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

Percentage Accurate: 89.3% → 98.8%

Time: 13.3s

Alternatives: 13

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: 89.3% 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: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+61} \lor \neg \left(t_1 \leq 2 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (or (<= t_1 -1e+61) (not (<= t_1 2e+17)))
     (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= -1e+61) || !(t_1 <= 2e+17)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if ((t_1 <= (-1d+61)) .or. (.not. (t_1 <= 2d+17))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= -1e+61) || !(t_1 <= 2e+17)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if (t_1 <= -1e+61) or not (t_1 <= 2e+17):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if ((t_1 <= -1e+61) || !(t_1 <= 2e+17))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if ((t_1 <= -1e+61) || ~((t_1 <= 2e+17)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+61], N[Not[LessEqual[t$95$1, 2e+17]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -9.99999999999999949e60 or 2e17 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 73.7%

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

      1. *-commutative 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in y around inf 73.7%

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

      1. associate-/l* 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in t around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. unsub-neg 99.9%

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

   9. Simplified 99.9%

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

   if -9.99999999999999949e60 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 2e17

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -1 \cdot 10^{+61} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 2: 96.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := z \cdot t - x\\ \mathsf{fma}\left(\frac{y}{x + 1}, \frac{z}{t_2}, t_1\right) - \frac{t_1}{t_2} \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))) (t_2 (- (* z t) x)))
   (- (fma (/ y (+ x 1.0)) (/ z t_2) t_1) (/ t_1 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = (z * t) - x;
	return fma((y / (x + 1.0)), (z / t_2), t_1) - (t_1 / t_2);
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	t_2 = Float64(Float64(z * t) - x)
	return Float64(fma(Float64(y / Float64(x + 1.0)), Float64(z / t_2), t_1) - Float64(t_1 / t_2))
end

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. *-commutative 92.2%

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

3. Simplified 92.2%

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

4. Taylor expanded in y around 0 92.2%

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

   1. +-commutative 92.2%

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

   2. times-frac 98.4%

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

   3. fma-def 98.4%

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

   4. +-commutative 98.4%

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

   5. +-commutative 98.4%

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

   6. associate-/r* 98.4%

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

   7. +-commutative 98.4%

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

6. Simplified 98.4%

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

7. Final simplification 98.4%

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

Alternative 3: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-208}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-83}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.35e-49)
     t_1
     (if (<= t 3.2e-208)
       (- 1.0 (* (/ y x) (/ z (+ x 1.0))))
       (if (<= t 1.12e-175)
         (* (/ y (+ x 1.0)) (/ z (- (* z t) x)))
         (if (<= t 4.1e-83) (- 1.0 (/ (* z (/ y x)) (+ x 1.0))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.35e-49) {
		tmp = t_1;
	} else if (t <= 3.2e-208) {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	} else if (t <= 1.12e-175) {
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	} else if (t <= 4.1e-83) {
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.35d-49)) then
        tmp = t_1
    else if (t <= 3.2d-208) then
        tmp = 1.0d0 - ((y / x) * (z / (x + 1.0d0)))
    else if (t <= 1.12d-175) then
        tmp = (y / (x + 1.0d0)) * (z / ((z * t) - x))
    else if (t <= 4.1d-83) then
        tmp = 1.0d0 - ((z * (y / x)) / (x + 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.35e-49) {
		tmp = t_1;
	} else if (t <= 3.2e-208) {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	} else if (t <= 1.12e-175) {
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	} else if (t <= 4.1e-83) {
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -1.35e-49:
		tmp = t_1
	elif t <= 3.2e-208:
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)))
	elif t <= 1.12e-175:
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x))
	elif t <= 4.1e-83:
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1.35e-49)
		tmp = t_1;
	elseif (t <= 3.2e-208)
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / Float64(x + 1.0))));
	elseif (t <= 1.12e-175)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / Float64(Float64(z * t) - x)));
	elseif (t <= 4.1e-83)
		tmp = Float64(1.0 - Float64(Float64(z * Float64(y / x)) / Float64(x + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1.35e-49)
		tmp = t_1;
	elseif (t <= 3.2e-208)
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	elseif (t <= 1.12e-175)
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	elseif (t <= 4.1e-83)
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e-49], t$95$1, If[LessEqual[t, 3.2e-208], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e-175], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e-83], N[(1.0 - N[(N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.35e-49 or 4.1e-83 < t

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around inf 88.6%

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

   if -1.35e-49 < t < 3.2000000000000001e-208

   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. Taylor expanded in t around 0 85.6%

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

      1. associate-+r+ 85.6%

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

      2. mul-1-neg 85.6%

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

      3. unsub-neg 85.6%

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

      4. +-commutative 85.6%

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

      5. associate-/l* 85.6%

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

      6. +-commutative 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in y around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. sub-neg 85.6%

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

      3. times-frac 77.3%

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

      4. +-commutative 77.3%

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

   9. Simplified 77.3%

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

   if 3.2000000000000001e-208 < t < 1.1200000000000001e-175

   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. Taylor expanded in y around inf 82.6%

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

      1. associate-/l* 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in y around inf 82.5%

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

      1. times-frac 82.4%

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

      2. +-commutative 82.4%

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

      3. *-commutative 82.4%

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

   9. Simplified 82.4%

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

   if 1.1200000000000001e-175 < t < 4.1e-83

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around 0 88.2%

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

      1. associate-+r+ 88.2%

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

      2. mul-1-neg 88.2%

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

      3. unsub-neg 88.2%

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

      4. +-commutative 88.2%

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

      5. associate-/l* 94.0%

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

      6. +-commutative 94.0%

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

   6. Simplified 94.0%

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

      1. div-sub 94.0%

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

      2. pow1 94.0%

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

      3. pow1 94.0%

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

      4. pow-div 94.0%

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

      5. metadata-eval 94.0%

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

      6. metadata-eval 94.0%

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

      7. associate-/r/ 83.1%

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

   8. Applied egg-rr 83.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-49}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-208}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-83}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 4: 81.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-208}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-191}:\\ \;\;\;\;\frac{y \cdot z}{\left(x + 1\right) \cdot \left(z \cdot t - x\right)}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-87}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.7e-49)
     t_1
     (if (<= t 8e-208)
       (- 1.0 (* (/ y x) (/ z (+ x 1.0))))
       (if (<= t 2.65e-191)
         (/ (* y z) (* (+ x 1.0) (- (* z t) x)))
         (if (<= t 1.7e-87) (- 1.0 (/ (* z (/ y x)) (+ x 1.0))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.7e-49) {
		tmp = t_1;
	} else if (t <= 8e-208) {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	} else if (t <= 2.65e-191) {
		tmp = (y * z) / ((x + 1.0) * ((z * t) - x));
	} else if (t <= 1.7e-87) {
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.7d-49)) then
        tmp = t_1
    else if (t <= 8d-208) then
        tmp = 1.0d0 - ((y / x) * (z / (x + 1.0d0)))
    else if (t <= 2.65d-191) then
        tmp = (y * z) / ((x + 1.0d0) * ((z * t) - x))
    else if (t <= 1.7d-87) then
        tmp = 1.0d0 - ((z * (y / x)) / (x + 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.7e-49) {
		tmp = t_1;
	} else if (t <= 8e-208) {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	} else if (t <= 2.65e-191) {
		tmp = (y * z) / ((x + 1.0) * ((z * t) - x));
	} else if (t <= 1.7e-87) {
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -1.7e-49:
		tmp = t_1
	elif t <= 8e-208:
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)))
	elif t <= 2.65e-191:
		tmp = (y * z) / ((x + 1.0) * ((z * t) - x))
	elif t <= 1.7e-87:
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1.7e-49)
		tmp = t_1;
	elseif (t <= 8e-208)
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / Float64(x + 1.0))));
	elseif (t <= 2.65e-191)
		tmp = Float64(Float64(y * z) / Float64(Float64(x + 1.0) * Float64(Float64(z * t) - x)));
	elseif (t <= 1.7e-87)
		tmp = Float64(1.0 - Float64(Float64(z * Float64(y / x)) / Float64(x + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1.7e-49)
		tmp = t_1;
	elseif (t <= 8e-208)
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	elseif (t <= 2.65e-191)
		tmp = (y * z) / ((x + 1.0) * ((z * t) - x));
	elseif (t <= 1.7e-87)
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-49], t$95$1, If[LessEqual[t, 8e-208], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e-191], N[(N[(y * z), $MachinePrecision] / N[(N[(x + 1.0), $MachinePrecision] * N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-87], N[(1.0 - N[(N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.70000000000000002e-49 or 1.6999999999999999e-87 < t

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around inf 88.6%

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

   if -1.70000000000000002e-49 < t < 8.0000000000000008e-208

   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. Taylor expanded in t around 0 85.6%

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

      1. associate-+r+ 85.6%

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

      2. mul-1-neg 85.6%

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

      3. unsub-neg 85.6%

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

      4. +-commutative 85.6%

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

      5. associate-/l* 85.6%

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

      6. +-commutative 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in y around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. sub-neg 85.6%

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

      3. times-frac 77.3%

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

      4. +-commutative 77.3%

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

   9. Simplified 77.3%

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

   if 8.0000000000000008e-208 < t < 2.64999999999999993e-191

   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. Taylor expanded in y around inf 90.6%

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

      1. *-commutative 90.6%

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

      2. +-commutative 90.6%

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

   6. Simplified 90.6%

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

   if 2.64999999999999993e-191 < t < 1.6999999999999999e-87

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in t around 0 78.9%

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

      1. associate-+r+ 78.9%

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

      2. mul-1-neg 78.9%

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

      3. unsub-neg 78.9%

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

      4. +-commutative 78.9%

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

      5. associate-/l* 89.4%

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

      6. +-commutative 89.4%

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

   6. Simplified 89.4%

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

      1. div-sub 89.4%

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

      2. pow1 89.4%

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

      3. pow1 89.4%

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

      4. pow-div 89.4%

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

      5. metadata-eval 89.4%

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

      6. metadata-eval 89.4%

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

      7. associate-/r/ 79.6%

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

   8. Applied egg-rr 79.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-208}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-191}:\\ \;\;\;\;\frac{y \cdot z}{\left(x + 1\right) \cdot \left(z \cdot t - x\right)}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-87}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 5: 81.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-49} \lor \neg \left(t \leq 1.05 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.35e-49) (not (<= t 1.05e-88)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* (/ y x) (/ z (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e-49) || !(t <= 1.05e-88)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.35d-49)) .or. (.not. (t <= 1.05d-88))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y / x) * (z / (x + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e-49) || !(t <= 1.05e-88)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.35e-49) or not (t <= 1.05e-88):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.35e-49) || !(t <= 1.05e-88))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.35e-49) || ~((t <= 1.05e-88)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.35e-49], N[Not[LessEqual[t, 1.05e-88]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e-49 or 1.05e-88 < t

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around inf 88.6%

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

   if -1.35e-49 < t < 1.05e-88

   1. Initial program 97.7%

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

      1. *-commutative 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around 0 81.3%

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

      1. associate-+r+ 81.3%

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

      2. mul-1-neg 81.3%

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

      3. unsub-neg 81.3%

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

      4. +-commutative 81.3%

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

      5. associate-/l* 83.3%

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

      6. +-commutative 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. sub-neg 81.3%

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

      3. times-frac 74.5%

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

      4. +-commutative 74.5%

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

   9. Simplified 74.5%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-49} \lor \neg \left(t \leq 1.05 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \]

Alternative 6: 59.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-119}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{x}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+32}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= t -1.9e+106)
     t_1
     (if (<= t -3.5e-119)
       1.0
       (if (<= t -8.2e-158) (/ (* y (- z)) x) (if (<= t 2e+32) 1.0 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (t <= -1.9e+106) {
		tmp = t_1;
	} else if (t <= -3.5e-119) {
		tmp = 1.0;
	} else if (t <= -8.2e-158) {
		tmp = (y * -z) / x;
	} else if (t <= 2e+32) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (t <= (-1.9d+106)) then
        tmp = t_1
    else if (t <= (-3.5d-119)) then
        tmp = 1.0d0
    else if (t <= (-8.2d-158)) then
        tmp = (y * -z) / x
    else if (t <= 2d+32) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (t <= -1.9e+106) {
		tmp = t_1;
	} else if (t <= -3.5e-119) {
		tmp = 1.0;
	} else if (t <= -8.2e-158) {
		tmp = (y * -z) / x;
	} else if (t <= 2e+32) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if t <= -1.9e+106:
		tmp = t_1
	elif t <= -3.5e-119:
		tmp = 1.0
	elif t <= -8.2e-158:
		tmp = (y * -z) / x
	elif t <= 2e+32:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1.9e+106)
		tmp = t_1;
	elseif (t <= -3.5e-119)
		tmp = 1.0;
	elseif (t <= -8.2e-158)
		tmp = Float64(Float64(y * Float64(-z)) / x);
	elseif (t <= 2e+32)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (t <= -1.9e+106)
		tmp = t_1;
	elseif (t <= -3.5e-119)
		tmp = 1.0;
	elseif (t <= -8.2e-158)
		tmp = (y * -z) / x;
	elseif (t <= 2e+32)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+106], t$95$1, If[LessEqual[t, -3.5e-119], 1.0, If[LessEqual[t, -8.2e-158], N[(N[(y * (-z)), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[t, 2e+32], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8999999999999999e106 or 2.00000000000000011e32 < t

   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. Taylor expanded in t around inf 74.8%

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

      1. +-commutative 74.8%

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

   6. Simplified 74.8%

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

   if -1.8999999999999999e106 < t < -3.5e-119 or -8.20000000000000008e-158 < t < 2.00000000000000011e32

   1. Initial program 94.6%

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

      1. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around inf 81.9%

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

      1. associate-/l* 86.7%

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

   6. Simplified 86.7%

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

   7. Taylor expanded in x around inf 54.3%

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

   if -3.5e-119 < t < -8.20000000000000008e-158

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 89.7%

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

      1. associate-+r+ 89.7%

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

      2. mul-1-neg 89.7%

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

      3. unsub-neg 89.7%

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

      4. +-commutative 89.7%

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

      5. associate-/l* 89.7%

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

      6. +-commutative 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in x around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. associate-*r* 70.6%

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

      3. mul-1-neg 70.6%

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

   9. Simplified 70.6%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-119}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{x}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+32}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 7: 77.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-101} \lor \neg \left(t \leq 6.3 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z}{\frac{x}{t - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.35e-101) (not (<= t 6.3e-87)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (/ z (/ x (- t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.35e-101) || !(t <= 6.3e-87)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (z / (x / (t - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.35d-101)) .or. (.not. (t <= 6.3d-87))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + (z / (x / (t - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.35e-101) || !(t <= 6.3e-87)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (z / (x / (t - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.35e-101) or not (t <= 6.3e-87):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (z / (x / (t - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.35e-101) || !(t <= 6.3e-87))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(z / Float64(x / Float64(t - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.35e-101) || ~((t <= 6.3e-87)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (z / (x / (t - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.35e-101], N[Not[LessEqual[t, 6.3e-87]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z / N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.35e-101 or 6.29999999999999976e-87 < t

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in z around inf 86.4%

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

   if -2.35e-101 < t < 6.29999999999999976e-87

   1. Initial program 97.5%

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

      1. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 76.0%

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

   5. Taylor expanded in x around 0 74.4%

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

      1. associate-/l* 66.2%

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

      2. mul-1-neg 66.2%

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

      3. sub-neg 66.2%

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

   7. Simplified 66.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-101} \lor \neg \left(t \leq 6.3 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z}{\frac{x}{t - y}}\\ \end{array} \]

Alternative 8: 88.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x + (y / (t - (x / z)))) / (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 + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. *-commutative 92.2%

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

3. Simplified 92.2%

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

4. Taylor expanded in y around inf 84.3%

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

   1. associate-/l* 90.5%

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

6. Simplified 90.5%

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

7. Taylor expanded in t around 0 92.0%

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

   1. neg-mul-1 92.0%

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

   2. unsub-neg 92.0%

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

9. Simplified 92.0%

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

10. Final simplification 92.0%

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

Alternative 9: 68.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-42}:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.8) (/ x (+ x 1.0)) (if (<= x 9e-42) (/ y (* (+ x 1.0) t)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8) {
		tmp = x / (x + 1.0);
	} else if (x <= 9e-42) {
		tmp = y / ((x + 1.0) * t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 9d-42) then
        tmp = y / ((x + 1.0d0) * t)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8) {
		tmp = x / (x + 1.0);
	} else if (x <= 9e-42) {
		tmp = y / ((x + 1.0) * t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.8:
		tmp = x / (x + 1.0)
	elif x <= 9e-42:
		tmp = y / ((x + 1.0) * t)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 9e-42)
		tmp = Float64(y / Float64(Float64(x + 1.0) * t));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = x / (x + 1.0);
	elseif (x <= 9e-42)
		tmp = y / ((x + 1.0) * t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.8], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-42], N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 93.2%

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

      1. +-commutative 93.2%

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

   6. Simplified 93.2%

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

   if -3.7999999999999998 < x < 9e-42

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around inf 66.1%

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

      1. *-commutative 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in y around inf 53.1%

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

      1. +-commutative 53.1%

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

   9. Simplified 53.1%

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

   if 9e-42 < x

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around inf 84.0%

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

      1. associate-/l* 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in x around inf 84.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-42}:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 61.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+106} \lor \neg \left(t \leq 8.6 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.9e+106) (not (<= t 8.6e+31))) (/ x (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.9e+106) || !(t <= 8.6e+31)) {
		tmp = x / (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 ((t <= (-1.9d+106)) .or. (.not. (t <= 8.6d+31))) then
        tmp = x / (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 ((t <= -1.9e+106) || !(t <= 8.6e+31)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.9e+106) or not (t <= 8.6e+31):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.9e+106) || !(t <= 8.6e+31))
		tmp = Float64(x / 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 ((t <= -1.9e+106) || ~((t <= 8.6e+31)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.9e+106], N[Not[LessEqual[t, 8.6e+31]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < -1.8999999999999999e106 or 8.59999999999999978e31 < t

   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. Taylor expanded in t around inf 74.8%

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

      1. +-commutative 74.8%

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

   6. Simplified 74.8%

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

   if -1.8999999999999999e106 < t < 8.59999999999999978e31

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around inf 83.1%

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

      1. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in x around inf 52.3%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+106} \lor \neg \left(t \leq 8.6 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 55.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-200}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.000105:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2e-200) 1.0 (if (<= x 0.000105) (* x (- 1.0 x)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2e-200) {
		tmp = 1.0;
	} else if (x <= 0.000105) {
		tmp = x * (1.0 - 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 <= (-2d-200)) then
        tmp = 1.0d0
    else if (x <= 0.000105d0) then
        tmp = x * (1.0d0 - 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 <= -2e-200) {
		tmp = 1.0;
	} else if (x <= 0.000105) {
		tmp = x * (1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2e-200:
		tmp = 1.0
	elif x <= 0.000105:
		tmp = x * (1.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2e-200)
		tmp = 1.0;
	elseif (x <= 0.000105)
		tmp = Float64(x * Float64(1.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2e-200)
		tmp = 1.0;
	elseif (x <= 0.000105)
		tmp = x * (1.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2e-200], 1.0, If[LessEqual[x, 0.000105], N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2e-200 or 1.05e-4 < x

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around inf 85.9%

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

      1. associate-/l* 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in x around inf 77.6%

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

   if -2e-200 < x < 1.05e-4

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around inf 24.2%

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

      1. +-commutative 24.2%

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

   6. Simplified 24.2%

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

      1. div-inv 24.2%

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

   8. Applied egg-rr 24.2%

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

   9. Taylor expanded in x around 0 24.0%

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

       1. neg-mul-1 24.0%

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

       2. unsub-neg 24.0%

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

   11. Simplified 24.0%

       \[\leadsto x \cdot \color{blue}{\left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-200}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.000105:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12: 55.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-199}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.45e-199) 1.0 (if (<= x 1.65e-39) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e-199) {
		tmp = 1.0;
	} else if (x <= 1.65e-39) {
		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 <= (-1.45d-199)) then
        tmp = 1.0d0
    else if (x <= 1.65d-39) 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 <= -1.45e-199) {
		tmp = 1.0;
	} else if (x <= 1.65e-39) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.45e-199:
		tmp = 1.0
	elif x <= 1.65e-39:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.45e-199)
		tmp = 1.0;
	elseif (x <= 1.65e-39)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.45e-199)
		tmp = 1.0;
	elseif (x <= 1.65e-39)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.45e-199], 1.0, If[LessEqual[x, 1.65e-39], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e-199 or 1.64999999999999992e-39 < x

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in y around inf 84.5%

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

      1. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

   7. Taylor expanded in x around inf 75.0%

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

   if -1.45e-199 < x < 1.64999999999999992e-39

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in t around inf 22.2%

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

      1. +-commutative 22.2%

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

   6. Simplified 22.2%

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

   7. Taylor expanded in x around 0 22.2%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-199}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 53.7% 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 92.2%

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

   1. *-commutative 92.2%

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

3. Simplified 92.2%

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

4. Taylor expanded in y around inf 84.3%

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

   1. associate-/l* 90.5%

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

6. Simplified 90.5%

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

7. Taylor expanded in x around inf 52.0%

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

8. Final simplification 52.0%

   \[\leadsto 1 \]

Developer target: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023322 
(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)))