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

Percentage Accurate: 90.0% → 96.8%

Time: 12.2s

Alternatives: 12

Speedup: 0.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% 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: 96.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ t_3 := \frac{x}{x + 1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\frac{z}{t\_1} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + t\_3\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+226}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3 + \frac{\frac{y}{x - -1} - \frac{\frac{x}{z}}{x + 1}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0)))
        (t_3 (/ x (+ x 1.0))))
   (if (<= t_2 -5e+28)
     (* (/ z t_1) (/ y (+ x 1.0)))
     (if (<= t_2 5e-29)
       (- (+ (/ y (* t (+ x 1.0))) t_3) (/ x (* t (* z (+ x 1.0)))))
       (if (<= t_2 5e+226)
         t_2
         (+ t_3 (/ (- (/ y (- x -1.0)) (/ (/ x z) (+ x 1.0))) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double t_3 = x / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+28) {
		tmp = (z / t_1) * (y / (x + 1.0));
	} else if (t_2 <= 5e-29) {
		tmp = ((y / (t * (x + 1.0))) + t_3) - (x / (t * (z * (x + 1.0))));
	} else if (t_2 <= 5e+226) {
		tmp = t_2;
	} else {
		tmp = t_3 + (((y / (x - -1.0)) - ((x / z) / (x + 1.0))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    t_3 = x / (x + 1.0d0)
    if (t_2 <= (-5d+28)) then
        tmp = (z / t_1) * (y / (x + 1.0d0))
    else if (t_2 <= 5d-29) then
        tmp = ((y / (t * (x + 1.0d0))) + t_3) - (x / (t * (z * (x + 1.0d0))))
    else if (t_2 <= 5d+226) then
        tmp = t_2
    else
        tmp = t_3 + (((y / (x - (-1.0d0))) - ((x / z) / (x + 1.0d0))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double t_3 = x / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+28) {
		tmp = (z / t_1) * (y / (x + 1.0));
	} else if (t_2 <= 5e-29) {
		tmp = ((y / (t * (x + 1.0))) + t_3) - (x / (t * (z * (x + 1.0))));
	} else if (t_2 <= 5e+226) {
		tmp = t_2;
	} else {
		tmp = t_3 + (((y / (x - -1.0)) - ((x / z) / (x + 1.0))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	t_3 = x / (x + 1.0)
	tmp = 0
	if t_2 <= -5e+28:
		tmp = (z / t_1) * (y / (x + 1.0))
	elif t_2 <= 5e-29:
		tmp = ((y / (t * (x + 1.0))) + t_3) - (x / (t * (z * (x + 1.0))))
	elif t_2 <= 5e+226:
		tmp = t_2
	else:
		tmp = t_3 + (((y / (x - -1.0)) - ((x / z) / (x + 1.0))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	t_3 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -5e+28)
		tmp = Float64(Float64(z / t_1) * Float64(y / Float64(x + 1.0)));
	elseif (t_2 <= 5e-29)
		tmp = Float64(Float64(Float64(y / Float64(t * Float64(x + 1.0))) + t_3) - Float64(x / Float64(t * Float64(z * Float64(x + 1.0)))));
	elseif (t_2 <= 5e+226)
		tmp = t_2;
	else
		tmp = Float64(t_3 + Float64(Float64(Float64(y / Float64(x - -1.0)) - Float64(Float64(x / z) / Float64(x + 1.0))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	t_3 = x / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -5e+28)
		tmp = (z / t_1) * (y / (x + 1.0));
	elseif (t_2 <= 5e-29)
		tmp = ((y / (t * (x + 1.0))) + t_3) - (x / (t * (z * (x + 1.0))));
	elseif (t_2 <= 5e+226)
		tmp = t_2;
	else
		tmp = t_3 + (((y / (x - -1.0)) - ((x / z) / (x + 1.0))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+28], N[(N[(z / t$95$1), $MachinePrecision] * N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-29], N[(N[(N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(x / N[(t * N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+226], t$95$2, N[(t$95$3 + N[(N[(N[(y / N[(x - -1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.99999999999999957e28

   1. Initial program 76.7%

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

      1. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. +-commutative 76.5%

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

      3. *-commutative 76.5%

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

      4. times-frac 96.9%

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

   7. Applied egg-rr 96.9%

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

   if -4.99999999999999957e28 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999986e-29

   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 t around inf 100.0%

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

   if 4.99999999999999986e-29 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000005e226

   1. Initial program 99.9%

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

   if 5.0000000000000005e226 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 37.8%

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

      1. *-commutative 37.8%

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

   3. Simplified 37.8%

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

   5. Taylor expanded in t around -inf 89.4%

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

      1. +-commutative 89.4%

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

      2. mul-1-neg 89.4%

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

      3. unsub-neg 89.4%

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

      4. +-commutative 89.4%

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

      5. sub-neg 89.4%

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

      6. mul-1-neg 89.4%

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

      7. distribute-neg-frac2 89.4%

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

      8. distribute-neg-in 89.4%

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

      9. metadata-eval 89.4%

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

      10. unsub-neg 89.4%

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

      11. mul-1-neg 89.4%

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

      12. remove-double-neg 89.4%

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

      13. associate-/r* 89.4%

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

      14. +-commutative 89.4%

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

   7. Simplified 89.4%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\frac{z}{z \cdot t - x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+226}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x - -1} - \frac{\frac{x}{z}}{x + 1}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\frac{z}{t\_1} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+226}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x - -1} - \frac{\frac{x}{z}}{x + 1}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -5e+28)
     (* (/ z t_1) (/ y (+ x 1.0)))
     (if (<= t_2 5e-29)
       (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0))
       (if (<= t_2 5e+226)
         t_2
         (+
          (/ x (+ x 1.0))
          (/ (- (/ y (- x -1.0)) (/ (/ x z) (+ x 1.0))) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+28) {
		tmp = (z / t_1) * (y / (x + 1.0));
	} else if (t_2 <= 5e-29) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_2 <= 5e+226) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x - -1.0)) - ((x / z) / (x + 1.0))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-5d+28)) then
        tmp = (z / t_1) * (y / (x + 1.0d0))
    else if (t_2 <= 5d-29) then
        tmp = (x + ((y - (x / z)) / t)) / (x + 1.0d0)
    else if (t_2 <= 5d+226) then
        tmp = t_2
    else
        tmp = (x / (x + 1.0d0)) + (((y / (x - (-1.0d0))) - ((x / z) / (x + 1.0d0))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+28) {
		tmp = (z / t_1) * (y / (x + 1.0));
	} else if (t_2 <= 5e-29) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_2 <= 5e+226) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x - -1.0)) - ((x / z) / (x + 1.0))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -5e+28:
		tmp = (z / t_1) * (y / (x + 1.0))
	elif t_2 <= 5e-29:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	elif t_2 <= 5e+226:
		tmp = t_2
	else:
		tmp = (x / (x + 1.0)) + (((y / (x - -1.0)) - ((x / z) / (x + 1.0))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -5e+28)
		tmp = Float64(Float64(z / t_1) * Float64(y / Float64(x + 1.0)));
	elseif (t_2 <= 5e-29)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	elseif (t_2 <= 5e+226)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(Float64(y / Float64(x - -1.0)) - Float64(Float64(x / z) / Float64(x + 1.0))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -5e+28)
		tmp = (z / t_1) * (y / (x + 1.0));
	elseif (t_2 <= 5e-29)
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	elseif (t_2 <= 5e+226)
		tmp = t_2;
	else
		tmp = (x / (x + 1.0)) + (((y / (x - -1.0)) - ((x / z) / (x + 1.0))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+28], N[(N[(z / t$95$1), $MachinePrecision] * N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-29], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+226], t$95$2, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(x - -1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.99999999999999957e28

   1. Initial program 76.7%

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

      1. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. +-commutative 76.5%

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

      3. *-commutative 76.5%

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

      4. times-frac 96.9%

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

   7. Applied egg-rr 96.9%

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

   if -4.99999999999999957e28 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999986e-29

   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 t around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-lft-out-- 99.9%

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

   7. Simplified 99.9%

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

   if 4.99999999999999986e-29 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000005e226

   1. Initial program 99.9%

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

   if 5.0000000000000005e226 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 37.8%

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

      1. *-commutative 37.8%

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

   3. Simplified 37.8%

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

   5. Taylor expanded in t around -inf 89.4%

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

      1. +-commutative 89.4%

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

      2. mul-1-neg 89.4%

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

      3. unsub-neg 89.4%

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

      4. +-commutative 89.4%

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

      5. sub-neg 89.4%

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

      6. mul-1-neg 89.4%

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

      7. distribute-neg-frac2 89.4%

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

      8. distribute-neg-in 89.4%

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

      9. metadata-eval 89.4%

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

      10. unsub-neg 89.4%

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

      11. mul-1-neg 89.4%

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

      12. remove-double-neg 89.4%

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

      13. associate-/r* 89.4%

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

      14. +-commutative 89.4%

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

   7. Simplified 89.4%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\frac{z}{z \cdot t - x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+226}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x - -1} - \frac{\frac{x}{z}}{x + 1}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ t_3 := \frac{y}{x + 1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\frac{z}{t\_1} \cdot t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+226}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t + t\_3}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0)))
        (t_3 (/ y (+ x 1.0))))
   (if (<= t_2 -5e+28)
     (* (/ z t_1) t_3)
     (if (<= t_2 5e-29)
       (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0))
       (if (<= t_2 5e+226) t_2 (/ (+ t t_3) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double t_3 = y / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+28) {
		tmp = (z / t_1) * t_3;
	} else if (t_2 <= 5e-29) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_2 <= 5e+226) {
		tmp = t_2;
	} else {
		tmp = (t + t_3) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    t_3 = y / (x + 1.0d0)
    if (t_2 <= (-5d+28)) then
        tmp = (z / t_1) * t_3
    else if (t_2 <= 5d-29) then
        tmp = (x + ((y - (x / z)) / t)) / (x + 1.0d0)
    else if (t_2 <= 5d+226) then
        tmp = t_2
    else
        tmp = (t + t_3) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double t_3 = y / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+28) {
		tmp = (z / t_1) * t_3;
	} else if (t_2 <= 5e-29) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_2 <= 5e+226) {
		tmp = t_2;
	} else {
		tmp = (t + t_3) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	t_3 = y / (x + 1.0)
	tmp = 0
	if t_2 <= -5e+28:
		tmp = (z / t_1) * t_3
	elif t_2 <= 5e-29:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	elif t_2 <= 5e+226:
		tmp = t_2
	else:
		tmp = (t + t_3) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	t_3 = Float64(y / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -5e+28)
		tmp = Float64(Float64(z / t_1) * t_3);
	elseif (t_2 <= 5e-29)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	elseif (t_2 <= 5e+226)
		tmp = t_2;
	else
		tmp = Float64(Float64(t + t_3) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	t_3 = y / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -5e+28)
		tmp = (z / t_1) * t_3;
	elseif (t_2 <= 5e-29)
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	elseif (t_2 <= 5e+226)
		tmp = t_2;
	else
		tmp = (t + t_3) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+28], N[(N[(z / t$95$1), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[t$95$2, 5e-29], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+226], t$95$2, N[(N[(t + t$95$3), $MachinePrecision] / t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.99999999999999957e28

   1. Initial program 76.7%

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

      1. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. +-commutative 76.5%

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

      3. *-commutative 76.5%

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

      4. times-frac 96.9%

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

   7. Applied egg-rr 96.9%

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

   if -4.99999999999999957e28 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999986e-29

   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 t around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-lft-out-- 99.9%

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

   7. Simplified 99.9%

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

   if 4.99999999999999986e-29 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000005e226

   1. Initial program 99.9%

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

   if 5.0000000000000005e226 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 37.8%

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

      1. *-commutative 37.8%

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

   3. Simplified 37.8%

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

   5. Taylor expanded in z around inf 82.7%

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

      1. +-commutative 82.7%

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

      2. +-commutative 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in t around 0 79.0%

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

   9. Taylor expanded in x around inf 86.1%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\frac{z}{z \cdot t - x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+226}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + \frac{y}{x + 1}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e-33)
   (/ (+ x (/ y t)) (+ x 1.0))
   (if (<= z 2.7e+17)
     (/ (+ (- x (* y (/ z x))) 1.0) (+ x 1.0))
     (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-33) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 2.7e+17) {
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	} else {
		tmp = (x + ((y - (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 <= (-2.1d-33)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (z <= 2.7d+17) then
        tmp = ((x - (y * (z / x))) + 1.0d0) / (x + 1.0d0)
    else
        tmp = (x + ((y - (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 <= -2.1e-33) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 2.7e+17) {
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	} else {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e-33:
		tmp = (x + (y / t)) / (x + 1.0)
	elif z <= 2.7e+17:
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0)
	else:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e-33)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (z <= 2.7e+17)
		tmp = Float64(Float64(Float64(x - Float64(y * Float64(z / x))) + 1.0) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.1e-33)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (z <= 2.7e+17)
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	else
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e-33], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+17], N[(N[(N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e-33

   1. Initial program 78.3%

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

      1. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. +-commutative 87.3%

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

   7. Simplified 87.3%

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

   if -2.1e-33 < z < 2.7e17

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

      3. associate-/l* 79.1%

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

      4. +-commutative 79.1%

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

   7. Simplified 79.1%

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

   if 2.7e17 < z

   1. Initial program 77.8%

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

      1. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in t around -inf 90.7%

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

      1. mul-1-neg 90.7%

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

      2. distribute-lft-out-- 90.7%

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

   7. Simplified 90.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{-34}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 10^{+18}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.3e-34)
   (/ (+ x (/ y t)) (+ x 1.0))
   (if (<= z 1e+18)
     (/ (+ (- x (* y (/ z x))) 1.0) (+ x 1.0))
     (+ (/ x (+ x 1.0)) (/ (/ y t) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.3e-34) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 1e+18) {
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) + ((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 (z <= (-7.3d-34)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (z <= 1d+18) then
        tmp = ((x - (y * (z / x))) + 1.0d0) / (x + 1.0d0)
    else
        tmp = (x / (x + 1.0d0)) + ((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 (z <= -7.3e-34) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 1e+18) {
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.3e-34:
		tmp = (x + (y / t)) / (x + 1.0)
	elif z <= 1e+18:
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0)
	else:
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.3e-34)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (z <= 1e+18)
		tmp = Float64(Float64(Float64(x - Float64(y * Float64(z / x))) + 1.0) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(y / t) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.3e-34)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (z <= 1e+18)
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	else
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.3e-34], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+18], N[(N[(N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.29999999999999996e-34

   1. Initial program 78.3%

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

      1. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. +-commutative 87.3%

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

   7. Simplified 87.3%

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

   if -7.29999999999999996e-34 < z < 1e18

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

      3. associate-/l* 79.1%

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

      4. +-commutative 79.1%

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

   7. Simplified 79.1%

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

   if 1e18 < z

   1. Initial program 77.8%

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

      1. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in z around inf 90.5%

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

      1. +-commutative 90.5%

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

      2. +-commutative 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in y around 0 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-/r* 90.5%

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

      3. +-commutative 90.5%

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

   10. Simplified 90.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{-34}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 10^{+18}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+17}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.1e-148)
   (/ (+ x (/ y t)) (+ x 1.0))
   (if (<= z 2.7e+17)
     (- 1.0 (* y (/ z x)))
     (+ (/ x (+ x 1.0)) (/ (/ y t) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.1e-148) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 2.7e+17) {
		tmp = 1.0 - (y * (z / x));
	} else {
		tmp = (x / (x + 1.0)) + ((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 (z <= (-5.1d-148)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (z <= 2.7d+17) then
        tmp = 1.0d0 - (y * (z / x))
    else
        tmp = (x / (x + 1.0d0)) + ((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 (z <= -5.1e-148) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 2.7e+17) {
		tmp = 1.0 - (y * (z / x));
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.1e-148:
		tmp = (x + (y / t)) / (x + 1.0)
	elif z <= 2.7e+17:
		tmp = 1.0 - (y * (z / x))
	else:
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.1e-148)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (z <= 2.7e+17)
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(y / t) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.1e-148)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (z <= 2.7e+17)
		tmp = 1.0 - (y * (z / x));
	else
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.1e-148], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+17], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1e-148

   1. Initial program 82.9%

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

      1. *-commutative 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in z around inf 83.6%

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

      1. +-commutative 83.6%

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

      2. +-commutative 83.6%

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

   7. Simplified 83.6%

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

   if -5.1e-148 < z < 2.7e17

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 71.9%

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

   6. Taylor expanded in x around 0 74.6%

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

      1. associate-/l* 68.7%

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

      2. neg-mul-1 68.7%

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

      3. sub-neg 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in t around 0 77.8%

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

       1. mul-1-neg 77.8%

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

       2. unsub-neg 77.8%

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

       3. associate-/l* 77.8%

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

   11. Simplified 77.8%

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

   if 2.7e17 < z

   1. Initial program 77.8%

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

      1. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in z around inf 90.5%

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

      1. +-commutative 90.5%

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

      2. +-commutative 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in y around 0 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-/r* 90.5%

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

      3. +-commutative 90.5%

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

   10. Simplified 90.5%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+17}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-147} \lor \neg \left(z \leq 2.7 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.25e-147) (not (<= z 2.7e+17)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* y (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e-147) || !(z <= 2.7e+17)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.25d-147)) .or. (.not. (z <= 2.7d+17))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - (y * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e-147) || !(z <= 2.7e+17)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.25e-147) or not (z <= 2.7e+17):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - (y * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.25e-147) || !(z <= 2.7e+17))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.25e-147) || ~((z <= 2.7e+17)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - (y * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.25e-147], N[Not[LessEqual[z, 2.7e+17]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.24999999999999986e-147 or 2.7e17 < z

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in z around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. +-commutative 86.0%

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

   7. Simplified 86.0%

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

   if -2.24999999999999986e-147 < z < 2.7e17

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 71.9%

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

   6. Taylor expanded in x around 0 74.6%

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

      1. associate-/l* 68.7%

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

      2. neg-mul-1 68.7%

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

      3. sub-neg 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in t around 0 77.8%

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

       1. mul-1-neg 77.8%

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

       2. unsub-neg 77.8%

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

       3. associate-/l* 77.8%

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

   11. Simplified 77.8%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-147} \lor \neg \left(z \leq 2.7 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -730:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-98}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -730.0)
   1.0
   (if (<= x 2.55e-98) (/ (/ y (+ x 1.0)) t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -730.0) {
		tmp = 1.0;
	} else if (x <= 2.55e-98) {
		tmp = (y / (x + 1.0)) / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-730.0d0)) then
        tmp = 1.0d0
    else if (x <= 2.55d-98) then
        tmp = (y / (x + 1.0d0)) / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -730.0) {
		tmp = 1.0;
	} else if (x <= 2.55e-98) {
		tmp = (y / (x + 1.0)) / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -730.0:
		tmp = 1.0
	elif x <= 2.55e-98:
		tmp = (y / (x + 1.0)) / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -730.0)
		tmp = 1.0;
	elseif (x <= 2.55e-98)
		tmp = Float64(Float64(y / Float64(x + 1.0)) / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -730.0)
		tmp = 1.0;
	elseif (x <= 2.55e-98)
		tmp = (y / (x + 1.0)) / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -730.0], 1.0, If[LessEqual[x, 2.55e-98], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -730

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 82.1%

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

   if -730 < x < 2.55000000000000011e-98

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. +-commutative 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in t around 0 67.5%

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

   9. Taylor expanded in y around inf 52.6%

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

       1. +-commutative 52.6%

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

   11. Simplified 52.6%

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

   if 2.55000000000000011e-98 < x

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around inf 72.5%

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

      1. +-commutative 72.5%

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

   7. Simplified 72.5%

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

Alternative 9: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -730:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-98}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -730.0)
   1.0
   (if (<= x 1.3e-98) (/ y (* t (+ x 1.0))) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -730.0) {
		tmp = 1.0;
	} else if (x <= 1.3e-98) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-730.0d0)) then
        tmp = 1.0d0
    else if (x <= 1.3d-98) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -730.0) {
		tmp = 1.0;
	} else if (x <= 1.3e-98) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -730.0:
		tmp = 1.0
	elif x <= 1.3e-98:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -730.0)
		tmp = 1.0;
	elseif (x <= 1.3e-98)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -730.0)
		tmp = 1.0;
	elseif (x <= 1.3e-98)
		tmp = y / (t * (x + 1.0));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -730.0], 1.0, If[LessEqual[x, 1.3e-98], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -730

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 82.1%

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

   if -730 < x < 1.30000000000000007e-98

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. +-commutative 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in y around inf 52.6%

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

   if 1.30000000000000007e-98 < x

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around inf 72.5%

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

      1. +-commutative 72.5%

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

   7. Simplified 72.5%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -730:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-98}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-11}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9e-11) 1.0 (if (<= x 6.5e-99) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9e-11) {
		tmp = 1.0;
	} else if (x <= 6.5e-99) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-9d-11)) then
        tmp = 1.0d0
    else if (x <= 6.5d-99) then
        tmp = y / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9e-11) {
		tmp = 1.0;
	} else if (x <= 6.5e-99) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9e-11:
		tmp = 1.0
	elif x <= 6.5e-99:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9e-11)
		tmp = 1.0;
	elseif (x <= 6.5e-99)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9e-11)
		tmp = 1.0;
	elseif (x <= 6.5e-99)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9e-11], 1.0, If[LessEqual[x, 6.5e-99], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.9999999999999999e-11

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around inf 80.8%

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

   if -8.9999999999999999e-11 < x < 6.50000000000000033e-99

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in x around 0 52.7%

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

   if 6.50000000000000033e-99 < x

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around inf 72.5%

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

      1. +-commutative 72.5%

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

   7. Simplified 72.5%

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

Alternative 11: 68.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-98}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.7e-10) 1.0 (if (<= x 1.45e-98) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.7e-10) {
		tmp = 1.0;
	} else if (x <= 1.45e-98) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.7d-10)) then
        tmp = 1.0d0
    else if (x <= 1.45d-98) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.7e-10) {
		tmp = 1.0;
	} else if (x <= 1.45e-98) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.7e-10:
		tmp = 1.0
	elif x <= 1.45e-98:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.7e-10)
		tmp = 1.0;
	elseif (x <= 1.45e-98)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.7e-10)
		tmp = 1.0;
	elseif (x <= 1.45e-98)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.7e-10], 1.0, If[LessEqual[x, 1.45e-98], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e-10 or 1.45e-98 < x

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around inf 74.5%

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

   if -2.7e-10 < x < 1.45e-98

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in x around 0 52.7%

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

Alternative 12: 54.2% 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 88.1%

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

   1. *-commutative 88.1%

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

3. Simplified 88.1%

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

5. Taylor expanded in x around inf 46.6%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 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 2024180 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1)))

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