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

Percentage Accurate: 89.2% → 96.6%

Time: 13.9s

Alternatives: 11

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+164}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 10^{+246}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\ \end{array} \end{array} \]

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 -1e+164)
     (* (/ y (+ x 1.0)) (/ z t_1))
     (if (<= t_2 1e+246)
       t_2
       (-
        (+ (/ y (* t (+ x 1.0))) (/ x (+ x 1.0)))
        (/ x (* t (* z (+ x 1.0)))))))))

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 <= -1e+164) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 1e+246) {
		tmp = t_2;
	} else {
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / (t * (z * (x + 1.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: 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 <= (-1d+164)) then
        tmp = (y / (x + 1.0d0)) * (z / t_1)
    else if (t_2 <= 1d+246) then
        tmp = t_2
    else
        tmp = ((y / (t * (x + 1.0d0))) + (x / (x + 1.0d0))) - (x / (t * (z * (x + 1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+164) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 1e+246) {
		tmp = t_2;
	} else {
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / (t * (z * (x + 1.0))));
	}
	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 <= -1e+164:
		tmp = (y / (x + 1.0)) * (z / t_1)
	elif t_2 <= 1e+246:
		tmp = t_2
	else:
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / (t * (z * (x + 1.0))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e+164)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / t_1));
	elseif (t_2 <= 1e+246)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / Float64(t * Float64(x + 1.0))) + Float64(x / Float64(x + 1.0))) - Float64(x / Float64(t * Float64(z * Float64(x + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e+164)
		tmp = (y / (x + 1.0)) * (z / t_1);
	elseif (t_2 <= 1e+246)
		tmp = t_2;
	else
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / (t * (z * (x + 1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+164], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+246], t$95$2, N[(N[(N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(t * N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -1e164

   1. Initial program 65.2%

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

      1. *-commutative 65.2%

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

   3. Simplified 65.2%

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

      1. div-inv 65.2%

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

      2. fma-neg 65.2%

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

   6. Applied egg-rr 65.2%

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

   7. Taylor expanded in y around inf 64.5%

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

      1. times-frac 90.2%

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

      2. +-commutative 90.2%

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

   9. Simplified 90.2%

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

   if -1e164 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.00000000000000007e246

   1. Initial program 99.9%

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

   if 1.00000000000000007e246 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 18.2%

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

      1. *-commutative 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in t around inf 89.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -1 \cdot 10^{+164}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 10^{+246}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+164}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 10^{+246}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

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 -1e+164)
     (* (/ y (+ x 1.0)) (/ z t_1))
     (if (<= t_2 1e+246) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))

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 <= -1e+164) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 1e+246) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-1d+164)) then
        tmp = (y / (x + 1.0d0)) * (z / t_1)
    else if (t_2 <= 1d+246) then
        tmp = t_2
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+164) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 1e+246) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	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 <= -1e+164:
		tmp = (y / (x + 1.0)) * (z / t_1)
	elif t_2 <= 1e+246:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e+164)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / t_1));
	elseif (t_2 <= 1e+246)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e+164)
		tmp = (y / (x + 1.0)) * (z / t_1);
	elseif (t_2 <= 1e+246)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(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, -1e+164], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+246], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -1e164

   1. Initial program 65.2%

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

      1. *-commutative 65.2%

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

   3. Simplified 65.2%

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

      1. div-inv 65.2%

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

      2. fma-neg 65.2%

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

   6. Applied egg-rr 65.2%

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

   7. Taylor expanded in y around inf 64.5%

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

      1. times-frac 90.2%

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

      2. +-commutative 90.2%

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

   9. Simplified 90.2%

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

   if -1e164 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.00000000000000007e246

   1. Initial program 99.9%

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

   if 1.00000000000000007e246 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 18.2%

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

      1. *-commutative 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in z around inf 85.4%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -1 \cdot 10^{+164}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 10^{+246}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+270}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-58} \lor \neg \left(y \leq 8 \cdot 10^{-189}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t\_1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (<= y -1.6e+270)
     (* (/ y (+ x 1.0)) (/ z t_1))
     (if (or (<= y -5.6e-58) (not (<= y 8e-189)))
       (/ (+ x (/ (* y z) t_1)) (+ x 1.0))
       (/ (- x (/ x t_1)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (y <= -1.6e+270) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if ((y <= -5.6e-58) || !(y <= 8e-189)) {
		tmp = (x + ((y * z) / t_1)) / (x + 1.0);
	} else {
		tmp = (x - (x / t_1)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * t) - x
    if (y <= (-1.6d+270)) then
        tmp = (y / (x + 1.0d0)) * (z / t_1)
    else if ((y <= (-5.6d-58)) .or. (.not. (y <= 8d-189))) then
        tmp = (x + ((y * z) / t_1)) / (x + 1.0d0)
    else
        tmp = (x - (x / t_1)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (y <= -1.6e+270) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if ((y <= -5.6e-58) || !(y <= 8e-189)) {
		tmp = (x + ((y * z) / t_1)) / (x + 1.0);
	} else {
		tmp = (x - (x / t_1)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if y <= -1.6e+270:
		tmp = (y / (x + 1.0)) * (z / t_1)
	elif (y <= -5.6e-58) or not (y <= 8e-189):
		tmp = (x + ((y * z) / t_1)) / (x + 1.0)
	else:
		tmp = (x - (x / t_1)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (y <= -1.6e+270)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / t_1));
	elseif ((y <= -5.6e-58) || !(y <= 8e-189))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t_1)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if (y <= -1.6e+270)
		tmp = (y / (x + 1.0)) * (z / t_1);
	elseif ((y <= -5.6e-58) || ~((y <= 8e-189)))
		tmp = (x + ((y * z) / t_1)) / (x + 1.0);
	else
		tmp = (x - (x / t_1)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[y, -1.6e+270], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.6e-58], N[Not[LessEqual[y, 8e-189]], $MachinePrecision]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6000000000000001e270

   1. Initial program 53.0%

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

      1. *-commutative 53.0%

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

   3. Simplified 53.0%

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

      1. div-inv 53.3%

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

      2. fma-neg 53.3%

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

   6. Applied egg-rr 53.3%

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

   7. Taylor expanded in y around inf 43.9%

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

      1. times-frac 91.3%

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

      2. +-commutative 91.3%

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

   9. Simplified 91.3%

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

   if -1.6000000000000001e270 < y < -5.6000000000000001e-58 or 8.00000000000000055e-189 < y

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in y around inf 83.4%

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

   if -5.6000000000000001e-58 < y < 8.00000000000000055e-189

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+270}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-58} \lor \neg \left(y \leq 8 \cdot 10^{-189}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-119}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.4e-84)
   (/ x (+ x 1.0))
   (if (<= x 1.22e-119)
     (/ y t)
     (if (<= x 1.55e-42) (* x (+ 1.0 (/ -1.0 (* z t)))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.4e-84) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.22e-119) {
		tmp = y / t;
	} else if (x <= 1.55e-42) {
		tmp = x * (1.0 + (-1.0 / (z * 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 <= (-3.4d-84)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 1.22d-119) then
        tmp = y / t
    else if (x <= 1.55d-42) then
        tmp = x * (1.0d0 + ((-1.0d0) / (z * 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 <= -3.4e-84) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.22e-119) {
		tmp = y / t;
	} else if (x <= 1.55e-42) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.4e-84:
		tmp = x / (x + 1.0)
	elif x <= 1.22e-119:
		tmp = y / t
	elif x <= 1.55e-42:
		tmp = x * (1.0 + (-1.0 / (z * t)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.4e-84)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 1.22e-119)
		tmp = Float64(y / t);
	elseif (x <= 1.55e-42)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.4e-84)
		tmp = x / (x + 1.0);
	elseif (x <= 1.22e-119)
		tmp = y / t;
	elseif (x <= 1.55e-42)
		tmp = x * (1.0 + (-1.0 / (z * t)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.4e-84], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e-119], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.55e-42], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.40000000000000021e-84

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in t around inf 81.3%

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

      1. +-commutative 81.3%

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

   7. Simplified 81.3%

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

   if -3.40000000000000021e-84 < x < 1.22e-119

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

   3. Simplified 90.5%

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

      1. div-inv 90.4%

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

      2. fma-neg 90.4%

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

   6. Applied egg-rr 90.4%

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

      1. clear-num 90.3%

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

      2. inv-pow 90.3%

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

      3. fma-neg 90.3%

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

      4. un-div-inv 90.4%

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

   8. Applied egg-rr 90.4%

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

   9. Taylor expanded in x around 0 54.7%

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

   if 1.22e-119 < x < 1.5500000000000001e-42

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around 0 60.1%

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

   6. Taylor expanded in x around 0 61.3%

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

   7. Taylor expanded in x around 0 61.4%

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

   if 1.5500000000000001e-42 < x

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in z around inf 75.4%

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

   6. Taylor expanded in x around inf 80.5%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-119}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-117}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.35e-71)
   1.0
   (if (<= x 2e-117)
     (/ y t)
     (if (<= x 6.8e-44) x (if (<= x 1.65e-31) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-71) {
		tmp = 1.0;
	} else if (x <= 2e-117) {
		tmp = y / t;
	} else if (x <= 6.8e-44) {
		tmp = x;
	} else if (x <= 1.65e-31) {
		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 <= (-1.35d-71)) then
        tmp = 1.0d0
    else if (x <= 2d-117) then
        tmp = y / t
    else if (x <= 6.8d-44) then
        tmp = x
    else if (x <= 1.65d-31) 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 <= -1.35e-71) {
		tmp = 1.0;
	} else if (x <= 2e-117) {
		tmp = y / t;
	} else if (x <= 6.8e-44) {
		tmp = x;
	} else if (x <= 1.65e-31) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e-71:
		tmp = 1.0
	elif x <= 2e-117:
		tmp = y / t
	elif x <= 6.8e-44:
		tmp = x
	elif x <= 1.65e-31:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e-71)
		tmp = 1.0;
	elseif (x <= 2e-117)
		tmp = Float64(y / t);
	elseif (x <= 6.8e-44)
		tmp = x;
	elseif (x <= 1.65e-31)
		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 <= -1.35e-71)
		tmp = 1.0;
	elseif (x <= 2e-117)
		tmp = y / t;
	elseif (x <= 6.8e-44)
		tmp = x;
	elseif (x <= 1.65e-31)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.35e-71], 1.0, If[LessEqual[x, 2e-117], N[(y / t), $MachinePrecision], If[LessEqual[x, 6.8e-44], x, If[LessEqual[x, 1.65e-31], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3500000000000001e-71 or 1.65e-31 < 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 z around inf 74.4%

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

   6. Taylor expanded in x around inf 82.3%

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

   if -1.3500000000000001e-71 < x < 2.00000000000000006e-117 or 6.80000000000000033e-44 < x < 1.65e-31

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

      1. div-inv 90.3%

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

      2. fma-neg 90.3%

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

   6. Applied egg-rr 90.3%

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

      1. clear-num 90.3%

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

      2. inv-pow 90.3%

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

      3. fma-neg 90.3%

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

      4. un-div-inv 90.3%

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

   8. Applied egg-rr 90.3%

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

   9. Taylor expanded in x around 0 53.4%

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

   if 2.00000000000000006e-117 < x < 6.80000000000000033e-44

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around inf 56.1%

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

      1. +-commutative 56.1%

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

   7. Simplified 56.1%

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

   8. Taylor expanded in x around 0 56.1%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-117}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-117}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.8e-84)
   (/ x (+ x 1.0))
   (if (<= x 4.6e-117)
     (/ y t)
     (if (<= x 6.6e-43) x (if (<= x 4.2e-30) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-84) {
		tmp = x / (x + 1.0);
	} else if (x <= 4.6e-117) {
		tmp = y / t;
	} else if (x <= 6.6e-43) {
		tmp = x;
	} else if (x <= 4.2e-30) {
		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 <= (-1.8d-84)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 4.6d-117) then
        tmp = y / t
    else if (x <= 6.6d-43) then
        tmp = x
    else if (x <= 4.2d-30) 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 <= -1.8e-84) {
		tmp = x / (x + 1.0);
	} else if (x <= 4.6e-117) {
		tmp = y / t;
	} else if (x <= 6.6e-43) {
		tmp = x;
	} else if (x <= 4.2e-30) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8e-84:
		tmp = x / (x + 1.0)
	elif x <= 4.6e-117:
		tmp = y / t
	elif x <= 6.6e-43:
		tmp = x
	elif x <= 4.2e-30:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8e-84)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 4.6e-117)
		tmp = Float64(y / t);
	elseif (x <= 6.6e-43)
		tmp = x;
	elseif (x <= 4.2e-30)
		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 <= -1.8e-84)
		tmp = x / (x + 1.0);
	elseif (x <= 4.6e-117)
		tmp = y / t;
	elseif (x <= 6.6e-43)
		tmp = x;
	elseif (x <= 4.2e-30)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e-84], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-117], N[(y / t), $MachinePrecision], If[LessEqual[x, 6.6e-43], x, If[LessEqual[x, 4.2e-30], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.80000000000000002e-84

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in t around inf 81.3%

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

      1. +-commutative 81.3%

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

   7. Simplified 81.3%

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

   if -1.80000000000000002e-84 < x < 4.59999999999999989e-117 or 6.60000000000000031e-43 < x < 4.2000000000000004e-30

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

   3. Simplified 90.0%

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

      1. div-inv 90.0%

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

      2. fma-neg 90.0%

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

   6. Applied egg-rr 90.0%

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

      1. clear-num 90.0%

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

      2. inv-pow 90.0%

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

      3. fma-neg 90.0%

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

      4. un-div-inv 90.0%

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

   8. Applied egg-rr 90.0%

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

   9. Taylor expanded in x around 0 55.1%

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

   if 4.59999999999999989e-117 < x < 6.60000000000000031e-43

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around inf 56.1%

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

      1. +-commutative 56.1%

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

   7. Simplified 56.1%

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

   8. Taylor expanded in x around 0 56.1%

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

   if 4.2000000000000004e-30 < x

   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 z around inf 76.2%

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

   6. Taylor expanded in x around inf 82.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-117}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-18} \lor \neg \left(z \leq 5.8 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.4e-18) (not (<= z 5.8e-150)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e-18) || !(z <= 5.8e-150)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.4d-18)) .or. (.not. (z <= 5.8d-150))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e-18) || !(z <= 5.8e-150)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.4e-18) or not (z <= 5.8e-150):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.4e-18) || !(z <= 5.8e-150))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.4e-18) || ~((z <= 5.8e-150)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.4e-18], N[Not[LessEqual[z, 5.8e-150]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999994e-18 or 5.7999999999999996e-150 < z

   1. Initial program 83.4%

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

      1. *-commutative 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in z around inf 84.3%

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

   if -2.39999999999999994e-18 < z < 5.7999999999999996e-150

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 83.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-18} \lor \neg \left(z \leq 5.8 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -13000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -13000000.0)
   1.0
   (if (<= x 5.5e-29) (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -13000000.0) {
		tmp = 1.0;
	} else if (x <= 5.5e-29) {
		tmp = (x + ((y - (x / z)) / 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 <= (-13000000.0d0)) then
        tmp = 1.0d0
    else if (x <= 5.5d-29) then
        tmp = (x + ((y - (x / z)) / 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 <= -13000000.0) {
		tmp = 1.0;
	} else if (x <= 5.5e-29) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -13000000.0:
		tmp = 1.0
	elif x <= 5.5e-29:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -13000000.0)
		tmp = 1.0;
	elseif (x <= 5.5e-29)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / 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 <= -13000000.0)
		tmp = 1.0;
	elseif (x <= 5.5e-29)
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -13000000.0], 1.0, If[LessEqual[x, 5.5e-29], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e7 or 5.4999999999999999e-29 < 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 z around inf 75.2%

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

   6. Taylor expanded in x around inf 85.9%

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

   if -1.3e7 < x < 5.4999999999999999e-29

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in t around inf 67.9%

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

   6. Taylor expanded in y around 0 75.7%

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

      1. +-commutative 75.7%

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

      2. mul-1-neg 75.7%

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

      3. sub-neg 75.7%

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

      4. *-commutative 75.7%

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

      5. associate-/r* 76.7%

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

      6. div-sub 76.7%

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

   8. Simplified 76.7%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -13000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-17} \lor \neg \left(z \leq 7.2 \cdot 10^{-152}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3e-17) (not (<= z 7.2e-152))) (/ (+ x (/ y t)) (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e-17) || !(z <= 7.2e-152)) {
		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 ((z <= (-3d-17)) .or. (.not. (z <= 7.2d-152))) 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 ((z <= -3e-17) || !(z <= 7.2e-152)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3e-17) or not (z <= 7.2e-152):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3e-17) || !(z <= 7.2e-152))
		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 ((z <= -3e-17) || ~((z <= 7.2e-152)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3e-17], N[Not[LessEqual[z, 7.2e-152]], $MachinePrecision]], 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 z < -3.00000000000000006e-17 or 7.2e-152 < z

   1. Initial program 83.4%

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

      1. *-commutative 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in z around inf 84.3%

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

   if -3.00000000000000006e-17 < z < 7.2e-152

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 53.4%

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

   6. Taylor expanded in x around inf 71.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-17} \lor \neg \left(z \leq 7.2 \cdot 10^{-152}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-210}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4e-210) 1.0 (if (<= x 1.9e-42) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e-210) {
		tmp = 1.0;
	} else if (x <= 1.9e-42) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4d-210)) then
        tmp = 1.0d0
    else if (x <= 1.9d-42) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e-210) {
		tmp = 1.0;
	} else if (x <= 1.9e-42) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4e-210:
		tmp = 1.0
	elif x <= 1.9e-42:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4e-210)
		tmp = 1.0;
	elseif (x <= 1.9e-42)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4e-210)
		tmp = 1.0;
	elseif (x <= 1.9e-42)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4e-210], 1.0, If[LessEqual[x, 1.9e-42], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0000000000000002e-210 or 1.90000000000000009e-42 < x

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around inf 72.2%

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

   6. Taylor expanded in x around inf 72.6%

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

   if -4.0000000000000002e-210 < x < 1.90000000000000009e-42

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in t around inf 24.7%

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

      1. +-commutative 24.7%

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

   7. Simplified 24.7%

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

   8. Taylor expanded in x around 0 24.7%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-210}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 90.1%

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

   1. *-commutative 90.1%

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

3. Simplified 90.1%

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

5. Taylor expanded in z around inf 71.8%

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

6. Taylor expanded in x around inf 55.6%

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

7. Final simplification 55.6%

   \[\leadsto 1 \]
8. 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 2024027 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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