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

Percentage Accurate: 89.0% → 95.2%

Time: 12.4s

Alternatives: 14

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;t\_1 + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+134}:\\ \;\;\;\;\frac{x + \frac{\mathsf{fma}\left(z, y, -x\right)}{\mathsf{fma}\left(t, z, -x\right)}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{\frac{y}{x + 1} + \frac{x}{z \cdot \left(-1 - x\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= z -2.3e+103)
     (+ t_1 (/ y (* (+ x 1.0) t)))
     (if (<= z 1.35e+134)
       (/ (+ x (/ (fma z y (- x)) (fma t z (- x)))) (+ x 1.0))
       (+ t_1 (/ (+ (/ y (+ x 1.0)) (/ x (* z (- -1.0 x)))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (z <= -2.3e+103) {
		tmp = t_1 + (y / ((x + 1.0) * t));
	} else if (z <= 1.35e+134) {
		tmp = (x + (fma(z, y, -x) / fma(t, z, -x))) / (x + 1.0);
	} else {
		tmp = t_1 + (((y / (x + 1.0)) + (x / (z * (-1.0 - x)))) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -2.3e+103)
		tmp = Float64(t_1 + Float64(y / Float64(Float64(x + 1.0) * t)));
	elseif (z <= 1.35e+134)
		tmp = Float64(Float64(x + Float64(fma(z, y, Float64(-x)) / fma(t, z, Float64(-x)))) / Float64(x + 1.0));
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(y / Float64(x + 1.0)) + Float64(x / Float64(z * Float64(-1.0 - x)))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+103], N[(t$95$1 + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+134], N[(N[(x + N[(N[(z * y + (-x)), $MachinePrecision] / N[(t * z + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / N[(z * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000008e103

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. +-commutative 70.6%

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

      3. sub-neg 70.6%

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

      4. *-commutative 70.6%

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

      5. *-commutative 70.6%

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

      6. div-sub 70.6%

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

      7. fma-neg 70.6%

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

      8. fma-define 70.6%

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

      9. *-commutative 70.6%

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

      10. fma-undefine 70.6%

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

      11. *-commutative 70.6%

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

      12. fma-neg 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in y around inf 70.6%

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

      1. *-commutative 70.6%

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

      2. sub-neg 70.6%

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

      3. *-commutative 70.6%

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

      4. *-rgt-identity 70.6%

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

      5. fma-undefine 70.6%

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

      6. *-rgt-identity 70.6%

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

   10. Simplified 70.6%

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

   11. Taylor expanded in t around inf 91.2%

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

       1. +-commutative 91.2%

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

       2. +-commutative 91.2%

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

   13. Simplified 91.2%

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

   if -2.30000000000000008e103 < z < 1.35e134

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 98.3%

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

      1. mul-1-neg 98.3%

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

      2. +-commutative 98.3%

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

      3. sub-neg 98.3%

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

      4. *-commutative 98.3%

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

      5. *-commutative 98.3%

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

      6. div-sub 98.3%

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

      7. fma-neg 98.3%

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

      8. fma-define 98.3%

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

      9. *-commutative 98.3%

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

      10. fma-undefine 98.3%

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

      11. *-commutative 98.3%

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

      12. fma-neg 98.3%

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

   7. Simplified 98.3%

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

   if 1.35e134 < z

   1. Initial program 64.4%

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

      1. *-commutative 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in t around -inf 96.0%

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

      1. +-commutative 96.0%

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

      2. mul-1-neg 96.0%

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

      3. unsub-neg 96.0%

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

      4. +-commutative 96.0%

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

      5. sub-neg 96.0%

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

      6. mul-1-neg 96.0%

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

      7. distribute-neg-frac2 96.0%

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

      8. distribute-neg-in 96.0%

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

      9. metadata-eval 96.0%

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

      10. unsub-neg 96.0%

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

      11. mul-1-neg 96.0%

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

      12. remove-double-neg 96.0%

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

      13. +-commutative 96.0%

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

   7. Simplified 96.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+134}:\\ \;\;\;\;\frac{x + \frac{\mathsf{fma}\left(z, y, -x\right)}{\mathsf{fma}\left(t, z, -x\right)}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} + \frac{x}{z \cdot \left(-1 - x\right)}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := 1 - y \cdot \frac{z}{x}\\ \mathbf{if}\;x \leq -4 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))) (t_2 (- 1.0 (* y (/ z x)))))
   (if (<= x -4e-70)
     t_1
     (if (<= x -1.1e-107)
       t_2
       (if (<= x -3.1e-218)
         t_1
         (if (<= x 2.2e-169) (/ y t) (if (<= x 7.4e-72) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = 1.0 - (y * (z / x));
	double tmp;
	if (x <= -4e-70) {
		tmp = t_1;
	} else if (x <= -1.1e-107) {
		tmp = t_2;
	} else if (x <= -3.1e-218) {
		tmp = t_1;
	} else if (x <= 2.2e-169) {
		tmp = y / t;
	} else if (x <= 7.4e-72) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    t_2 = 1.0d0 - (y * (z / x))
    if (x <= (-4d-70)) then
        tmp = t_1
    else if (x <= (-1.1d-107)) then
        tmp = t_2
    else if (x <= (-3.1d-218)) then
        tmp = t_1
    else if (x <= 2.2d-169) then
        tmp = y / t
    else if (x <= 7.4d-72) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = 1.0 - (y * (z / x));
	double tmp;
	if (x <= -4e-70) {
		tmp = t_1;
	} else if (x <= -1.1e-107) {
		tmp = t_2;
	} else if (x <= -3.1e-218) {
		tmp = t_1;
	} else if (x <= 2.2e-169) {
		tmp = y / t;
	} else if (x <= 7.4e-72) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	t_2 = 1.0 - (y * (z / x))
	tmp = 0
	if x <= -4e-70:
		tmp = t_1
	elif x <= -1.1e-107:
		tmp = t_2
	elif x <= -3.1e-218:
		tmp = t_1
	elif x <= 2.2e-169:
		tmp = y / t
	elif x <= 7.4e-72:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	t_2 = Float64(1.0 - Float64(y * Float64(z / x)))
	tmp = 0.0
	if (x <= -4e-70)
		tmp = t_1;
	elseif (x <= -1.1e-107)
		tmp = t_2;
	elseif (x <= -3.1e-218)
		tmp = t_1;
	elseif (x <= 2.2e-169)
		tmp = Float64(y / t);
	elseif (x <= 7.4e-72)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	t_2 = 1.0 - (y * (z / x));
	tmp = 0.0;
	if (x <= -4e-70)
		tmp = t_1;
	elseif (x <= -1.1e-107)
		tmp = t_2;
	elseif (x <= -3.1e-218)
		tmp = t_1;
	elseif (x <= 2.2e-169)
		tmp = y / t;
	elseif (x <= 7.4e-72)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e-70], t$95$1, If[LessEqual[x, -1.1e-107], t$95$2, If[LessEqual[x, -3.1e-218], t$95$1, If[LessEqual[x, 2.2e-169], N[(y / t), $MachinePrecision], If[LessEqual[x, 7.4e-72], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.99999999999999998e-70 or -1.10000000000000006e-107 < x < -3.09999999999999997e-218 or 7.3999999999999997e-72 < x

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t around inf 78.9%

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

      1. +-commutative 78.9%

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

   7. Simplified 78.9%

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

   if -3.99999999999999998e-70 < x < -1.10000000000000006e-107 or 2.20000000000000007e-169 < x < 7.3999999999999997e-72

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around 0 51.2%

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

   6. Taylor expanded in y around inf 51.3%

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

   7. Taylor expanded in z around 0 60.3%

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

      1. associate-*r/ 60.3%

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

      2. associate-*r* 60.3%

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

      3. neg-mul-1 60.3%

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

      4. *-commutative 60.3%

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

      5. +-commutative 60.3%

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

   9. Simplified 60.3%

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

   10. Taylor expanded in x around 0 60.3%

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

       1. mul-1-neg 60.3%

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

       2. associate-/l* 60.4%

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

   12. Simplified 60.4%

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

   if -3.09999999999999997e-218 < x < 2.20000000000000007e-169

   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 y around inf 55.9%

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

      1. associate-/l* 57.9%

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

      2. +-commutative 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in x around 0 60.9%

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

      1. un-div-inv 61.1%

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

      2. *-un-lft-identity 61.1%

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

      3. associate-/r* 61.1%

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

   10. Applied egg-rr 61.1%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-107}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-218}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-72}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-79} \lor \neg \left(t \leq 2.2 \cdot 10^{-201}\right) \land \left(t \leq 8.5 \cdot 10^{-194} \lor \neg \left(t \leq 5.2 \cdot 10^{+49}\right)\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e-79)
         (and (not (<= t 2.2e-201)) (or (<= t 8.5e-194) (not (<= t 5.2e+49)))))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* y (/ (/ z x) (- -1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-79) || (!(t <= 2.2e-201) && ((t <= 8.5e-194) || !(t <= 5.2e+49)))) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (y * ((z / 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 ((t <= (-3.2d-79)) .or. (.not. (t <= 2.2d-201)) .and. (t <= 8.5d-194) .or. (.not. (t <= 5.2d+49))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + (y * ((z / 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 ((t <= -3.2e-79) || (!(t <= 2.2e-201) && ((t <= 8.5e-194) || !(t <= 5.2e+49)))) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.2e-79) or (not (t <= 2.2e-201) and ((t <= 8.5e-194) or not (t <= 5.2e+49))):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e-79) || (!(t <= 2.2e-201) && ((t <= 8.5e-194) || !(t <= 5.2e+49))))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(y * Float64(Float64(z / x) / Float64(-1.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.2e-79) || (~((t <= 2.2e-201)) && ((t <= 8.5e-194) || ~((t <= 5.2e+49)))))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e-79], And[N[Not[LessEqual[t, 2.2e-201]], $MachinePrecision], Or[LessEqual[t, 8.5e-194], N[Not[LessEqual[t, 5.2e+49]], $MachinePrecision]]]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(N[(z / x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999988e-79 or 2.2e-201 < t < 8.5000000000000005e-194 or 5.19999999999999977e49 < t

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around inf 86.9%

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

   if -3.19999999999999988e-79 < t < 2.2e-201 or 8.5000000000000005e-194 < t < 5.19999999999999977e49

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 79.5%

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

   6. Taylor expanded in y around inf 80.3%

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

   7. Taylor expanded in z around 0 80.2%

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

      1. associate-*r/ 80.2%

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

      2. associate-*r* 80.2%

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

      3. neg-mul-1 80.2%

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

      4. *-commutative 80.2%

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

      5. +-commutative 80.2%

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

   9. Simplified 80.2%

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

   10. Taylor expanded in z around 0 80.2%

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

       1. mul-1-neg 80.2%

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

       2. associate-/l* 82.5%

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

       3. distribute-rgt-neg-in 82.5%

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

       4. associate-/r* 82.5%

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

       5. +-commutative 82.5%

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

       6. distribute-neg-frac2 82.5%

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

       7. +-commutative 82.5%

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

       8. distribute-neg-in 82.5%

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

       9. metadata-eval 82.5%

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

       10. unsub-neg 82.5%

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

   12. Simplified 82.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-79} \lor \neg \left(t \leq 2.2 \cdot 10^{-201}\right) \land \left(t \leq 8.5 \cdot 10^{-194} \lor \neg \left(t \leq 5.2 \cdot 10^{+49}\right)\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-201} \lor \neg \left(t \leq 7.8 \cdot 10^{-194}\right) \land t \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e-78)
   (+ (/ x (+ x 1.0)) (/ y (* (+ x 1.0) t)))
   (if (or (<= t 2.2e-201) (and (not (<= t 7.8e-194)) (<= t 5.2e+49)))
     (+ 1.0 (* y (/ (/ z x) (- -1.0 x))))
     (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-78) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if ((t <= 2.2e-201) || (!(t <= 7.8e-194) && (t <= 5.2e+49))) {
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.8d-78)) then
        tmp = (x / (x + 1.0d0)) + (y / ((x + 1.0d0) * t))
    else if ((t <= 2.2d-201) .or. (.not. (t <= 7.8d-194)) .and. (t <= 5.2d+49)) then
        tmp = 1.0d0 + (y * ((z / x) / ((-1.0d0) - x)))
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-78) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if ((t <= 2.2e-201) || (!(t <= 7.8e-194) && (t <= 5.2e+49))) {
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e-78:
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t))
	elif (t <= 2.2e-201) or (not (t <= 7.8e-194) and (t <= 5.2e+49)):
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)))
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e-78)
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(Float64(x + 1.0) * t)));
	elseif ((t <= 2.2e-201) || (!(t <= 7.8e-194) && (t <= 5.2e+49)))
		tmp = Float64(1.0 + Float64(y * Float64(Float64(z / x) / Float64(-1.0 - x))));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.8e-78)
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	elseif ((t <= 2.2e-201) || (~((t <= 7.8e-194)) && (t <= 5.2e+49)))
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.8e-78], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.2e-201], And[N[Not[LessEqual[t, 7.8e-194]], $MachinePrecision], LessEqual[t, 5.2e+49]]], N[(1.0 + N[(y * N[(N[(z / x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $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 t < -1.8000000000000001e-78

   1. Initial program 80.6%

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

      1. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in y around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. +-commutative 80.6%

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

      3. sub-neg 80.6%

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

      4. *-commutative 80.6%

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

      5. *-commutative 80.6%

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

      6. div-sub 80.6%

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

      7. fma-neg 80.6%

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

      8. fma-define 80.6%

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

      9. *-commutative 80.6%

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

      10. fma-undefine 80.6%

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

      11. *-commutative 80.6%

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

      12. fma-neg 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in y around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. sub-neg 74.2%

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

      3. *-commutative 74.2%

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

      4. *-rgt-identity 74.2%

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

      5. fma-undefine 74.2%

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

      6. *-rgt-identity 74.2%

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

   10. Simplified 74.2%

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

   11. Taylor expanded in t around inf 85.8%

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

       1. +-commutative 85.8%

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

       2. +-commutative 85.8%

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

   13. Simplified 85.8%

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

   if -1.8000000000000001e-78 < t < 2.2e-201 or 7.7999999999999997e-194 < t < 5.19999999999999977e49

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 79.5%

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

   6. Taylor expanded in y around inf 80.3%

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

   7. Taylor expanded in z around 0 80.2%

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

      1. associate-*r/ 80.2%

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

      2. associate-*r* 80.2%

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

      3. neg-mul-1 80.2%

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

      4. *-commutative 80.2%

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

      5. +-commutative 80.2%

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

   9. Simplified 80.2%

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

   10. Taylor expanded in z around 0 80.2%

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

       1. mul-1-neg 80.2%

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

       2. associate-/l* 82.5%

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

       3. distribute-rgt-neg-in 82.5%

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

       4. associate-/r* 82.5%

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

       5. +-commutative 82.5%

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

       6. distribute-neg-frac2 82.5%

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

       7. +-commutative 82.5%

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

       8. distribute-neg-in 82.5%

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

       9. metadata-eval 82.5%

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

       10. unsub-neg 82.5%

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

   12. Simplified 82.5%

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

   if 2.2e-201 < t < 7.7999999999999997e-194 or 5.19999999999999977e49 < t

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in z around inf 93.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-201} \lor \neg \left(t \leq 7.8 \cdot 10^{-194}\right) \land t \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+103}:\\ \;\;\;\;t\_1 + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+136}:\\ \;\;\;\;\frac{x - \frac{z \cdot y - x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{\frac{y}{x + 1} + \frac{x}{z \cdot \left(-1 - x\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= z -1.4e+103)
     (+ t_1 (/ y (* (+ x 1.0) t)))
     (if (<= z 2.1e+136)
       (/ (- x (/ (- (* z y) x) (- x (* z t)))) (+ x 1.0))
       (+ t_1 (/ (+ (/ y (+ x 1.0)) (/ x (* z (- -1.0 x)))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (z <= -1.4e+103) {
		tmp = t_1 + (y / ((x + 1.0) * t));
	} else if (z <= 2.1e+136) {
		tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0);
	} else {
		tmp = t_1 + (((y / (x + 1.0)) + (x / (z * (-1.0 - x)))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (z <= (-1.4d+103)) then
        tmp = t_1 + (y / ((x + 1.0d0) * t))
    else if (z <= 2.1d+136) then
        tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0d0)
    else
        tmp = t_1 + (((y / (x + 1.0d0)) + (x / (z * ((-1.0d0) - x)))) / t)
    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 (z <= -1.4e+103) {
		tmp = t_1 + (y / ((x + 1.0) * t));
	} else if (z <= 2.1e+136) {
		tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0);
	} else {
		tmp = t_1 + (((y / (x + 1.0)) + (x / (z * (-1.0 - x)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if z <= -1.4e+103:
		tmp = t_1 + (y / ((x + 1.0) * t))
	elif z <= 2.1e+136:
		tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0)
	else:
		tmp = t_1 + (((y / (x + 1.0)) + (x / (z * (-1.0 - x)))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -1.4e+103)
		tmp = Float64(t_1 + Float64(y / Float64(Float64(x + 1.0) * t)));
	elseif (z <= 2.1e+136)
		tmp = Float64(Float64(x - Float64(Float64(Float64(z * y) - x) / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(y / Float64(x + 1.0)) + Float64(x / Float64(z * Float64(-1.0 - x)))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (z <= -1.4e+103)
		tmp = t_1 + (y / ((x + 1.0) * t));
	elseif (z <= 2.1e+136)
		tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0);
	else
		tmp = t_1 + (((y / (x + 1.0)) + (x / (z * (-1.0 - x)))) / t);
	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[z, -1.4e+103], N[(t$95$1 + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+136], N[(N[(x - N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / N[(z * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000004e103

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. +-commutative 70.6%

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

      3. sub-neg 70.6%

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

      4. *-commutative 70.6%

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

      5. *-commutative 70.6%

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

      6. div-sub 70.6%

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

      7. fma-neg 70.6%

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

      8. fma-define 70.6%

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

      9. *-commutative 70.6%

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

      10. fma-undefine 70.6%

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

      11. *-commutative 70.6%

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

      12. fma-neg 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in y around inf 70.6%

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

      1. *-commutative 70.6%

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

      2. sub-neg 70.6%

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

      3. *-commutative 70.6%

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

      4. *-rgt-identity 70.6%

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

      5. fma-undefine 70.6%

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

      6. *-rgt-identity 70.6%

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

   10. Simplified 70.6%

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

   11. Taylor expanded in t around inf 91.2%

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

       1. +-commutative 91.2%

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

       2. +-commutative 91.2%

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

   13. Simplified 91.2%

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

   if -1.40000000000000004e103 < z < 2.0999999999999999e136

   1. Initial program 98.3%

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

   if 2.0999999999999999e136 < z

   1. Initial program 64.4%

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

      1. *-commutative 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in t around -inf 96.0%

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

      1. +-commutative 96.0%

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

      2. mul-1-neg 96.0%

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

      3. unsub-neg 96.0%

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

      4. +-commutative 96.0%

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

      5. sub-neg 96.0%

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

      6. mul-1-neg 96.0%

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

      7. distribute-neg-frac2 96.0%

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

      8. distribute-neg-in 96.0%

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

      9. metadata-eval 96.0%

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

      10. unsub-neg 96.0%

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

      11. mul-1-neg 96.0%

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

      12. remove-double-neg 96.0%

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

      13. +-commutative 96.0%

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

   7. Simplified 96.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+136}:\\ \;\;\;\;\frac{x - \frac{z \cdot y - x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} + \frac{x}{z \cdot \left(-1 - x\right)}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+87} \lor \neg \left(z \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{z \cdot y - x}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.4e+87) (not (<= z 3.4e+50)))
   (+ (/ x (+ x 1.0)) (/ y (* (+ x 1.0) t)))
   (/ (+ x (/ 1.0 (/ (- (* z t) x) (- (* z y) x)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.4e+87) || !(z <= 3.4e+50)) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else {
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.4d+87)) .or. (.not. (z <= 3.4d+50))) then
        tmp = (x / (x + 1.0d0)) + (y / ((x + 1.0d0) * t))
    else
        tmp = (x + (1.0d0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.4e+87) || !(z <= 3.4e+50)) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else {
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.4e+87) or not (z <= 3.4e+50):
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t))
	else:
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.4e+87) || !(z <= 3.4e+50))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(Float64(x + 1.0) * t)));
	else
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(Float64(z * t) - x) / Float64(Float64(z * y) - x)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.4e+87) || ~((z <= 3.4e+50)))
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	else
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.4e+87], N[Not[LessEqual[z, 3.4e+50]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.40000000000000013e87 or 3.3999999999999998e50 < z

   1. Initial program 74.0%

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

      1. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in y around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. +-commutative 74.0%

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

      3. sub-neg 74.0%

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

      4. *-commutative 74.0%

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

      5. *-commutative 74.0%

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

      6. div-sub 74.0%

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

      7. fma-neg 74.0%

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

      8. fma-define 74.0%

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

      9. *-commutative 74.0%

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

      10. fma-undefine 74.0%

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

      11. *-commutative 74.0%

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

      12. fma-neg 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. sub-neg 74.0%

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

      3. *-commutative 74.0%

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

      4. *-rgt-identity 74.0%

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

      5. fma-undefine 74.1%

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

      6. *-rgt-identity 74.1%

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

   10. Simplified 74.1%

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

   11. Taylor expanded in t around inf 93.8%

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

       1. +-commutative 93.8%

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

       2. +-commutative 93.8%

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

   13. Simplified 93.8%

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

   if -5.40000000000000013e87 < z < 3.3999999999999998e50

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

   3. Simplified 98.6%

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

      1. clear-num 98.6%

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

      2. inv-pow 98.6%

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

      3. fma-neg 98.6%

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

   6. Applied egg-rr 98.6%

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

      1. unpow-1 98.6%

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

      2. *-commutative 98.6%

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

      3. fma-neg 98.6%

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

      4. *-commutative 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+87} \lor \neg \left(z \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{z \cdot y - x}}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+102} \lor \neg \left(z \leq 3.25 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{z \cdot y - x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+102) (not (<= z 3.25e+50)))
   (+ (/ x (+ x 1.0)) (/ y (* (+ x 1.0) t)))
   (/ (- x (/ (- (* z y) x) (- x (* z t)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+102) || !(z <= 3.25e+50)) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else {
		tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.2d+102)) .or. (.not. (z <= 3.25d+50))) then
        tmp = (x / (x + 1.0d0)) + (y / ((x + 1.0d0) * t))
    else
        tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+102) || !(z <= 3.25e+50)) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else {
		tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+102) or not (z <= 3.25e+50):
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t))
	else:
		tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+102) || !(z <= 3.25e+50))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(Float64(x + 1.0) * t)));
	else
		tmp = Float64(Float64(x - Float64(Float64(Float64(z * y) - x) / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e+102) || ~((z <= 3.25e+50)))
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	else
		tmp = (x - (((z * y) - x) / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+102], N[Not[LessEqual[z, 3.25e+50]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999973e102 or 3.2500000000000001e50 < z

   1. Initial program 72.2%

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

      1. *-commutative 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in y around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. +-commutative 72.2%

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

      3. sub-neg 72.2%

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

      4. *-commutative 72.2%

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

      5. *-commutative 72.2%

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

      6. div-sub 72.2%

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

      7. fma-neg 72.2%

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

      8. fma-define 72.2%

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

      9. *-commutative 72.2%

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

      10. fma-undefine 72.2%

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

      11. *-commutative 72.2%

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

      12. fma-neg 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in y around inf 72.2%

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

      1. *-commutative 72.2%

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

      2. sub-neg 72.2%

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

      3. *-commutative 72.2%

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

      4. *-rgt-identity 72.2%

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

      5. fma-undefine 72.2%

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

      6. *-rgt-identity 72.2%

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

   10. Simplified 72.2%

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

   11. Taylor expanded in t around inf 93.4%

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

       1. +-commutative 93.4%

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

       2. +-commutative 93.4%

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

   13. Simplified 93.4%

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

   if -6.19999999999999973e102 < z < 3.2500000000000001e50

   1. Initial program 98.7%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+102} \lor \neg \left(z \leq 3.25 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{z \cdot y - x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+60} \lor \neg \left(z \leq 2.1 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e+60) (not (<= z 2.1e+24)))
   (+ (/ x (+ x 1.0)) (/ y (* (+ x 1.0) t)))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+60) || !(z <= 2.1e+24)) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.8d+60)) .or. (.not. (z <= 2.1d+24))) then
        tmp = (x / (x + 1.0d0)) + (y / ((x + 1.0d0) * t))
    else
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+60) || !(z <= 2.1e+24)) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e+60) or not (z <= 2.1e+24):
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t))
	else:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e+60) || !(z <= 2.1e+24))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(Float64(x + 1.0) * t)));
	else
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.8e+60) || ~((z <= 2.1e+24)))
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	else
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e+60], N[Not[LessEqual[z, 2.1e+24]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999999e60 or 2.1000000000000001e24 < z

   1. Initial program 75.5%

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

      1. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in y around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. +-commutative 75.5%

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

      3. sub-neg 75.5%

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

      4. *-commutative 75.5%

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

      5. *-commutative 75.5%

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

      6. div-sub 75.5%

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

      7. fma-neg 75.5%

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

      8. fma-define 75.5%

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

      9. *-commutative 75.5%

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

      10. fma-undefine 75.5%

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

      11. *-commutative 75.5%

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

      12. fma-neg 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in y around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. sub-neg 75.5%

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

      3. *-commutative 75.5%

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

      4. *-rgt-identity 75.5%

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

      5. fma-undefine 75.5%

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

      6. *-rgt-identity 75.5%

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

   10. Simplified 75.5%

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

   11. Taylor expanded in t around inf 92.7%

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

       1. +-commutative 92.7%

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

       2. +-commutative 92.7%

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

   13. Simplified 92.7%

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

   if -5.79999999999999999e60 < z < 2.1000000000000001e24

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 76.6%

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

      1. +-commutative 76.6%

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

   7. Simplified 76.6%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+60} \lor \neg \left(z \leq 2.1 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -90000:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \mathbf{elif}\;x \leq 29.5:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -90000.0)
   (+ 1.0 (* y (/ (/ z x) (- -1.0 x))))
   (if (<= x 29.5)
     (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
     (/ (+ x (/ x (- x (* z t)))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -90000.0) {
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	} else if (x <= 29.5) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-90000.0d0)) then
        tmp = 1.0d0 + (y * ((z / x) / ((-1.0d0) - x)))
    else if (x <= 29.5d0) then
        tmp = (x - (((x / z) - y) / t)) / (x + 1.0d0)
    else
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -90000.0) {
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	} else if (x <= 29.5) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -90000.0:
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)))
	elif x <= 29.5:
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0)
	else:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -90000.0)
		tmp = Float64(1.0 + Float64(y * Float64(Float64(z / x) / Float64(-1.0 - x))));
	elseif (x <= 29.5)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -90000.0)
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	elseif (x <= 29.5)
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	else
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -90000.0], N[(1.0 + N[(y * N[(N[(z / x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 29.5], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e4

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in z around 0 94.0%

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

   6. Taylor expanded in y around inf 94.0%

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

   7. Taylor expanded in z around 0 86.3%

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

      1. associate-*r/ 86.3%

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

      2. associate-*r* 86.3%

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

      3. neg-mul-1 86.3%

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

      4. *-commutative 86.3%

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

      5. +-commutative 86.3%

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

   9. Simplified 86.3%

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

   10. Taylor expanded in z around 0 86.3%

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

       1. mul-1-neg 86.3%

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

       2. associate-/l* 94.0%

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

       3. distribute-rgt-neg-in 94.0%

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

       4. associate-/r* 94.0%

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

       5. +-commutative 94.0%

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

       6. distribute-neg-frac2 94.0%

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

       7. +-commutative 94.0%

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

       8. distribute-neg-in 94.0%

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

       9. metadata-eval 94.0%

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

       10. unsub-neg 94.0%

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

   12. Simplified 94.0%

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

   if -9e4 < x < 29.5

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t around -inf 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

      3. cancel-sign-sub-inv 75.8%

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

      4. metadata-eval 75.8%

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

      5. *-lft-identity 75.8%

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

      6. +-commutative 75.8%

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

      7. mul-1-neg 75.8%

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

      8. unsub-neg 75.8%

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

   7. Simplified 75.8%

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

   if 29.5 < x

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in y around 0 93.1%

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

      1. +-commutative 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -90000:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \mathbf{elif}\;x \leq 29.5:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -112000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -112000.0) 1.0 (if (<= x 6.5e+28) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -112000.0) {
		tmp = 1.0;
	} else if (x <= 6.5e+28) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-112000.0d0)) then
        tmp = 1.0d0
    else if (x <= 6.5d+28) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -112000.0) {
		tmp = 1.0;
	} else if (x <= 6.5e+28) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -112000.0:
		tmp = 1.0
	elif x <= 6.5e+28:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -112000.0)
		tmp = 1.0;
	elseif (x <= 6.5e+28)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -112000.0)
		tmp = 1.0;
	elseif (x <= 6.5e+28)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -112000.0], 1.0, If[LessEqual[x, 6.5e+28], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -112000 or 6.5000000000000001e28 < x

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in y around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. +-commutative 87.3%

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

      3. sub-neg 87.3%

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

      4. *-commutative 87.3%

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

      5. *-commutative 87.3%

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

      6. div-sub 87.3%

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

      7. fma-neg 87.3%

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

      8. fma-define 87.3%

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

      9. *-commutative 87.3%

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

      10. fma-undefine 87.3%

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

      11. *-commutative 87.3%

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

      12. fma-neg 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in y around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. sub-neg 87.1%

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

      3. *-commutative 87.1%

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

      4. *-rgt-identity 87.1%

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

      5. fma-undefine 87.1%

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

      6. *-rgt-identity 87.1%

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

   10. Simplified 87.1%

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

   11. Taylor expanded in x around inf 90.8%

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

   if -112000 < x < 6.5000000000000001e28

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in z around inf 70.4%

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

Alternative 11: 66.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-218} \lor \neg \left(x \leq 2.9 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e-218) (not (<= x 2.9e-81))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-218) || !(x <= 2.9e-81)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.1d-218)) .or. (.not. (x <= 2.9d-81))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-218) || !(x <= 2.9e-81)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.1e-218) or not (x <= 2.9e-81):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e-218) || !(x <= 2.9e-81))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.1e-218) || ~((x <= 2.9e-81)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e-218], N[Not[LessEqual[x, 2.9e-81]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.09999999999999997e-218 or 2.89999999999999989e-81 < x

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in t around inf 74.5%

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

      1. +-commutative 74.5%

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

   7. Simplified 74.5%

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

   if -3.09999999999999997e-218 < x < 2.89999999999999989e-81

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around inf 54.8%

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

      1. associate-/l* 57.8%

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

      2. +-commutative 57.8%

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

   7. Simplified 57.8%

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

   8. Taylor expanded in x around 0 54.9%

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

      1. un-div-inv 55.0%

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

      2. *-un-lft-identity 55.0%

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

      3. associate-/r* 55.0%

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

   10. Applied egg-rr 55.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-218} \lor \neg \left(x \leq 2.9 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-218} \lor \neg \left(x \leq 1.02 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e-218) (not (<= x 1.02e-115)))
   (/ x (+ x 1.0))
   (* y (/ 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-218) || !(x <= 1.02e-115)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y * (1.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.1d-218)) .or. (.not. (x <= 1.02d-115))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y * (1.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-218) || !(x <= 1.02e-115)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y * (1.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.1e-218) or not (x <= 1.02e-115):
		tmp = x / (x + 1.0)
	else:
		tmp = y * (1.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e-218) || !(x <= 1.02e-115))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y * Float64(1.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.1e-218) || ~((x <= 1.02e-115)))
		tmp = x / (x + 1.0);
	else
		tmp = y * (1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e-218], N[Not[LessEqual[x, 1.02e-115]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.09999999999999997e-218 or 1.02e-115 < x

   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 t around inf 73.5%

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

      1. +-commutative 73.5%

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

   7. Simplified 73.5%

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

   if -3.09999999999999997e-218 < x < 1.02e-115

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in y around inf 55.0%

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

      1. associate-/l* 58.2%

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

      2. +-commutative 58.2%

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

   7. Simplified 58.2%

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

   8. Taylor expanded in x around 0 56.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-218} \lor \neg \left(x \leq 1.02 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-47}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.2e-47) 1.0 (if (<= x 1.5e-7) (* y (/ 1.0 t)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e-47) {
		tmp = 1.0;
	} else if (x <= 1.5e-7) {
		tmp = y * (1.0 / 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 <= (-4.2d-47)) then
        tmp = 1.0d0
    else if (x <= 1.5d-7) then
        tmp = y * (1.0d0 / 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 <= -4.2e-47) {
		tmp = 1.0;
	} else if (x <= 1.5e-7) {
		tmp = y * (1.0 / t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.2e-47:
		tmp = 1.0
	elif x <= 1.5e-7:
		tmp = y * (1.0 / t)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.2e-47)
		tmp = 1.0;
	elseif (x <= 1.5e-7)
		tmp = Float64(y * Float64(1.0 / t));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.2e-47)
		tmp = 1.0;
	elseif (x <= 1.5e-7)
		tmp = y * (1.0 / t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.2e-47], 1.0, If[LessEqual[x, 1.5e-7], N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000001e-47 or 1.4999999999999999e-7 < x

   1. Initial program 85.2%

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

      1. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in y around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. +-commutative 85.2%

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

      3. sub-neg 85.2%

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

      4. *-commutative 85.2%

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

      5. *-commutative 85.2%

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

      6. div-sub 85.2%

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

      7. fma-neg 85.2%

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

      8. fma-define 85.2%

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

      9. *-commutative 85.2%

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

      10. fma-undefine 85.2%

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

      11. *-commutative 85.2%

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

      12. fma-neg 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in y around inf 82.2%

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

      1. *-commutative 82.2%

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

      2. sub-neg 82.2%

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

      3. *-commutative 82.2%

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

      4. *-rgt-identity 82.2%

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

      5. fma-undefine 82.2%

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

      6. *-rgt-identity 82.2%

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

   10. Simplified 82.2%

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

   11. Taylor expanded in x around inf 84.8%

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

   if -4.2000000000000001e-47 < x < 1.4999999999999999e-7

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in y around inf 49.7%

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

      1. associate-/l* 51.4%

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

      2. +-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in x around 0 44.1%

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

Alternative 14: 53.5% 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 88.4%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
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 0 88.4%

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

   1. mul-1-neg 88.4%

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

   2. +-commutative 88.4%

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

   3. sub-neg 88.4%

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

   4. *-commutative 88.4%

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

   5. *-commutative 88.4%

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

   6. div-sub 88.4%

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

   7. fma-neg 88.4%

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

   8. fma-define 88.4%

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

   9. *-commutative 88.4%

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

   10. fma-undefine 88.4%

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

   11. *-commutative 88.4%

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

   12. fma-neg 88.4%

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

7. Simplified 88.4%

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

8. Taylor expanded in y around inf 79.2%

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

   1. *-commutative 79.2%

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

   2. sub-neg 79.2%

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

   3. *-commutative 79.2%

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

   4. *-rgt-identity 79.2%

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

   5. fma-undefine 79.2%

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

   6. *-rgt-identity 79.2%

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

10. Simplified 79.2%

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

11. Taylor expanded in x around inf 52.6%

    \[\leadsto \color{blue}{1} \]
12. 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 2024100 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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