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

Percentage Accurate: 89.0% → 98.5%

Time: 13.4s

Alternatives: 12

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+47} \lor \neg \left(z \leq 6 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e+47) (not (<= z 6e+83)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (+ x (/ (- (* z y) x) (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+47) || !(z <= 6e+83)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - 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 <= (-1.4d+47)) .or. (.not. (z <= 6d+83))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x + (((z * y) - 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 <= -1.4e+47) || !(z <= 6e+83)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e+47) or not (z <= 6e+83):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e+47) || !(z <= 6e+83))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - 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 <= -1.4e+47) || ~((z <= 6e+83)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e+47], N[Not[LessEqual[z, 6e+83]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / 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 < -1.39999999999999994e47 or 5.9999999999999999e83 < z

   1. Initial program 73.1%

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

      1. *-commutative 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in y around inf 100.0%

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

   if -1.39999999999999994e47 < z < 5.9999999999999999e83

   1. Initial program 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+47} \lor \neg \left(z \leq 6 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -29000000:\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{z \cdot y}{x}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;1 - z \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -29000000.0)
   (+ 1.0 (/ -1.0 x))
   (if (<= x -7e-173)
     (- 1.0 (/ (* z y) x))
     (if (<= x 4.2e-122)
       (/ y (* t (+ x 1.0)))
       (if (<= x 2.9e-47) (- 1.0 (* z (/ y x))) (/ x (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -29000000.0) {
		tmp = 1.0 + (-1.0 / x);
	} else if (x <= -7e-173) {
		tmp = 1.0 - ((z * y) / x);
	} else if (x <= 4.2e-122) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= 2.9e-47) {
		tmp = 1.0 - (z * (y / x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-29000000.0d0)) then
        tmp = 1.0d0 + ((-1.0d0) / x)
    else if (x <= (-7d-173)) then
        tmp = 1.0d0 - ((z * y) / x)
    else if (x <= 4.2d-122) then
        tmp = y / (t * (x + 1.0d0))
    else if (x <= 2.9d-47) then
        tmp = 1.0d0 - (z * (y / x))
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -29000000.0) {
		tmp = 1.0 + (-1.0 / x);
	} else if (x <= -7e-173) {
		tmp = 1.0 - ((z * y) / x);
	} else if (x <= 4.2e-122) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= 2.9e-47) {
		tmp = 1.0 - (z * (y / x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -29000000.0:
		tmp = 1.0 + (-1.0 / x)
	elif x <= -7e-173:
		tmp = 1.0 - ((z * y) / x)
	elif x <= 4.2e-122:
		tmp = y / (t * (x + 1.0))
	elif x <= 2.9e-47:
		tmp = 1.0 - (z * (y / x))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -29000000.0)
		tmp = Float64(1.0 + Float64(-1.0 / x));
	elseif (x <= -7e-173)
		tmp = Float64(1.0 - Float64(Float64(z * y) / x));
	elseif (x <= 4.2e-122)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	elseif (x <= 2.9e-47)
		tmp = Float64(1.0 - Float64(z * Float64(y / x)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -29000000.0)
		tmp = 1.0 + (-1.0 / x);
	elseif (x <= -7e-173)
		tmp = 1.0 - ((z * y) / x);
	elseif (x <= 4.2e-122)
		tmp = y / (t * (x + 1.0));
	elseif (x <= 2.9e-47)
		tmp = 1.0 - (z * (y / x));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -29000000.0], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-173], N[(1.0 - N[(N[(z * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-122], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-47], N[(1.0 - N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.9e7

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 100.0%

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

   if -2.9e7 < x < -7.00000000000000029e-173

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

      3. associate-/l* 56.0%

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

      4. +-commutative 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in y around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. sub-neg 56.1%

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

      3. times-frac 49.9%

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

      4. +-commutative 49.9%

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

   10. Simplified 49.9%

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

   11. Taylor expanded in x around 0 54.5%

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

   if -7.00000000000000029e-173 < x < 4.19999999999999985e-122

   1. Initial program 80.2%

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

      1. *-commutative 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in z around inf 81.6%

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

   6. Taylor expanded in y around inf 68.8%

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

   if 4.19999999999999985e-122 < x < 2.9e-47

   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 t around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

      3. associate-/l* 75.8%

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

      4. +-commutative 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. sub-neg 75.9%

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

      3. times-frac 75.9%

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

      4. +-commutative 75.9%

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

   10. Simplified 75.9%

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

   11. Taylor expanded in x around 0 75.9%

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

   if 2.9e-47 < x

   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. Taylor expanded in t around inf 78.6%

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

      1. +-commutative 78.6%

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

   7. Simplified 78.6%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -29000000:\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{z \cdot y}{x}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;1 - z \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12500000000:\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{z \cdot y}{x}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-47}:\\ \;\;\;\;1 - z \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -12500000000.0)
   (+ 1.0 (/ -1.0 x))
   (if (<= x -6.3e-173)
     (- 1.0 (/ (* z y) x))
     (if (<= x 3.5e-125)
       (/ (/ y t) (+ x 1.0))
       (if (<= x 1.35e-47) (- 1.0 (* z (/ y x))) (/ x (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -12500000000.0) {
		tmp = 1.0 + (-1.0 / x);
	} else if (x <= -6.3e-173) {
		tmp = 1.0 - ((z * y) / x);
	} else if (x <= 3.5e-125) {
		tmp = (y / t) / (x + 1.0);
	} else if (x <= 1.35e-47) {
		tmp = 1.0 - (z * (y / x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-12500000000.0d0)) then
        tmp = 1.0d0 + ((-1.0d0) / x)
    else if (x <= (-6.3d-173)) then
        tmp = 1.0d0 - ((z * y) / x)
    else if (x <= 3.5d-125) then
        tmp = (y / t) / (x + 1.0d0)
    else if (x <= 1.35d-47) then
        tmp = 1.0d0 - (z * (y / x))
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -12500000000.0) {
		tmp = 1.0 + (-1.0 / x);
	} else if (x <= -6.3e-173) {
		tmp = 1.0 - ((z * y) / x);
	} else if (x <= 3.5e-125) {
		tmp = (y / t) / (x + 1.0);
	} else if (x <= 1.35e-47) {
		tmp = 1.0 - (z * (y / x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -12500000000.0:
		tmp = 1.0 + (-1.0 / x)
	elif x <= -6.3e-173:
		tmp = 1.0 - ((z * y) / x)
	elif x <= 3.5e-125:
		tmp = (y / t) / (x + 1.0)
	elif x <= 1.35e-47:
		tmp = 1.0 - (z * (y / x))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -12500000000.0)
		tmp = Float64(1.0 + Float64(-1.0 / x));
	elseif (x <= -6.3e-173)
		tmp = Float64(1.0 - Float64(Float64(z * y) / x));
	elseif (x <= 3.5e-125)
		tmp = Float64(Float64(y / t) / Float64(x + 1.0));
	elseif (x <= 1.35e-47)
		tmp = Float64(1.0 - Float64(z * Float64(y / x)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -12500000000.0)
		tmp = 1.0 + (-1.0 / x);
	elseif (x <= -6.3e-173)
		tmp = 1.0 - ((z * y) / x);
	elseif (x <= 3.5e-125)
		tmp = (y / t) / (x + 1.0);
	elseif (x <= 1.35e-47)
		tmp = 1.0 - (z * (y / x));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -12500000000.0], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.3e-173], N[(1.0 - N[(N[(z * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-125], N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e-47], N[(1.0 - N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.25e10

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 100.0%

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

   if -1.25e10 < x < -6.29999999999999968e-173

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

      3. associate-/l* 56.0%

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

      4. +-commutative 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in y around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. sub-neg 56.1%

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

      3. times-frac 49.9%

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

      4. +-commutative 49.9%

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

   10. Simplified 49.9%

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

   11. Taylor expanded in x around 0 54.5%

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

   if -6.29999999999999968e-173 < x < 3.49999999999999998e-125

   1. Initial program 80.2%

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

      1. *-commutative 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in z around inf 81.6%

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

   6. Taylor expanded in y around inf 68.8%

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

      1. associate-/r* 68.8%

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

      2. +-commutative 68.8%

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

   8. Simplified 68.8%

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

   if 3.49999999999999998e-125 < x < 1.3499999999999999e-47

   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 t around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

      3. associate-/l* 75.8%

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

      4. +-commutative 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. sub-neg 75.9%

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

      3. times-frac 75.9%

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

      4. +-commutative 75.9%

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

   10. Simplified 75.9%

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

   11. Taylor expanded in x around 0 75.9%

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

   if 1.3499999999999999e-47 < x

   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. Taylor expanded in t around inf 78.6%

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

      1. +-commutative 78.6%

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

   7. Simplified 78.6%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12500000000:\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{z \cdot y}{x}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-47}:\\ \;\;\;\;1 - z \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-27} \lor \neg \left(t \leq 1.15 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - y \cdot \frac{z}{x}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.3e-27) (not (<= t 1.15e-157)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ 1.0 (- x (* y (/ z x)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e-27) || !(t <= 1.15e-157)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (y * (z / x)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.3d-27)) .or. (.not. (t <= 1.15d-157))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (1.0d0 + (x - (y * (z / x)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e-27) || !(t <= 1.15e-157)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (y * (z / x)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.3e-27) or not (t <= 1.15e-157):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (1.0 + (x - (y * (z / x)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.3e-27) || !(t <= 1.15e-157))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y * Float64(z / x)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.3e-27) || ~((t <= 1.15e-157)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (1.0 + (x - (y * (z / x)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.3e-27], N[Not[LessEqual[t, 1.15e-157]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2999999999999999e-27 or 1.14999999999999994e-157 < t

   1. Initial program 84.2%

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

      1. *-commutative 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in z around inf 85.1%

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

   if -2.2999999999999999e-27 < t < 1.14999999999999994e-157

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in t around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

      3. associate-/l* 80.6%

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

      4. +-commutative 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-27} \lor \neg \left(t \leq 1.15 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - y \cdot \frac{z}{x}\right)}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-219} \lor \neg \left(z \leq 1.65 \cdot 10^{-233}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e-219) (not (<= z 1.65e-233)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (- 1.0 (* y (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-219) || !(z <= 1.65e-233)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d-219)) .or. (.not. (z <= 1.65d-233))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = 1.0d0 - (y * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-219) || !(z <= 1.65e-233)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e-219) or not (z <= 1.65e-233):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = 1.0 - (y * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-219) || !(z <= 1.65e-233))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-219) || ~((z <= 1.65e-233)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = 1.0 - (y * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e-219], N[Not[LessEqual[z, 1.65e-233]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999999e-219 or 1.65e-233 < z

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in z around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in y around inf 92.6%

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

   if -1.59999999999999999e-219 < z < 1.65e-233

   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 t around 0 91.6%

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

      1. mul-1-neg 91.6%

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

      2. unsub-neg 91.6%

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

      3. associate-/l* 91.6%

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

      4. +-commutative 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in y around 0 91.6%

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

      1. mul-1-neg 91.6%

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

      2. sub-neg 91.6%

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

      3. times-frac 85.7%

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

      4. +-commutative 85.7%

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

   10. Simplified 85.7%

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

   11. Taylor expanded in x around 0 91.6%

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

       1. associate-/l* 91.6%

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

   13. Simplified 91.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-219} \lor \neg \left(z \leq 1.65 \cdot 10^{-233}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-161} \lor \neg \left(y \leq 4.9 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.5e-161) (not (<= y 4.9e-42)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.5e-161) || !(y <= 4.9e-42)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.5d-161)) .or. (.not. (y <= 4.9d-42))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.5e-161) || !(y <= 4.9e-42)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.5e-161) or not (y <= 4.9e-42):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.5e-161) || !(y <= 4.9e-42))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.5e-161) || ~((y <= 4.9e-42)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.5e-161], N[Not[LessEqual[y, 4.9e-42]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e-161 or 4.9e-42 < y

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in z around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. unsub-neg 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in y around inf 93.0%

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

   if -5.5e-161 < y < 4.9e-42

   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 95.1%

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

      1. +-commutative 95.1%

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

   7. Simplified 95.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-161} \lor \neg \left(y \leq 4.9 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-30} \lor \neg \left(t \leq 1.2 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.8e-30) (not (<= t 1.2e-157)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* (/ y x) (/ z (- -1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-30) || !(t <= 1.2e-157)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.8d-30)) .or. (.not. (t <= 1.2d-157))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((y / x) * (z / ((-1.0d0) - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-30) || !(t <= 1.2e-157)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.8e-30) or not (t <= 1.2e-157):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.8e-30) || !(t <= 1.2e-157))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(y / x) * Float64(z / Float64(-1.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.8e-30) || ~((t <= 1.2e-157)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.8e-30], N[Not[LessEqual[t, 1.2e-157]], $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[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999988e-30 or 1.2e-157 < t

   1. Initial program 84.2%

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

      1. *-commutative 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in z around inf 85.1%

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

   if -2.79999999999999988e-30 < t < 1.2e-157

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in t around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

      3. associate-/l* 80.6%

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

      4. +-commutative 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in y around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. sub-neg 78.4%

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

      3. times-frac 78.5%

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

      4. +-commutative 78.5%

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

   10. Simplified 78.5%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-30} \lor \neg \left(t \leq 1.2 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-102} \lor \neg \left(z \leq 1.1 \cdot 10^{-229}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e-102) (not (<= z 1.1e-229)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* y (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e-102) || !(z <= 1.1e-229)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.8d-102)) .or. (.not. (z <= 1.1d-229))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - (y * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e-102) || !(z <= 1.1e-229)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e-102) or not (z <= 1.1e-229):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - (y * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e-102) || !(z <= 1.1e-229))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.8e-102) || ~((z <= 1.1e-229)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - (y * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e-102], N[Not[LessEqual[z, 1.1e-229]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999973e-102 or 1.0999999999999999e-229 < z

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in z around inf 80.5%

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

   if -5.79999999999999973e-102 < z < 1.0999999999999999e-229

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

      3. associate-/l* 83.2%

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

      4. +-commutative 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in y around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. sub-neg 83.2%

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

      3. times-frac 78.1%

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

      4. +-commutative 78.1%

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

   10. Simplified 78.1%

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

   11. Taylor expanded in x around 0 82.0%

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

       1. associate-/l* 82.0%

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

   13. Simplified 82.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-102} \lor \neg \left(z \leq 1.1 \cdot 10^{-229}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+27} \lor \neg \left(z \leq 6.2 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+27) (not (<= z 6.2e-78)))
   (/ x (+ x 1.0))
   (- 1.0 (* y (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+27) || !(z <= 6.2e-78)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.2d+27)) .or. (.not. (z <= 6.2d-78))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = 1.0d0 - (y * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+27) || !(z <= 6.2e-78)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+27) or not (z <= 6.2e-78):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0 - (y * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+27) || !(z <= 6.2e-78))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e+27) || ~((z <= 6.2e-78)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0 - (y * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+27], N[Not[LessEqual[z, 6.2e-78]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999992e27 or 6.20000000000000035e-78 < z

   1. Initial program 79.3%

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

      1. *-commutative 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around inf 56.9%

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

      1. +-commutative 56.9%

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

   7. Simplified 56.9%

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

   if -6.19999999999999992e27 < z < 6.20000000000000035e-78

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. unsub-neg 75.1%

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

      3. associate-/l* 75.1%

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

      4. +-commutative 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in y around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. sub-neg 75.1%

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

      3. times-frac 72.4%

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

      4. +-commutative 72.4%

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

   10. Simplified 72.4%

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

   11. Taylor expanded in x around 0 72.6%

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

       1. associate-/l* 72.6%

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

   13. Simplified 72.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+27} \lor \neg \left(z \leq 6.2 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+26} \lor \neg \left(z \leq 2.65 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.05e+26) (not (<= z 2.65e+85)))
   (/ x (+ x 1.0))
   (- 1.0 (/ (* z y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.05e+26) || !(z <= 2.65e+85)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 - ((z * y) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.05d+26)) .or. (.not. (z <= 2.65d+85))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((z * y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.05e+26) || !(z <= 2.65e+85)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 - ((z * y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.05e+26) or not (z <= 2.65e+85):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0 - ((z * y) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.05e+26) || !(z <= 2.65e+85))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(z * y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.05e+26) || ~((z <= 2.65e+85)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0 - ((z * y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.05e+26], N[Not[LessEqual[z, 2.65e+85]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(z * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.04999999999999992e26 or 2.65e85 < z

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in t around inf 58.5%

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

      1. +-commutative 58.5%

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

   7. Simplified 58.5%

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

   if -2.04999999999999992e26 < z < 2.65e85

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

      3. associate-/l* 72.2%

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

      4. +-commutative 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in y around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. sub-neg 72.2%

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

      3. times-frac 70.1%

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

      4. +-commutative 70.1%

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

   10. Simplified 70.1%

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

   11. Taylor expanded in x around 0 68.1%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+26} \lor \neg \left(z \leq 2.65 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z \cdot y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-22} \lor \neg \left(z \leq 2.3 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-22) (not (<= z 2.3e-80))) (/ x (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-22) || !(z <= 2.3e-80)) {
		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 ((z <= (-1.7d-22)) .or. (.not. (z <= 2.3d-80))) 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 ((z <= -1.7e-22) || !(z <= 2.3e-80)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-22) or not (z <= 2.3e-80):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-22) || !(z <= 2.3e-80))
		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 ((z <= -1.7e-22) || ~((z <= 2.3e-80)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e-22], N[Not[LessEqual[z, 2.3e-80]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if z < -1.6999999999999999e-22 or 2.2999999999999998e-80 < z

   1. Initial program 80.5%

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

      1. *-commutative 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around inf 57.8%

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

      1. +-commutative 57.8%

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

   7. Simplified 57.8%

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

   if -1.6999999999999999e-22 < z < 2.2999999999999998e-80

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 76.2%

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

   9. Taylor expanded in x around inf 63.8%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-22} \lor \neg \left(z \leq 2.3 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.4% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 88.3%

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

   1. *-commutative 88.3%

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

3. Simplified 88.3%

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

5. Taylor expanded in z around inf 88.3%

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

   1. mul-1-neg 88.3%

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

   2. unsub-neg 88.3%

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

7. Simplified 88.3%

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

8. Taylor expanded in y around inf 88.7%

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

9. Taylor expanded in x around inf 54.5%

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

10. Final simplification 54.5%

    \[\leadsto 1 \]
11. Add Preprocessing

Developer target: 99.4% 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 2024085 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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