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

Percentage Accurate: 89.3% → 94.2%

Time: 11.2s

Alternatives: 11

Speedup: 0.8×

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: 94.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+86} \lor \neg \left(z \leq 6.5 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e+86) (not (<= z 6.5e+49)))
   (/ (+ x (/ y t)) (+ 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 <= -1e+86) || !(z <= 6.5e+49)) {
		tmp = (x + (y / t)) / (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 <= (-1d+86)) .or. (.not. (z <= 6.5d+49))) then
        tmp = (x + (y / t)) / (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 <= -1e+86) || !(z <= 6.5e+49)) {
		tmp = (x + (y / t)) / (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 <= -1e+86) or not (z <= 6.5e+49):
		tmp = (x + (y / t)) / (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 <= -1e+86) || !(z <= 6.5e+49))
		tmp = Float64(Float64(x + Float64(y / t)) / 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 <= -1e+86) || ~((z <= 6.5e+49)))
		tmp = (x + (y / t)) / (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, -1e+86], N[Not[LessEqual[z, 6.5e+49]], $MachinePrecision]], N[(N[(x + N[(y / t), $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 < -1e86 or 6.5000000000000005e49 < z

   1. Initial program 74.3%

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

      1. *-commutative 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in z around inf 92.6%

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

   if -1e86 < z < 6.5000000000000005e49

   1. Initial program 99.8%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+86} \lor \neg \left(z \leq 6.5 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 2: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{z \cdot y}{t_1}}{x + 1}\\ t_3 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -6.7 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-183}:\\ \;\;\;\;\frac{x - \frac{x}{t_1}}{x + 1}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (+ x (/ (* z y) t_1)) (+ x 1.0)))
        (t_3 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -6.7e+84)
     t_3
     (if (<= z -2.3e-106)
       t_2
       (if (<= z 1.15e-183)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= z 6.5e+49) t_2 t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + ((z * y) / t_1)) / (x + 1.0);
	double t_3 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -6.7e+84) {
		tmp = t_3;
	} else if (z <= -2.3e-106) {
		tmp = t_2;
	} else if (z <= 1.15e-183) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (z <= 6.5e+49) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + ((z * y) / t_1)) / (x + 1.0d0)
    t_3 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-6.7d+84)) then
        tmp = t_3
    else if (z <= (-2.3d-106)) then
        tmp = t_2
    else if (z <= 1.15d-183) then
        tmp = (x - (x / t_1)) / (x + 1.0d0)
    else if (z <= 6.5d+49) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + ((z * y) / t_1)) / (x + 1.0);
	double t_3 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -6.7e+84) {
		tmp = t_3;
	} else if (z <= -2.3e-106) {
		tmp = t_2;
	} else if (z <= 1.15e-183) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (z <= 6.5e+49) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + ((z * y) / t_1)) / (x + 1.0)
	t_3 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -6.7e+84:
		tmp = t_3
	elif z <= -2.3e-106:
		tmp = t_2
	elif z <= 1.15e-183:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif z <= 6.5e+49:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(z * y) / t_1)) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -6.7e+84)
		tmp = t_3;
	elseif (z <= -2.3e-106)
		tmp = t_2;
	elseif (z <= 1.15e-183)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (z <= 6.5e+49)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + ((z * y) / t_1)) / (x + 1.0);
	t_3 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -6.7e+84)
		tmp = t_3;
	elseif (z <= -2.3e-106)
		tmp = t_2;
	elseif (z <= 1.15e-183)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (z <= 6.5e+49)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.7e+84], t$95$3, If[LessEqual[z, -2.3e-106], t$95$2, If[LessEqual[z, 1.15e-183], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+49], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.70000000000000041e84 or 6.5000000000000005e49 < z

   1. Initial program 74.3%

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

      1. *-commutative 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in z around inf 92.6%

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

   if -6.70000000000000041e84 < z < -2.3000000000000001e-106 or 1.15000000000000008e-183 < z < 6.5000000000000005e49

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 84.6%

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

      1. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   if -2.3000000000000001e-106 < z < 1.15000000000000008e-183

   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 y around 0 79.9%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+84}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-106}:\\ \;\;\;\;\frac{x + \frac{z \cdot y}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-183}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{x + \frac{z \cdot y}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 79.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{\left(x - \frac{y}{\frac{x}{z}}\right) + 1}{x + 1}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-102} \lor \neg \left(z \leq 9 \cdot 10^{+20}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -6.6e+67)
     t_1
     (if (<= z -3.5e-8)
       (/ (+ (- x (/ y (/ x z))) 1.0) (+ x 1.0))
       (if (or (<= z -1.75e-102) (not (<= z 9e+20)))
         t_1
         (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -6.6e+67) {
		tmp = t_1;
	} else if (z <= -3.5e-8) {
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0);
	} else if ((z <= -1.75e-102) || !(z <= 9e+20)) {
		tmp = t_1;
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-6.6d+67)) then
        tmp = t_1
    else if (z <= (-3.5d-8)) then
        tmp = ((x - (y / (x / z))) + 1.0d0) / (x + 1.0d0)
    else if ((z <= (-1.75d-102)) .or. (.not. (z <= 9d+20))) then
        tmp = t_1
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -6.6e+67) {
		tmp = t_1;
	} else if (z <= -3.5e-8) {
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0);
	} else if ((z <= -1.75e-102) || !(z <= 9e+20)) {
		tmp = t_1;
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -6.6e+67:
		tmp = t_1
	elif z <= -3.5e-8:
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0)
	elif (z <= -1.75e-102) or not (z <= 9e+20):
		tmp = t_1
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	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 (z <= -6.6e+67)
		tmp = t_1;
	elseif (z <= -3.5e-8)
		tmp = Float64(Float64(Float64(x - Float64(y / Float64(x / z))) + 1.0) / Float64(x + 1.0));
	elseif ((z <= -1.75e-102) || !(z <= 9e+20))
		tmp = t_1;
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -6.6e+67)
		tmp = t_1;
	elseif (z <= -3.5e-8)
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0);
	elseif ((z <= -1.75e-102) || ~((z <= 9e+20)))
		tmp = t_1;
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	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[z, -6.6e+67], t$95$1, If[LessEqual[z, -3.5e-8], N[(N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.75e-102], N[Not[LessEqual[z, 9e+20]], $MachinePrecision]], t$95$1, N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6000000000000006e67 or -3.50000000000000024e-8 < z < -1.74999999999999993e-102 or 9e20 < z

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in z around inf 90.3%

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

   if -6.6000000000000006e67 < z < -3.50000000000000024e-8

   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 t around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. associate-/l* 85.0%

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

   6. Simplified 85.0%

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

   if -1.74999999999999993e-102 < z < 9e20

   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 y around 0 76.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+67}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{\left(x - \frac{y}{\frac{x}{z}}\right) + 1}{x + 1}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-102} \lor \neg \left(z \leq 9 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 4: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-83}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-105}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.4e-51)
   1.0
   (if (<= x -1.75e-81)
     (* z (/ y (- (* z t) x)))
     (if (<= x -1.6e-83)
       1.0
       (if (<= x -5.8e-105)
         (- x (/ (/ x t) z))
         (if (<= x 9.8e-60) (/ y (* t (+ x 1.0))) 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-51) {
		tmp = 1.0;
	} else if (x <= -1.75e-81) {
		tmp = z * (y / ((z * t) - x));
	} else if (x <= -1.6e-83) {
		tmp = 1.0;
	} else if (x <= -5.8e-105) {
		tmp = x - ((x / t) / z);
	} else if (x <= 9.8e-60) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.4d-51)) then
        tmp = 1.0d0
    else if (x <= (-1.75d-81)) then
        tmp = z * (y / ((z * t) - x))
    else if (x <= (-1.6d-83)) then
        tmp = 1.0d0
    else if (x <= (-5.8d-105)) then
        tmp = x - ((x / t) / z)
    else if (x <= 9.8d-60) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-51) {
		tmp = 1.0;
	} else if (x <= -1.75e-81) {
		tmp = z * (y / ((z * t) - x));
	} else if (x <= -1.6e-83) {
		tmp = 1.0;
	} else if (x <= -5.8e-105) {
		tmp = x - ((x / t) / z);
	} else if (x <= 9.8e-60) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.4e-51:
		tmp = 1.0
	elif x <= -1.75e-81:
		tmp = z * (y / ((z * t) - x))
	elif x <= -1.6e-83:
		tmp = 1.0
	elif x <= -5.8e-105:
		tmp = x - ((x / t) / z)
	elif x <= 9.8e-60:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.4e-51)
		tmp = 1.0;
	elseif (x <= -1.75e-81)
		tmp = Float64(z * Float64(y / Float64(Float64(z * t) - x)));
	elseif (x <= -1.6e-83)
		tmp = 1.0;
	elseif (x <= -5.8e-105)
		tmp = Float64(x - Float64(Float64(x / t) / z));
	elseif (x <= 9.8e-60)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.4e-51)
		tmp = 1.0;
	elseif (x <= -1.75e-81)
		tmp = z * (y / ((z * t) - x));
	elseif (x <= -1.6e-83)
		tmp = 1.0;
	elseif (x <= -5.8e-105)
		tmp = x - ((x / t) / z);
	elseif (x <= 9.8e-60)
		tmp = y / (t * (x + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.4e-51], 1.0, If[LessEqual[x, -1.75e-81], N[(z * N[(y / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e-83], 1.0, If[LessEqual[x, -5.8e-105], N[(x - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e-60], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e-51 or -1.74999999999999993e-81 < x < -1.6000000000000001e-83 or 9.79999999999999977e-60 < x

   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 y around inf 80.1%

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

      1. *-commutative 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in x around inf 81.8%

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

   if -2.4e-51 < x < -1.74999999999999993e-81

   1. Initial program 72.1%

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

      1. *-commutative 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in y around inf 58.1%

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

      1. *-commutative 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in y around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. +-commutative 58.6%

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

      3. *-commutative 58.6%

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

      4. fma-neg 58.6%

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

      5. times-frac 71.8%

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

      6. fma-neg 71.8%

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

   9. Simplified 71.8%

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

   10. Taylor expanded in x around 0 71.8%

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

   if -1.6000000000000001e-83 < x < -5.80000000000000007e-105

   1. Initial program 80.0%

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

      1. *-commutative 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in t around inf 80.0%

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

   5. Taylor expanded in x around inf 80.3%

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

      1. *-commutative 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in x around 0 80.3%

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

      1. metadata-eval 80.3%

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

      2. associate-*r/ 80.3%

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

      3. cancel-sign-sub-inv 80.3%

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

      4. metadata-eval 80.3%

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

      5. *-lft-identity 80.3%

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

      6. distribute-rgt-in 80.3%

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

      7. *-lft-identity 80.3%

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

      8. associate-*l/ 80.3%

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

      9. associate-*r/ 80.3%

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

      10. mul-1-neg 80.3%

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

      11. unsub-neg 80.3%

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

      12. associate-/r* 80.3%

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

   10. Simplified 80.3%

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

   if -5.80000000000000007e-105 < x < 9.79999999999999977e-60

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 53.7%

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

   5. Taylor expanded in z around inf 53.0%

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

      1. +-commutative 53.0%

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

   7. Simplified 53.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-83}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-105}:\\ \;\;\;\;x - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 78.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+65} \lor \neg \left(z \leq 9 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - \frac{y}{\frac{x}{z}}\right) + 1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.7e+65) (not (<= z 9e-124)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ (- x (/ y (/ x z))) 1.0) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.7e+65) || !(z <= 9e-124)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x - (y / (x / z))) + 1.0) / (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 <= (-3.7d+65)) .or. (.not. (z <= 9d-124))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = ((x - (y / (x / z))) + 1.0d0) / (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 <= -3.7e+65) || !(z <= 9e-124)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.7e+65) or not (z <= 9e-124):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.7e+65) || !(z <= 9e-124))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x - Float64(y / Float64(x / z))) + 1.0) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.7e+65) || ~((z <= 9e-124)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.7e+65], N[Not[LessEqual[z, 9e-124]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999995e65 or 8.9999999999999992e-124 < z

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around inf 85.7%

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

   if -3.69999999999999995e65 < z < 8.9999999999999992e-124

   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 71.0%

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

      1. mul-1-neg 71.0%

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

      2. unsub-neg 71.0%

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

      3. associate-/l* 71.0%

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

   6. Simplified 71.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+65} \lor \neg \left(z \leq 9 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - \frac{y}{\frac{x}{z}}\right) + 1}{x + 1}\\ \end{array} \]

Alternative 6: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - \frac{y}{\frac{x}{z}}\right) + 1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.2e-51)
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))
   (if (<= x 1.45e-51)
     (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
     (/ (+ (- x (/ y (/ x z))) 1.0) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e-51) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else if (x <= 1.45e-51) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else {
		tmp = ((x - (y / (x / z))) + 1.0) / (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 <= (-6.2d-51)) then
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    else if (x <= 1.45d-51) then
        tmp = (x - (((x / z) - y) / t)) / (x + 1.0d0)
    else
        tmp = ((x - (y / (x / z))) + 1.0d0) / (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 <= -6.2e-51) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else if (x <= 1.45e-51) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else {
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.2e-51:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	elif x <= 1.45e-51:
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0)
	else:
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.2e-51)
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	elseif (x <= 1.45e-51)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x - Float64(y / Float64(x / z))) + 1.0) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.2e-51)
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	elseif (x <= 1.45e-51)
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	else
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.2e-51], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e-51], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.1999999999999995e-51

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around 0 87.6%

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

   if -6.1999999999999995e-51 < x < 1.44999999999999986e-51

   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. Taylor expanded in t around -inf 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-lft-out-- 82.9%

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

   6. Simplified 82.9%

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

   if 1.44999999999999986e-51 < x

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in t around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

      3. associate-/l* 92.4%

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

   6. Simplified 92.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - \frac{y}{\frac{x}{z}}\right) + 1}{x + 1}\\ \end{array} \]

Alternative 7: 77.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-24}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.6e+36) 1.0 (if (<= x 3.4e-24) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.6e+36) {
		tmp = 1.0;
	} else if (x <= 3.4e-24) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-9.6d+36)) then
        tmp = 1.0d0
    else if (x <= 3.4d-24) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.6e+36) {
		tmp = 1.0;
	} else if (x <= 3.4e-24) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.6e+36:
		tmp = 1.0
	elif x <= 3.4e-24:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.6e+36)
		tmp = 1.0;
	elseif (x <= 3.4e-24)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.6e+36)
		tmp = 1.0;
	elseif (x <= 3.4e-24)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.6e+36], 1.0, If[LessEqual[x, 3.4e-24], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5999999999999997e36 or 3.39999999999999992e-24 < x

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in x around inf 90.9%

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

   if -9.5999999999999997e36 < x < 3.39999999999999992e-24

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in z around inf 64.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-24}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 77.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.4e+37)
   (/ (- x (/ y (/ x z))) (+ x 1.0))
   (if (<= x 7.2e-25) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.4e+37) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (x <= 7.2e-25) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.4d+37)) then
        tmp = (x - (y / (x / z))) / (x + 1.0d0)
    else if (x <= 7.2d-25) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.4e+37) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (x <= 7.2e-25) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.4e+37:
		tmp = (x - (y / (x / z))) / (x + 1.0)
	elif x <= 7.2e-25:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.4e+37)
		tmp = Float64(Float64(x - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (x <= 7.2e-25)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.4e+37)
		tmp = (x - (y / (x / z))) / (x + 1.0);
	elseif (x <= 7.2e-25)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.4e+37], N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-25], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -3.40000000000000006e37

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in y around inf 89.8%

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

      1. *-commutative 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in x around inf 89.9%

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

      1. mul-1-neg 89.9%

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

      2. unsub-neg 89.9%

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

      3. associate-/l* 96.8%

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

   9. Simplified 96.8%

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

   if -3.40000000000000006e37 < x < 7.1999999999999998e-25

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in z around inf 64.8%

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

   if 7.1999999999999998e-25 < x

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in y around inf 79.3%

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

      1. *-commutative 79.3%

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

   6. Simplified 79.3%

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

   7. Taylor expanded in x around inf 87.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 68.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-51}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.9e-51) 1.0 (if (<= x 9.8e-60) (/ y (* t (+ x 1.0))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.9e-51) {
		tmp = 1.0;
	} else if (x <= 9.8e-60) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.9d-51)) then
        tmp = 1.0d0
    else if (x <= 9.8d-60) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.9e-51) {
		tmp = 1.0;
	} else if (x <= 9.8e-60) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.9e-51:
		tmp = 1.0
	elif x <= 9.8e-60:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.9e-51)
		tmp = 1.0;
	elseif (x <= 9.8e-60)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.9e-51)
		tmp = 1.0;
	elseif (x <= 9.8e-60)
		tmp = y / (t * (x + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.9e-51], 1.0, If[LessEqual[x, 9.8e-60], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8999999999999997e-51 or 9.79999999999999977e-60 < x

   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 y around inf 80.6%

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

      1. *-commutative 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in x around inf 81.7%

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

   if -3.8999999999999997e-51 < x < 9.79999999999999977e-60

   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. Taylor expanded in y around inf 51.3%

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

   5. Taylor expanded in z around inf 52.1%

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

      1. +-commutative 52.1%

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

   7. Simplified 52.1%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-51}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 68.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.4e-51) 1.0 (if (<= x 6.1e-52) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-51) {
		tmp = 1.0;
	} else if (x <= 6.1e-52) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.4d-51)) then
        tmp = 1.0d0
    else if (x <= 6.1d-52) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-51) {
		tmp = 1.0;
	} else if (x <= 6.1e-52) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.4e-51:
		tmp = 1.0
	elif x <= 6.1e-52:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.4e-51)
		tmp = 1.0;
	elseif (x <= 6.1e-52)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.4e-51)
		tmp = 1.0;
	elseif (x <= 6.1e-52)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.4e-51], 1.0, If[LessEqual[x, 6.1e-52], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e-51 or 6.0999999999999999e-52 < x

   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 y around inf 80.6%

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

      1. *-commutative 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in x around inf 81.7%

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

   if -2.4e-51 < x < 6.0999999999999999e-52

   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. Taylor expanded in z around inf 68.6%

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

   5. Taylor expanded in x around 0 52.1%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 53.3% 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 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 y around inf 74.9%

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

   1. *-commutative 74.9%

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

6. Simplified 74.9%

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

7. Taylor expanded in x around inf 50.9%

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

8. Final simplification 50.9%

   \[\leadsto 1 \]

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 2023305 
(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)))