-1 - x} \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.2e-56) (not (<= t 1.2e-92)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* (/ y (- -1.0 x)) (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e-56) || !(t <= 1.2e-92)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y / (-1.0 - x)) * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.2d-56)) .or. (.not. (t <= 1.2d-92))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((y / ((-1.0d0) - x)) * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e-56) || !(t <= 1.2e-92)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y / (-1.0 - x)) * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.2e-56) or not (t <= 1.2e-92):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + ((y / (-1.0 - x)) * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.2e-56) || !(t <= 1.2e-92))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(y / Float64(-1.0 - x)) * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.2e-56) || ~((t <= 1.2e-92)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + ((y / (-1.0 - x)) * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.2e-56], N[Not[LessEqual[t, 1.2e-92]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.19999999999999994e-56 or 1.2000000000000001e-92 < t

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in z around inf 90.2%

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

   if -5.19999999999999994e-56 < t < 1.2000000000000001e-92

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around 0 78.5%

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

      1. associate-+r+ 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. +-commutative 78.5%

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

      5. associate-/l* 82.5%

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

      6. +-commutative 82.5%

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

   7. Simplified 82.5%

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

      1. div-sub 82.5%

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

      2. pow1 82.5%

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

      3. pow1 82.5%

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

      4. pow-div 82.5%

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

      5. metadata-eval 82.5%

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

      6. metadata-eval 82.5%

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

   9. Applied egg-rr 82.5%

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

   10. Taylor expanded in y around 0 78.4%

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

       1. +-commutative 78.4%

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

       2. *-commutative 78.4%

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

       3. times-frac 82.5%

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

   12. Simplified 82.5%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-56} \lor \neg \left(t \leq 1.2 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{-1 - x} \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-61} \lor \neg \left(z \leq 3.2 \cdot 10^{-165}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e-61) (not (<= z 3.2e-165)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* y (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e-61) || !(z <= 3.2e-165)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.15d-61)) .or. (.not. (z <= 3.2d-165))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - (y * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e-61) || !(z <= 3.2e-165)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e-61) or not (z <= 3.2e-165):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - (y * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e-61) || !(z <= 3.2e-165))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15e-61) || ~((z <= 3.2e-165)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - (y * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15e-61], N[Not[LessEqual[z, 3.2e-165]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999996e-61 or 3.20000000000000013e-165 < z

   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. Add Preprocessing

   5. Taylor expanded in z around inf 84.4%

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

   if -1.14999999999999996e-61 < z < 3.20000000000000013e-165

   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 t around 0 81.9%

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

      1. associate-+r+ 81.9%

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

      2. mul-1-neg 81.9%

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

      3. unsub-neg 81.9%

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

      4. +-commutative 81.9%

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

      5. associate-/l* 81.9%

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

      6. +-commutative 81.9%

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

   7. Simplified 81.9%

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

      1. div-sub 81.9%

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

      2. pow1 81.9%

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

      3. pow1 81.9%

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

      4. pow-div 81.9%

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

      5. metadata-eval 81.9%

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

      6. metadata-eval 81.9%

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

   9. Applied egg-rr 81.9%

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

   10. Taylor expanded in x around 0 79.6%

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

       1. associate-*r/ 79.6%

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

   12. Simplified 79.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-61} \lor \neg \left(z \leq 3.2 \cdot 10^{-165}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-29}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e-29) 1.0 (if (<= x 2.3e-18) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-29) {
		tmp = 1.0;
	} else if (x <= 2.3e-18) {
		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 <= (-2.6d-29)) then
        tmp = 1.0d0
    else if (x <= 2.3d-18) 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 <= -2.6e-29) {
		tmp = 1.0;
	} else if (x <= 2.3e-18) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e-29:
		tmp = 1.0
	elif x <= 2.3e-18:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e-29)
		tmp = 1.0;
	elseif (x <= 2.3e-18)
		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 <= -2.6e-29)
		tmp = 1.0;
	elseif (x <= 2.3e-18)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e-29], 1.0, If[LessEqual[x, 2.3e-18], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6000000000000002e-29 or 2.3000000000000001e-18 < x

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around inf 71.5%

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

      1. div-inv 71.4%

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

   7. Applied egg-rr 71.4%

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

   8. Taylor expanded in x around inf 86.1%

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

   if -2.6000000000000002e-29 < x < 2.3000000000000001e-18

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in z around inf 76.2%

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

      1. div-inv 76.2%

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

   7. Applied egg-rr 76.2%

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

   8. Taylor expanded in x around 0 54.6%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-29}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.4% 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. Add Preprocessing

5. Taylor expanded in z around inf 73.7%

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

   1. div-inv 73.6%

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

7. Applied egg-rr 73.6%

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

8. Taylor expanded in x around inf 52.6%

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

9. Final simplification 52.6%

   \[\leadsto 1 \]
10. 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 2024041 
(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)))