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

Percentage Accurate: 89.2% → 97.3%

Time: 15.4s

Alternatives: 12

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ t_2 := \frac{x + \frac{t_1}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t - \frac{x}{z}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{\frac{t_1}{z}} - \frac{x}{t_1}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x)) (t_2 (/ (+ x (/ t_1 (- (* z t) x))) (+ x 1.0))))
   (if (<= t_2 -1e+73)
     (/ (/ y (+ x 1.0)) (- t (/ x z)))
     (if (<= t_2 5e+262)
       (/ (+ x (/ 1.0 (- (/ t (/ t_1 z)) (/ x t_1)))) (+ x 1.0))
       (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (x + (t_1 / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+73) {
		tmp = (y / (x + 1.0)) / (t - (x / z));
	} else if (t_2 <= 5e+262) {
		tmp = (x + (1.0 / ((t / (t_1 / z)) - (x / t_1)))) / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) - x
    t_2 = (x + (t_1 / ((z * t) - x))) / (x + 1.0d0)
    if (t_2 <= (-1d+73)) then
        tmp = (y / (x + 1.0d0)) / (t - (x / z))
    else if (t_2 <= 5d+262) then
        tmp = (x + (1.0d0 / ((t / (t_1 / z)) - (x / t_1)))) / (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 t_1 = (y * z) - x;
	double t_2 = (x + (t_1 / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+73) {
		tmp = (y / (x + 1.0)) / (t - (x / z));
	} else if (t_2 <= 5e+262) {
		tmp = (x + (1.0 / ((t / (t_1 / z)) - (x / t_1)))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - x
	t_2 = (x + (t_1 / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= -1e+73:
		tmp = (y / (x + 1.0)) / (t - (x / z))
	elif t_2 <= 5e+262:
		tmp = (x + (1.0 / ((t / (t_1 / z)) - (x / t_1)))) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - x)
	t_2 = Float64(Float64(x + Float64(t_1 / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e+73)
		tmp = Float64(Float64(y / Float64(x + 1.0)) / Float64(t - Float64(x / z)));
	elseif (t_2 <= 5e+262)
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(t / Float64(t_1 / z)) - Float64(x / t_1)))) / 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)
	t_1 = (y * z) - x;
	t_2 = (x + (t_1 / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e+73)
		tmp = (y / (x + 1.0)) / (t - (x / z));
	elseif (t_2 <= 5e+262)
		tmp = (x + (1.0 / ((t / (t_1 / z)) - (x / t_1)))) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(t$95$1 / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+73], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+262], N[(N[(x + N[(1.0 / N[(N[(t / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -9.99999999999999983e72

   1. Initial program 69.0%

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

      1. *-commutative 69.0%

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

   3. Simplified 69.0%

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

      1. clear-num 68.9%

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

      2. inv-pow 68.9%

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

      3. fma-neg 68.9%

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

   6. Applied egg-rr 68.9%

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

      1. unpow-1 68.9%

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

      2. *-commutative 68.9%

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

      3. fma-neg 68.9%

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

      4. *-commutative 68.9%

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

   8. Simplified 68.9%

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

      1. div-inv 68.9%

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

      2. fma-neg 68.9%

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

   10. Applied egg-rr 68.9%

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

   11. Taylor expanded in t around 0 61.7%

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

       1. +-commutative 61.7%

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

       2. mul-1-neg 61.7%

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

       3. unsub-neg 61.7%

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

       4. associate-/l* 61.7%

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

   13. Simplified 61.7%

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

   14. Taylor expanded in y around inf 89.2%

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

       1. associate-/r* 89.3%

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

       2. +-commutative 89.3%

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

   16. Simplified 89.3%

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

   if -9.99999999999999983e72 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 5.00000000000000008e262

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.3%

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

      2. inv-pow 99.3%

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

      3. fma-neg 99.3%

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

   6. Applied egg-rr 99.3%

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

      1. unpow-1 99.3%

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

      2. *-commutative 99.3%

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

      3. fma-neg 99.3%

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

      4. *-commutative 99.3%

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

   8. Simplified 99.3%

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

      1. div-inv 99.2%

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

      2. fma-neg 99.2%

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

   10. Applied egg-rr 99.2%

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

   11. Taylor expanded in t around 0 99.3%

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

       1. +-commutative 99.3%

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

       2. mul-1-neg 99.3%

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

       3. unsub-neg 99.3%

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

       4. associate-/l* 99.8%

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

   13. Simplified 99.8%

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

   if 5.00000000000000008e262 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 31.3%

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

      1. *-commutative 31.3%

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

   3. Simplified 31.3%

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

   5. Taylor expanded in z around inf 96.4%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -1 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t - \frac{x}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{\frac{y \cdot z - x}{z}} - \frac{x}{y \cdot z - x}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t - \frac{x}{z}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 -1e+83)
     (/ (/ y (+ x 1.0)) (- t (/ x z)))
     (if (<= t_1 5e+262) t_1 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -1e+83) {
		tmp = (y / (x + 1.0)) / (t - (x / z));
	} else if (t_1 <= 5e+262) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= (-1d+83)) then
        tmp = (y / (x + 1.0d0)) / (t - (x / z))
    else if (t_1 <= 5d+262) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -1e+83) {
		tmp = (y / (x + 1.0)) / (t - (x / z));
	} else if (t_1 <= 5e+262) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -1e+83:
		tmp = (y / (x + 1.0)) / (t - (x / z))
	elif t_1 <= 5e+262:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -1e+83)
		tmp = Float64(Float64(y / Float64(x + 1.0)) / Float64(t - Float64(x / z)));
	elseif (t_1 <= 5e+262)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -1e+83)
		tmp = (y / (x + 1.0)) / (t - (x / z));
	elseif (t_1 <= 5e+262)
		tmp = t_1;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+83], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+262], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -1.00000000000000003e83

   1. Initial program 67.8%

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

      1. *-commutative 67.8%

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

   3. Simplified 67.8%

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

      1. clear-num 67.8%

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

      2. inv-pow 67.8%

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

      3. fma-neg 67.8%

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

   6. Applied egg-rr 67.8%

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

      1. unpow-1 67.8%

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

      2. *-commutative 67.8%

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

      3. fma-neg 67.8%

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

      4. *-commutative 67.8%

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

   8. Simplified 67.8%

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

      1. div-inv 67.7%

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

      2. fma-neg 67.7%

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

   10. Applied egg-rr 67.7%

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

   11. Taylor expanded in t around 0 60.3%

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

       1. +-commutative 60.3%

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

       2. mul-1-neg 60.3%

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

       3. unsub-neg 60.3%

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

       4. associate-/l* 60.4%

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

   13. Simplified 60.4%

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

   14. Taylor expanded in y around inf 88.8%

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

       1. associate-/r* 88.9%

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

       2. +-commutative 88.9%

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

   16. Simplified 88.9%

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

   if -1.00000000000000003e83 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 5.00000000000000008e262

   1. Initial program 99.3%

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

   if 5.00000000000000008e262 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 31.3%

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

      1. *-commutative 31.3%

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

   3. Simplified 31.3%

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

   5. Taylor expanded in z around inf 96.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -1 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t - \frac{x}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-110} \lor \neg \left(t \leq 2.25 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.6e-110) (not (<= t 2.25e-104)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* (/ y x) (/ z (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.6e-110) || !(t <= 2.25e-104)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.6d-110)) .or. (.not. (t <= 2.25d-104))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y / x) * (z / (x + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.6e-110) || !(t <= 2.25e-104)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.6e-110) or not (t <= 2.25e-104):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.6e-110) || !(t <= 2.25e-104))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.6e-110) || ~((t <= 2.25e-104)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.6e-110], N[Not[LessEqual[t, 2.25e-104]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5999999999999999e-110 or 2.2499999999999999e-104 < t

   1. Initial program 82.5%

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

      1. *-commutative 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in z around inf 86.4%

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

   if -2.5999999999999999e-110 < t < 2.2499999999999999e-104

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 80.8%

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

      1. associate-+r+ 80.8%

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

      2. mul-1-neg 80.8%

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

      3. unsub-neg 80.8%

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

      4. +-commutative 80.8%

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

      5. associate-/l* 80.7%

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

      6. +-commutative 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in y around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. sub-neg 80.8%

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

      3. times-frac 76.5%

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

      4. +-commutative 76.5%

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

   10. Simplified 76.5%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-110} \lor \neg \left(t \leq 2.25 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-111} \lor \neg \left(t \leq 2.65 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e-111) (not (<= t 2.65e-108)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (/ y (/ x z)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-111) || !(t <= 2.65e-108)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x / z)) / (x + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.5d-111)) .or. (.not. (t <= 2.65d-108))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y / (x / z)) / (x + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-111) || !(t <= 2.65e-108)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x / z)) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e-111) or not (t <= 2.65e-108):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y / (x / z)) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e-111) || !(t <= 2.65e-108))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y / Float64(x / z)) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.5e-111) || ~((t <= 2.65e-108)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y / (x / z)) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e-111], N[Not[LessEqual[t, 2.65e-108]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5e-111 or 2.64999999999999994e-108 < t

   1. Initial program 82.5%

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

      1. *-commutative 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in z around inf 86.4%

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

   if -3.5e-111 < t < 2.64999999999999994e-108

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 80.8%

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

      1. associate-+r+ 80.8%

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

      2. mul-1-neg 80.8%

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

      3. unsub-neg 80.8%

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

      4. +-commutative 80.8%

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

      5. associate-/l* 80.7%

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

      6. +-commutative 80.7%

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

   7. Simplified 80.7%

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

      1. div-sub 80.7%

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

      2. pow1 80.7%

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

      3. pow1 80.7%

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

      4. pow-div 80.7%

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

      5. metadata-eval 80.7%

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

      6. metadata-eval 80.7%

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

   9. Applied egg-rr 80.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-111} \lor \neg \left(t \leq 2.65 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-108} \lor \neg \left(t \leq 5.2 \cdot 10^{-107}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y \cdot z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.2e-108) (not (<= t 5.2e-107)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (/ (* y z) x) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e-108) || !(t <= 5.2e-107)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 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 <= (-5.2d-108)) .or. (.not. (t <= 5.2d-107))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 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 <= -5.2e-108) || !(t <= 5.2e-107)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (((y * z) / x) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.2e-108) or not (t <= 5.2e-107):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - (((y * z) / x) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.2e-108) || !(t <= 5.2e-107))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(Float64(y * z) / x) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.2e-108) || ~((t <= 5.2e-107)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - (((y * z) / x) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.2e-108], N[Not[LessEqual[t, 5.2e-107]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.19999999999999968e-108 or 5.2000000000000001e-107 < t

   1. Initial program 82.5%

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

      1. *-commutative 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in z around inf 86.4%

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

   if -5.19999999999999968e-108 < t < 5.2000000000000001e-107

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 80.8%

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

      1. associate-+r+ 80.8%

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

      2. mul-1-neg 80.8%

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

      3. unsub-neg 80.8%

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

      4. +-commutative 80.8%

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

      5. associate-/l* 80.7%

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

      6. +-commutative 80.7%

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

   7. Simplified 80.7%

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

      1. div-sub 80.7%

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

      2. pow1 80.7%

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

      3. pow1 80.7%

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

      4. pow-div 80.7%

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

      5. metadata-eval 80.7%

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

      6. metadata-eval 80.7%

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

   9. Applied egg-rr 80.7%

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

   10. Taylor expanded in y around 0 80.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-108} \lor \neg \left(t \leq 5.2 \cdot 10^{-107}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y \cdot z}{x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-111} \lor \neg \left(t \leq 4.8 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.4e-111) (not (<= t 4.8e-106)))
   (/ (+ 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 ((t <= -5.4e-111) || !(t <= 4.8e-106)) {
		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 ((t <= (-5.4d-111)) .or. (.not. (t <= 4.8d-106))) 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 ((t <= -5.4e-111) || !(t <= 4.8e-106)) {
		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 (t <= -5.4e-111) or not (t <= 4.8e-106):
		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 ((t <= -5.4e-111) || !(t <= 4.8e-106))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.4e-111) || ~((t <= 4.8e-106)))
		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[t, -5.4e-111], N[Not[LessEqual[t, 4.8e-106]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.39999999999999977e-111 or 4.7999999999999995e-106 < t

   1. Initial program 82.5%

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

      1. *-commutative 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in z around inf 86.4%

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

   if -5.39999999999999977e-111 < t < 4.7999999999999995e-106

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 80.8%

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

      1. associate-+r+ 80.8%

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

      2. mul-1-neg 80.8%

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

      3. unsub-neg 80.8%

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

      4. +-commutative 80.8%

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

      5. associate-/l* 80.7%

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

      6. +-commutative 80.7%

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

   7. Simplified 80.7%

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

      1. div-sub 80.7%

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

      2. pow1 80.7%

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

      3. pow1 80.7%

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

      4. pow-div 80.7%

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

      5. metadata-eval 80.7%

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

      6. metadata-eval 80.7%

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

   9. Applied egg-rr 80.7%

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

   10. Taylor expanded in x around 0 71.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-111} \lor \neg \left(t \leq 4.8 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.9e-75) 1.0 (if (<= x 1.45e-75) (/ y t) (/ 1.0 (/ (+ x 1.0) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e-75) {
		tmp = 1.0;
	} else if (x <= 1.45e-75) {
		tmp = y / t;
	} else {
		tmp = 1.0 / ((x + 1.0) / 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 (x <= (-2.9d-75)) then
        tmp = 1.0d0
    else if (x <= 1.45d-75) then
        tmp = y / t
    else
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e-75) {
		tmp = 1.0;
	} else if (x <= 1.45e-75) {
		tmp = y / t;
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.9e-75:
		tmp = 1.0
	elif x <= 1.45e-75:
		tmp = y / t
	else:
		tmp = 1.0 / ((x + 1.0) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.9e-75)
		tmp = 1.0;
	elseif (x <= 1.45e-75)
		tmp = Float64(y / t);
	else
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.9e-75)
		tmp = 1.0;
	elseif (x <= 1.45e-75)
		tmp = y / t;
	else
		tmp = 1.0 / ((x + 1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.9e-75], 1.0, If[LessEqual[x, 1.45e-75], N[(y / t), $MachinePrecision], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9000000000000002e-75

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. inv-pow 89.1%

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

      3. fma-neg 89.1%

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

   6. Applied egg-rr 89.1%

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

      1. unpow-1 89.1%

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

      2. *-commutative 89.1%

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

      3. fma-neg 89.1%

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

      4. *-commutative 89.1%

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

   8. Simplified 89.1%

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

      1. div-inv 89.0%

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

      2. fma-neg 89.0%

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

   10. Applied egg-rr 89.0%

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

   11. Taylor expanded in t around 0 87.7%

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

       1. +-commutative 87.7%

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

       2. mul-1-neg 87.7%

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

       3. unsub-neg 87.7%

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

       4. associate-/l* 87.8%

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

   13. Simplified 87.8%

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

   14. Taylor expanded in x around inf 78.3%

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

   if -2.9000000000000002e-75 < x < 1.4500000000000001e-75

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

      3. fma-neg 89.2%

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

   6. Applied egg-rr 89.2%

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

      1. unpow-1 89.2%

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

      2. *-commutative 89.2%

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

      3. fma-neg 89.2%

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

      4. *-commutative 89.2%

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

   8. Simplified 89.2%

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

   9. Taylor expanded in x around 0 56.9%

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

   if 1.4500000000000001e-75 < x

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around inf 80.2%

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

      1. +-commutative 80.2%

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

   7. Simplified 80.2%

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

      1. clear-num 80.2%

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

      2. inv-pow 80.2%

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

   9. Applied egg-rr 80.2%

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

       1. unpow-1 80.2%

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

   11. Simplified 80.2%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-75}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3e-75)
   (- 1.0 (* (/ y x) (/ z x)))
   (if (<= x 8.8e-75) (/ y t) (/ 1.0 (/ (+ x 1.0) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3e-75) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else if (x <= 8.8e-75) {
		tmp = y / t;
	} else {
		tmp = 1.0 / ((x + 1.0) / 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 (x <= (-3d-75)) then
        tmp = 1.0d0 - ((y / x) * (z / x))
    else if (x <= 8.8d-75) then
        tmp = y / t
    else
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3e-75) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else if (x <= 8.8e-75) {
		tmp = y / t;
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3e-75:
		tmp = 1.0 - ((y / x) * (z / x))
	elif x <= 8.8e-75:
		tmp = y / t
	else:
		tmp = 1.0 / ((x + 1.0) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3e-75)
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / x)));
	elseif (x <= 8.8e-75)
		tmp = Float64(y / t);
	else
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3e-75)
		tmp = 1.0 - ((y / x) * (z / x));
	elseif (x <= 8.8e-75)
		tmp = y / t;
	else
		tmp = 1.0 / ((x + 1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3e-75], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e-75], N[(y / t), $MachinePrecision], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9999999999999999e-75

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in t around 0 79.2%

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

      1. associate-+r+ 79.2%

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

      2. mul-1-neg 79.2%

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

      3. unsub-neg 79.2%

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

      4. +-commutative 79.2%

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

      5. associate-/l* 81.5%

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

      6. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. sub-neg 79.2%

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

      3. times-frac 81.5%

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

      4. +-commutative 81.5%

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

   10. Simplified 81.5%

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

   11. Taylor expanded in x around inf 78.8%

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

   if -2.9999999999999999e-75 < x < 8.80000000000000022e-75

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

      3. fma-neg 89.2%

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

   6. Applied egg-rr 89.2%

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

      1. unpow-1 89.2%

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

      2. *-commutative 89.2%

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

      3. fma-neg 89.2%

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

      4. *-commutative 89.2%

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

   8. Simplified 89.2%

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

   9. Taylor expanded in x around 0 56.9%

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

   if 8.80000000000000022e-75 < x

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around inf 80.2%

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

      1. +-commutative 80.2%

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

   7. Simplified 80.2%

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

      1. clear-num 80.2%

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

      2. inv-pow 80.2%

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

   9. Applied egg-rr 80.2%

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

       1. unpow-1 80.2%

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

   11. Simplified 80.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-75}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.3e-76) 1.0 (if (<= x 2.6e-72) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.3e-76) {
		tmp = 1.0;
	} else if (x <= 2.6e-72) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.3d-76)) then
        tmp = 1.0d0
    else if (x <= 2.6d-72) then
        tmp = y / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.3e-76) {
		tmp = 1.0;
	} else if (x <= 2.6e-72) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.3e-76:
		tmp = 1.0
	elif x <= 2.6e-72:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.3e-76)
		tmp = 1.0;
	elseif (x <= 2.6e-72)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.3e-76)
		tmp = 1.0;
	elseif (x <= 2.6e-72)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.3e-76], 1.0, If[LessEqual[x, 2.6e-72], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2999999999999999e-76

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. inv-pow 89.1%

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

      3. fma-neg 89.1%

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

   6. Applied egg-rr 89.1%

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

      1. unpow-1 89.1%

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

      2. *-commutative 89.1%

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

      3. fma-neg 89.1%

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

      4. *-commutative 89.1%

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

   8. Simplified 89.1%

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

      1. div-inv 89.0%

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

      2. fma-neg 89.0%

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

   10. Applied egg-rr 89.0%

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

   11. Taylor expanded in t around 0 87.7%

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

       1. +-commutative 87.7%

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

       2. mul-1-neg 87.7%

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

       3. unsub-neg 87.7%

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

       4. associate-/l* 87.8%

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

   13. Simplified 87.8%

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

   14. Taylor expanded in x around inf 78.3%

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

   if -4.2999999999999999e-76 < x < 2.59999999999999996e-72

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

      3. fma-neg 89.2%

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

   6. Applied egg-rr 89.2%

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

      1. unpow-1 89.2%

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

      2. *-commutative 89.2%

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

      3. fma-neg 89.2%

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

      4. *-commutative 89.2%

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

   8. Simplified 89.2%

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

   9. Taylor expanded in x around 0 56.9%

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

   if 2.59999999999999996e-72 < x

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around inf 80.2%

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

      1. +-commutative 80.2%

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

   7. Simplified 80.2%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.4e-75) 1.0 (if (<= x 2.7e-70) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.4e-75) {
		tmp = 1.0;
	} else if (x <= 2.7e-70) {
		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 <= (-8.4d-75)) then
        tmp = 1.0d0
    else if (x <= 2.7d-70) 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 <= -8.4e-75) {
		tmp = 1.0;
	} else if (x <= 2.7e-70) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.4e-75:
		tmp = 1.0
	elif x <= 2.7e-70:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.4e-75)
		tmp = 1.0;
	elseif (x <= 2.7e-70)
		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 <= -8.4e-75)
		tmp = 1.0;
	elseif (x <= 2.7e-70)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.4e-75], 1.0, If[LessEqual[x, 2.7e-70], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -8.4000000000000004e-75 or 2.7000000000000001e-70 < x

   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. Step-by-step derivation

      1. clear-num 87.7%

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

      2. inv-pow 87.7%

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

      3. fma-neg 87.7%

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

   6. Applied egg-rr 87.7%

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

      1. unpow-1 87.7%

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

      2. *-commutative 87.7%

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

      3. fma-neg 87.7%

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

      4. *-commutative 87.7%

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

   8. Simplified 87.7%

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

      1. div-inv 87.7%

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

      2. fma-neg 87.7%

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

   10. Applied egg-rr 87.7%

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

   11. Taylor expanded in t around 0 87.1%

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

       1. +-commutative 87.1%

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

       2. mul-1-neg 87.1%

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

       3. unsub-neg 87.1%

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

       4. associate-/l* 87.2%

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

   13. Simplified 87.2%

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

   14. Taylor expanded in x around inf 78.9%

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

   if -8.4000000000000004e-75 < x < 2.7000000000000001e-70

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

      3. fma-neg 89.2%

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

   6. Applied egg-rr 89.2%

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

      1. unpow-1 89.2%

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

      2. *-commutative 89.2%

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

      3. fma-neg 89.2%

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

      4. *-commutative 89.2%

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

   8. Simplified 89.2%

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

   9. Taylor expanded in x around 0 56.9%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.2e-6) 1.0 (if (<= x 1.8e-36) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.2e-6) {
		tmp = 1.0;
	} else if (x <= 1.8e-36) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.2d-6)) then
        tmp = 1.0d0
    else if (x <= 1.8d-36) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.2e-6) {
		tmp = 1.0;
	} else if (x <= 1.8e-36) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.2e-6:
		tmp = 1.0
	elif x <= 1.8e-36:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.2e-6)
		tmp = 1.0;
	elseif (x <= 1.8e-36)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.2e-6)
		tmp = 1.0;
	elseif (x <= 1.8e-36)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.2e-6], 1.0, If[LessEqual[x, 1.8e-36], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1999999999999999e-6 or 1.80000000000000016e-36 < x

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

   3. Simplified 87.0%

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

      1. clear-num 87.0%

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

      2. inv-pow 87.0%

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

      3. fma-neg 87.0%

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

   6. Applied egg-rr 87.0%

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

      1. unpow-1 87.0%

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

      2. *-commutative 87.0%

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

      3. fma-neg 87.0%

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

      4. *-commutative 87.0%

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

   8. Simplified 87.0%

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

      1. div-inv 87.0%

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

      2. fma-neg 87.0%

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

   10. Applied egg-rr 87.0%

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

   11. Taylor expanded in t around 0 87.0%

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

       1. +-commutative 87.0%

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

       2. mul-1-neg 87.0%

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

       3. unsub-neg 87.0%

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

       4. associate-/l* 87.1%

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

   13. Simplified 87.1%

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

   14. Taylor expanded in x around inf 85.1%

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

   if -3.1999999999999999e-6 < x < 1.80000000000000016e-36

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around inf 23.8%

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

      1. +-commutative 23.8%

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

   7. Simplified 23.8%

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

   8. Taylor expanded in x around 0 23.0%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.9% 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 88.3%

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

   1. *-commutative 88.3%

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

3. Simplified 88.3%

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

   1. clear-num 88.3%

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

   2. inv-pow 88.3%

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

   3. fma-neg 88.3%

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

6. Applied egg-rr 88.3%

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

   1. unpow-1 88.3%

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

   2. *-commutative 88.3%

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

   3. fma-neg 88.3%

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

   4. *-commutative 88.3%

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

8. Simplified 88.3%

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

   1. div-inv 88.2%

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

   2. fma-neg 88.2%

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

10. Applied egg-rr 88.2%

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

11. Taylor expanded in t around 0 87.5%

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

    1. +-commutative 87.5%

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

    2. mul-1-neg 87.5%

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

    3. unsub-neg 87.5%

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

    4. associate-/l* 88.0%

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

13. Simplified 88.0%

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

14. Taylor expanded in x around inf 52.7%

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

15. Final simplification 52.7%

    \[\leadsto 1 \]
16. Add Preprocessing

Developer target: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024018 
(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)))