Data.Colour.RGB:hslsv from colour-2.3.3, B

Percentage Accurate: 99.2% → 99.2%

Time: 14.0s

Alternatives: 17

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{-60 \cdot y + 60 \cdot x}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (+ (* -60.0 y) (* 60.0 x)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return (((-60.0 * y) + (60.0 * x)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((((-60.0d0) * y) + (60.0d0 * x)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (((-60.0 * y) + (60.0 * x)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return (((-60.0 * y) + (60.0 * x)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(Float64(-60.0 * y) + Float64(60.0 * x)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (((-60.0 * y) + (60.0 * x)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[(-60.0 * y), $MachinePrecision] + N[(60.0 * x), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

2. Taylor expanded in x around 0 99.8%

   \[\leadsto \frac{\color{blue}{-60 \cdot y + 60 \cdot x}}{z - t} + a \cdot 120 \]

3. Final simplification 99.8%

   \[\leadsto \frac{-60 \cdot y + 60 \cdot x}{z - t} + a \cdot 120 \]

Alternative 2: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-121} \lor \neg \left(a \cdot 120 \leq 10^{-89}\right) \land a \cdot 120 \leq 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-52)
   (* a 120.0)
   (if (or (<= (* a 120.0) 5e-121)
           (and (not (<= (* a 120.0) 1e-89)) (<= (* a 120.0) 1e-15)))
     (* 60.0 (/ (- x y) (- z t)))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-52) {
		tmp = a * 120.0;
	} else if (((a * 120.0) <= 5e-121) || (!((a * 120.0) <= 1e-89) && ((a * 120.0) <= 1e-15))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-52)) then
        tmp = a * 120.0d0
    else if (((a * 120.0d0) <= 5d-121) .or. (.not. ((a * 120.0d0) <= 1d-89)) .and. ((a * 120.0d0) <= 1d-15)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-52) {
		tmp = a * 120.0;
	} else if (((a * 120.0) <= 5e-121) || (!((a * 120.0) <= 1e-89) && ((a * 120.0) <= 1e-15))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-52:
		tmp = a * 120.0
	elif ((a * 120.0) <= 5e-121) or (not ((a * 120.0) <= 1e-89) and ((a * 120.0) <= 1e-15)):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-52)
		tmp = Float64(a * 120.0);
	elseif ((Float64(a * 120.0) <= 5e-121) || (!(Float64(a * 120.0) <= 1e-89) && (Float64(a * 120.0) <= 1e-15)))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-52)
		tmp = a * 120.0;
	elseif (((a * 120.0) <= 5e-121) || (~(((a * 120.0) <= 1e-89)) && ((a * 120.0) <= 1e-15)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-52], N[(a * 120.0), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-121], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-89]], $MachinePrecision], LessEqual[N[(a * 120.0), $MachinePrecision], 1e-15]]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -2e-52 or 4.99999999999999989e-121 < (*.f64 a 120) < 1.00000000000000004e-89 or 1.0000000000000001e-15 < (*.f64 a 120)

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 73.4%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2e-52 < (*.f64 a 120) < 4.99999999999999989e-121 or 1.00000000000000004e-89 < (*.f64 a 120) < 1.0000000000000001e-15

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 88.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-121} \lor \neg \left(a \cdot 120 \leq 10^{-89}\right) \land a \cdot 120 \leq 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-121} \lor \neg \left(a \cdot 120 \leq 10^{-89}\right) \land a \cdot 120 \leq 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-52)
   (+ (* a 120.0) (* 60.0 (/ y t)))
   (if (or (<= (* a 120.0) 5e-121)
           (and (not (<= (* a 120.0) 1e-89)) (<= (* a 120.0) 1e-15)))
     (* 60.0 (/ (- x y) (- z t)))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-52) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (((a * 120.0) <= 5e-121) || (!((a * 120.0) <= 1e-89) && ((a * 120.0) <= 1e-15))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-52)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if (((a * 120.0d0) <= 5d-121) .or. (.not. ((a * 120.0d0) <= 1d-89)) .and. ((a * 120.0d0) <= 1d-15)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-52) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (((a * 120.0) <= 5e-121) || (!((a * 120.0) <= 1e-89) && ((a * 120.0) <= 1e-15))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-52:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif ((a * 120.0) <= 5e-121) or (not ((a * 120.0) <= 1e-89) and ((a * 120.0) <= 1e-15)):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-52)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif ((Float64(a * 120.0) <= 5e-121) || (!(Float64(a * 120.0) <= 1e-89) && (Float64(a * 120.0) <= 1e-15)))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-52)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif (((a * 120.0) <= 5e-121) || (~(((a * 120.0) <= 1e-89)) && ((a * 120.0) <= 1e-15)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-52], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-121], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-89]], $MachinePrecision], LessEqual[N[(a * 120.0), $MachinePrecision], 1e-15]]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -2e-52

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0 84.7%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]

   3. Taylor expanded in z around 0 70.0%

      \[\leadsto \color{blue}{60 \cdot \frac{y}{t}} + a \cdot 120 \]

   if -2e-52 < (*.f64 a 120) < 4.99999999999999989e-121 or 1.00000000000000004e-89 < (*.f64 a 120) < 1.0000000000000001e-15

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 88.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   if 4.99999999999999989e-121 < (*.f64 a 120) < 1.00000000000000004e-89 or 1.0000000000000001e-15 < (*.f64 a 120)

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 77.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-121} \lor \neg \left(a \cdot 120 \leq 10^{-89}\right) \land a \cdot 120 \leq 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-121} \lor \neg \left(a \cdot 120 \leq 10^{-89}\right) \land a \cdot 120 \leq 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-52)
   (+ (* a 120.0) (/ 60.0 (/ t y)))
   (if (or (<= (* a 120.0) 5e-121)
           (and (not (<= (* a 120.0) 1e-89)) (<= (* a 120.0) 1e-15)))
     (* 60.0 (/ (- x y) (- z t)))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-52) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if (((a * 120.0) <= 5e-121) || (!((a * 120.0) <= 1e-89) && ((a * 120.0) <= 1e-15))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-52)) then
        tmp = (a * 120.0d0) + (60.0d0 / (t / y))
    else if (((a * 120.0d0) <= 5d-121) .or. (.not. ((a * 120.0d0) <= 1d-89)) .and. ((a * 120.0d0) <= 1d-15)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-52) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if (((a * 120.0) <= 5e-121) || (!((a * 120.0) <= 1e-89) && ((a * 120.0) <= 1e-15))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-52:
		tmp = (a * 120.0) + (60.0 / (t / y))
	elif ((a * 120.0) <= 5e-121) or (not ((a * 120.0) <= 1e-89) and ((a * 120.0) <= 1e-15)):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-52)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(t / y)));
	elseif ((Float64(a * 120.0) <= 5e-121) || (!(Float64(a * 120.0) <= 1e-89) && (Float64(a * 120.0) <= 1e-15)))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-52)
		tmp = (a * 120.0) + (60.0 / (t / y));
	elseif (((a * 120.0) <= 5e-121) || (~(((a * 120.0) <= 1e-89)) && ((a * 120.0) <= 1e-15)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-52], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-121], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-89]], $MachinePrecision], LessEqual[N[(a * 120.0), $MachinePrecision], 1e-15]]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -2e-52

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around 0 69.7%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{t}{x - y}}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. neg-mul-1 69.7%

         \[\leadsto \frac{60}{\color{blue}{-\frac{t}{x - y}}} + a \cdot 120 \]

      2. distribute-neg-frac 69.7%

         \[\leadsto \frac{60}{\color{blue}{\frac{-t}{x - y}}} + a \cdot 120 \]

   6. Simplified 69.7%

      \[\leadsto \frac{60}{\color{blue}{\frac{-t}{x - y}}} + a \cdot 120 \]

   7. Taylor expanded in x around 0 70.0%

      \[\leadsto \frac{60}{\color{blue}{\frac{t}{y}}} + a \cdot 120 \]

   if -2e-52 < (*.f64 a 120) < 4.99999999999999989e-121 or 1.00000000000000004e-89 < (*.f64 a 120) < 1.0000000000000001e-15

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 88.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   if 4.99999999999999989e-121 < (*.f64 a 120) < 1.00000000000000004e-89 or 1.0000000000000001e-15 < (*.f64 a 120)

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 77.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-121} \lor \neg \left(a \cdot 120 \leq 10^{-89}\right) \land a \cdot 120 \leq 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-121} \lor \neg \left(a \cdot 120 \leq 10^{-89}\right) \land a \cdot 120 \leq 10^{-15}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-52)
   (+ (* a 120.0) (/ 60.0 (/ t y)))
   (if (or (<= (* a 120.0) 5e-121)
           (and (not (<= (* a 120.0) 1e-89)) (<= (* a 120.0) 1e-15)))
     (/ (* 60.0 (- x y)) (- z t))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-52) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if (((a * 120.0) <= 5e-121) || (!((a * 120.0) <= 1e-89) && ((a * 120.0) <= 1e-15))) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-52)) then
        tmp = (a * 120.0d0) + (60.0d0 / (t / y))
    else if (((a * 120.0d0) <= 5d-121) .or. (.not. ((a * 120.0d0) <= 1d-89)) .and. ((a * 120.0d0) <= 1d-15)) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-52) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if (((a * 120.0) <= 5e-121) || (!((a * 120.0) <= 1e-89) && ((a * 120.0) <= 1e-15))) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-52:
		tmp = (a * 120.0) + (60.0 / (t / y))
	elif ((a * 120.0) <= 5e-121) or (not ((a * 120.0) <= 1e-89) and ((a * 120.0) <= 1e-15)):
		tmp = (60.0 * (x - y)) / (z - t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-52)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(t / y)));
	elseif ((Float64(a * 120.0) <= 5e-121) || (!(Float64(a * 120.0) <= 1e-89) && (Float64(a * 120.0) <= 1e-15)))
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-52)
		tmp = (a * 120.0) + (60.0 / (t / y));
	elseif (((a * 120.0) <= 5e-121) || (~(((a * 120.0) <= 1e-89)) && ((a * 120.0) <= 1e-15)))
		tmp = (60.0 * (x - y)) / (z - t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-52], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-121], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-89]], $MachinePrecision], LessEqual[N[(a * 120.0), $MachinePrecision], 1e-15]]], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -2e-52

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around 0 69.7%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{t}{x - y}}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. neg-mul-1 69.7%

         \[\leadsto \frac{60}{\color{blue}{-\frac{t}{x - y}}} + a \cdot 120 \]

      2. distribute-neg-frac 69.7%

         \[\leadsto \frac{60}{\color{blue}{\frac{-t}{x - y}}} + a \cdot 120 \]

   6. Simplified 69.7%

      \[\leadsto \frac{60}{\color{blue}{\frac{-t}{x - y}}} + a \cdot 120 \]

   7. Taylor expanded in x around 0 70.0%

      \[\leadsto \frac{60}{\color{blue}{\frac{t}{y}}} + a \cdot 120 \]

   if -2e-52 < (*.f64 a 120) < 4.99999999999999989e-121 or 1.00000000000000004e-89 < (*.f64 a 120) < 1.0000000000000001e-15

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      2. clear-num 99.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - t}{60 \cdot \left(x - y\right)}}} + a \cdot 120 \]

      3. associate-/r/ 99.5%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \left(60 \cdot \left(x - y\right)\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \left(60 \cdot \left(x - y\right)\right)} + a \cdot 120 \]

   6. Taylor expanded in a around 0 88.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 88.3%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   8. Simplified 88.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   if 4.99999999999999989e-121 < (*.f64 a 120) < 1.00000000000000004e-89 or 1.0000000000000001e-15 < (*.f64 a 120)

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 77.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-121} \lor \neg \left(a \cdot 120 \leq 10^{-89}\right) \land a \cdot 120 \leq 10^{-15}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 58.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-95}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.18 \cdot 10^{-297}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-180}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))))
   (if (<= a -2.7e-61)
     (* a 120.0)
     (if (<= a -9.5e-84)
       t_1
       (if (<= a -1.08e-95)
         (* a 120.0)
         (if (<= a -6.8e-191)
           (/ (* -60.0 y) (- z t))
           (if (<= a -3.3e-232)
             t_1
             (if (<= a -1.18e-297)
               (* 60.0 (/ (- y x) t))
               (if (<= a 4.2e-180)
                 (* 60.0 (/ x (- z t)))
                 (if (<= a 7.5e-18) t_1 (* a 120.0)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -2.7e-61) {
		tmp = a * 120.0;
	} else if (a <= -9.5e-84) {
		tmp = t_1;
	} else if (a <= -1.08e-95) {
		tmp = a * 120.0;
	} else if (a <= -6.8e-191) {
		tmp = (-60.0 * y) / (z - t);
	} else if (a <= -3.3e-232) {
		tmp = t_1;
	} else if (a <= -1.18e-297) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 4.2e-180) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 7.5e-18) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    if (a <= (-2.7d-61)) then
        tmp = a * 120.0d0
    else if (a <= (-9.5d-84)) then
        tmp = t_1
    else if (a <= (-1.08d-95)) then
        tmp = a * 120.0d0
    else if (a <= (-6.8d-191)) then
        tmp = ((-60.0d0) * y) / (z - t)
    else if (a <= (-3.3d-232)) then
        tmp = t_1
    else if (a <= (-1.18d-297)) then
        tmp = 60.0d0 * ((y - x) / t)
    else if (a <= 4.2d-180) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= 7.5d-18) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -2.7e-61) {
		tmp = a * 120.0;
	} else if (a <= -9.5e-84) {
		tmp = t_1;
	} else if (a <= -1.08e-95) {
		tmp = a * 120.0;
	} else if (a <= -6.8e-191) {
		tmp = (-60.0 * y) / (z - t);
	} else if (a <= -3.3e-232) {
		tmp = t_1;
	} else if (a <= -1.18e-297) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 4.2e-180) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 7.5e-18) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	tmp = 0
	if a <= -2.7e-61:
		tmp = a * 120.0
	elif a <= -9.5e-84:
		tmp = t_1
	elif a <= -1.08e-95:
		tmp = a * 120.0
	elif a <= -6.8e-191:
		tmp = (-60.0 * y) / (z - t)
	elif a <= -3.3e-232:
		tmp = t_1
	elif a <= -1.18e-297:
		tmp = 60.0 * ((y - x) / t)
	elif a <= 4.2e-180:
		tmp = 60.0 * (x / (z - t))
	elif a <= 7.5e-18:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (a <= -2.7e-61)
		tmp = Float64(a * 120.0);
	elseif (a <= -9.5e-84)
		tmp = t_1;
	elseif (a <= -1.08e-95)
		tmp = Float64(a * 120.0);
	elseif (a <= -6.8e-191)
		tmp = Float64(Float64(-60.0 * y) / Float64(z - t));
	elseif (a <= -3.3e-232)
		tmp = t_1;
	elseif (a <= -1.18e-297)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	elseif (a <= 4.2e-180)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= 7.5e-18)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	tmp = 0.0;
	if (a <= -2.7e-61)
		tmp = a * 120.0;
	elseif (a <= -9.5e-84)
		tmp = t_1;
	elseif (a <= -1.08e-95)
		tmp = a * 120.0;
	elseif (a <= -6.8e-191)
		tmp = (-60.0 * y) / (z - t);
	elseif (a <= -3.3e-232)
		tmp = t_1;
	elseif (a <= -1.18e-297)
		tmp = 60.0 * ((y - x) / t);
	elseif (a <= 4.2e-180)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= 7.5e-18)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e-61], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -9.5e-84], t$95$1, If[LessEqual[a, -1.08e-95], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6.8e-191], N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.3e-232], t$95$1, If[LessEqual[a, -1.18e-297], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-180], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-18], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.69999999999999993e-61 or -9.49999999999999941e-84 < a < -1.08e-95 or 7.50000000000000015e-18 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 73.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.69999999999999993e-61 < a < -9.49999999999999941e-84 or -6.79999999999999988e-191 < a < -3.29999999999999985e-232 or 4.1999999999999997e-180 < a < 7.50000000000000015e-18

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 74.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around inf 59.3%

      \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z}} \]

   if -1.08e-95 < a < -6.79999999999999988e-191

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      2. clear-num 99.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - t}{60 \cdot \left(x - y\right)}}} + a \cdot 120 \]

      3. associate-/r/ 99.5%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \left(60 \cdot \left(x - y\right)\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \left(60 \cdot \left(x - y\right)\right)} + a \cdot 120 \]

   6. Taylor expanded in a around 0 88.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 88.0%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   8. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   9. Taylor expanded in x around 0 58.0%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} \]

   if -3.29999999999999985e-232 < a < -1.17999999999999993e-297

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.2%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0 87.3%

      \[\leadsto 60 \cdot \color{blue}{\left(-1 \cdot \frac{x - y}{t}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 87.3%

         \[\leadsto 60 \cdot \color{blue}{\frac{-1 \cdot \left(x - y\right)}{t}} \]

      2. neg-mul-1 87.3%

         \[\leadsto 60 \cdot \frac{\color{blue}{-\left(x - y\right)}}{t} \]

   7. Simplified 87.3%

      \[\leadsto 60 \cdot \color{blue}{\frac{-\left(x - y\right)}{t}} \]

   8. Taylor expanded in t around 0 87.3%

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t}} \]

   if -1.17999999999999993e-297 < a < 4.1999999999999997e-180

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 95.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in x around inf 64.9%

      \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-84}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-95}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-232}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -1.18 \cdot 10^{-297}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-180}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-18}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 58.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{-95}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-191}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-298}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-180}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))))
   (if (<= a -4.5e-57)
     (* a 120.0)
     (if (<= a -2.4e-85)
       t_1
       (if (<= a -1.16e-95)
         (* a 120.0)
         (if (<= a -2.4e-191)
           (/ (* -60.0 y) (- z t))
           (if (<= a -1.45e-232)
             t_1
             (if (<= a -1.72e-298)
               (* 60.0 (/ (- y x) t))
               (if (<= a 3.2e-180)
                 (/ (* 60.0 x) (- z t))
                 (if (<= a 1.16e-17) t_1 (* a 120.0)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -4.5e-57) {
		tmp = a * 120.0;
	} else if (a <= -2.4e-85) {
		tmp = t_1;
	} else if (a <= -1.16e-95) {
		tmp = a * 120.0;
	} else if (a <= -2.4e-191) {
		tmp = (-60.0 * y) / (z - t);
	} else if (a <= -1.45e-232) {
		tmp = t_1;
	} else if (a <= -1.72e-298) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 3.2e-180) {
		tmp = (60.0 * x) / (z - t);
	} else if (a <= 1.16e-17) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    if (a <= (-4.5d-57)) then
        tmp = a * 120.0d0
    else if (a <= (-2.4d-85)) then
        tmp = t_1
    else if (a <= (-1.16d-95)) then
        tmp = a * 120.0d0
    else if (a <= (-2.4d-191)) then
        tmp = ((-60.0d0) * y) / (z - t)
    else if (a <= (-1.45d-232)) then
        tmp = t_1
    else if (a <= (-1.72d-298)) then
        tmp = 60.0d0 * ((y - x) / t)
    else if (a <= 3.2d-180) then
        tmp = (60.0d0 * x) / (z - t)
    else if (a <= 1.16d-17) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -4.5e-57) {
		tmp = a * 120.0;
	} else if (a <= -2.4e-85) {
		tmp = t_1;
	} else if (a <= -1.16e-95) {
		tmp = a * 120.0;
	} else if (a <= -2.4e-191) {
		tmp = (-60.0 * y) / (z - t);
	} else if (a <= -1.45e-232) {
		tmp = t_1;
	} else if (a <= -1.72e-298) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 3.2e-180) {
		tmp = (60.0 * x) / (z - t);
	} else if (a <= 1.16e-17) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	tmp = 0
	if a <= -4.5e-57:
		tmp = a * 120.0
	elif a <= -2.4e-85:
		tmp = t_1
	elif a <= -1.16e-95:
		tmp = a * 120.0
	elif a <= -2.4e-191:
		tmp = (-60.0 * y) / (z - t)
	elif a <= -1.45e-232:
		tmp = t_1
	elif a <= -1.72e-298:
		tmp = 60.0 * ((y - x) / t)
	elif a <= 3.2e-180:
		tmp = (60.0 * x) / (z - t)
	elif a <= 1.16e-17:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (a <= -4.5e-57)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.4e-85)
		tmp = t_1;
	elseif (a <= -1.16e-95)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.4e-191)
		tmp = Float64(Float64(-60.0 * y) / Float64(z - t));
	elseif (a <= -1.45e-232)
		tmp = t_1;
	elseif (a <= -1.72e-298)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	elseif (a <= 3.2e-180)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (a <= 1.16e-17)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	tmp = 0.0;
	if (a <= -4.5e-57)
		tmp = a * 120.0;
	elseif (a <= -2.4e-85)
		tmp = t_1;
	elseif (a <= -1.16e-95)
		tmp = a * 120.0;
	elseif (a <= -2.4e-191)
		tmp = (-60.0 * y) / (z - t);
	elseif (a <= -1.45e-232)
		tmp = t_1;
	elseif (a <= -1.72e-298)
		tmp = 60.0 * ((y - x) / t);
	elseif (a <= 3.2e-180)
		tmp = (60.0 * x) / (z - t);
	elseif (a <= 1.16e-17)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e-57], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.4e-85], t$95$1, If[LessEqual[a, -1.16e-95], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.4e-191], N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.45e-232], t$95$1, If[LessEqual[a, -1.72e-298], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-180], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e-17], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.49999999999999973e-57 or -2.4000000000000001e-85 < a < -1.15999999999999997e-95 or 1.16e-17 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 73.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -4.49999999999999973e-57 < a < -2.4000000000000001e-85 or -2.3999999999999999e-191 < a < -1.45e-232 or 3.20000000000000015e-180 < a < 1.16e-17

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 74.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around inf 59.3%

      \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z}} \]

   if -1.15999999999999997e-95 < a < -2.3999999999999999e-191

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      2. clear-num 99.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - t}{60 \cdot \left(x - y\right)}}} + a \cdot 120 \]

      3. associate-/r/ 99.5%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \left(60 \cdot \left(x - y\right)\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \left(60 \cdot \left(x - y\right)\right)} + a \cdot 120 \]

   6. Taylor expanded in a around 0 88.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 88.0%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   8. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   9. Taylor expanded in x around 0 58.0%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} \]

   if -1.45e-232 < a < -1.71999999999999992e-298

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.2%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0 87.3%

      \[\leadsto 60 \cdot \color{blue}{\left(-1 \cdot \frac{x - y}{t}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 87.3%

         \[\leadsto 60 \cdot \color{blue}{\frac{-1 \cdot \left(x - y\right)}{t}} \]

      2. neg-mul-1 87.3%

         \[\leadsto 60 \cdot \frac{\color{blue}{-\left(x - y\right)}}{t} \]

   7. Simplified 87.3%

      \[\leadsto 60 \cdot \color{blue}{\frac{-\left(x - y\right)}{t}} \]

   8. Taylor expanded in t around 0 87.3%

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t}} \]

   if -1.71999999999999992e-298 < a < 3.20000000000000015e-180

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      2. clear-num 99.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - t}{60 \cdot \left(x - y\right)}}} + a \cdot 120 \]

      3. associate-/r/ 99.4%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \left(60 \cdot \left(x - y\right)\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \left(60 \cdot \left(x - y\right)\right)} + a \cdot 120 \]

   6. Taylor expanded in a around 0 95.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 95.9%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   8. Simplified 95.9%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   9. Taylor expanded in x around inf 65.2%

      \[\leadsto \frac{\color{blue}{60 \cdot x}}{z - t} \]
   10. Step-by-step derivation

       1. *-commutative 65.2%

          \[\leadsto \frac{\color{blue}{x \cdot 60}}{z - t} \]

   11. Simplified 65.2%

       \[\leadsto \frac{\color{blue}{x \cdot 60}}{z - t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-85}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{-95}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-191}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-232}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-298}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-180}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-17}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8: 77.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+100}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-25} \lor \neg \left(z \leq 3 \cdot 10^{+19}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ x z)))))
   (if (<= z -2.8e+179)
     t_1
     (if (<= z -1.42e+100)
       (+ (* a 120.0) (* -60.0 (/ y z)))
       (if (or (<= z -1.46e-25) (not (<= z 3e+19)))
         t_1
         (+ (* a 120.0) (* (- x y) (/ -60.0 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (x / z));
	double tmp;
	if (z <= -2.8e+179) {
		tmp = t_1;
	} else if (z <= -1.42e+100) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((z <= -1.46e-25) || !(z <= 3e+19)) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (60.0d0 * (x / z))
    if (z <= (-2.8d+179)) then
        tmp = t_1
    else if (z <= (-1.42d+100)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((z <= (-1.46d-25)) .or. (.not. (z <= 3d+19))) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (x / z));
	double tmp;
	if (z <= -2.8e+179) {
		tmp = t_1;
	} else if (z <= -1.42e+100) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((z <= -1.46e-25) || !(z <= 3e+19)) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * (x / z))
	tmp = 0
	if z <= -2.8e+179:
		tmp = t_1
	elif z <= -1.42e+100:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (z <= -1.46e-25) or not (z <= 3e+19):
		tmp = t_1
	else:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)))
	tmp = 0.0
	if (z <= -2.8e+179)
		tmp = t_1;
	elseif (z <= -1.42e+100)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif ((z <= -1.46e-25) || !(z <= 3e+19))
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * (x / z));
	tmp = 0.0;
	if (z <= -2.8e+179)
		tmp = t_1;
	elseif (z <= -1.42e+100)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((z <= -1.46e-25) || ~((z <= 3e+19)))
		tmp = t_1;
	else
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+179], t$95$1, If[LessEqual[z, -1.42e+100], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.46e-25], N[Not[LessEqual[z, 3e+19]], $MachinePrecision]], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e179 or -1.41999999999999999e100 < z < -1.46e-25 or 3e19 < z

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in x around inf 80.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. associate-*r/ 80.7%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} + a \cdot 120 \]

      2. *-commutative 80.7%

         \[\leadsto \frac{\color{blue}{x \cdot 60}}{z - t} + a \cdot 120 \]

   6. Simplified 80.7%

      \[\leadsto \color{blue}{\frac{x \cdot 60}{z - t}} + a \cdot 120 \]

   7. Taylor expanded in z around inf 79.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z}} + a \cdot 120 \]

   if -2.8e179 < z < -1.41999999999999999e100

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0 98.1%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]

   3. Taylor expanded in z around inf 86.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} + a \cdot 120 \]

   if -1.46e-25 < z < 3e19

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0 99.8%

      \[\leadsto \frac{\color{blue}{-60 \cdot y + 60 \cdot x}}{z - t} + a \cdot 120 \]

   3. Taylor expanded in z around 0 83.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{-60 \cdot y + 60 \cdot x}{t}} + a \cdot 120 \]
   4. Step-by-step derivation

      1. fma-def 83.3%

         \[\leadsto -1 \cdot \frac{\color{blue}{\mathsf{fma}\left(-60, y, 60 \cdot x\right)}}{t} + a \cdot 120 \]

      2. associate-*r/ 83.3%

         \[\leadsto \color{blue}{\frac{-1 \cdot \mathsf{fma}\left(-60, y, 60 \cdot x\right)}{t}} + a \cdot 120 \]

      3. fma-def 83.3%

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(-60 \cdot y + 60 \cdot x\right)}}{t} + a \cdot 120 \]

      4. +-commutative 83.3%

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(60 \cdot x + -60 \cdot y\right)}}{t} + a \cdot 120 \]

      5. distribute-lft-in 83.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(60 \cdot x\right) + -1 \cdot \left(-60 \cdot y\right)}}{t} + a \cdot 120 \]

      6. neg-mul-1 83.3%

         \[\leadsto \frac{\color{blue}{\left(-60 \cdot x\right)} + -1 \cdot \left(-60 \cdot y\right)}{t} + a \cdot 120 \]

      7. distribute-lft-neg-in 83.3%

         \[\leadsto \frac{\color{blue}{\left(-60\right) \cdot x} + -1 \cdot \left(-60 \cdot y\right)}{t} + a \cdot 120 \]

      8. metadata-eval 83.3%

         \[\leadsto \frac{\color{blue}{-60} \cdot x + -1 \cdot \left(-60 \cdot y\right)}{t} + a \cdot 120 \]

      9. neg-mul-1 83.3%

         \[\leadsto \frac{-60 \cdot x + \color{blue}{\left(--60 \cdot y\right)}}{t} + a \cdot 120 \]

      10. distribute-rgt-neg-in 83.3%

          \[\leadsto \frac{-60 \cdot x + \color{blue}{-60 \cdot \left(-y\right)}}{t} + a \cdot 120 \]

      11. distribute-lft-in 83.3%

          \[\leadsto \frac{\color{blue}{-60 \cdot \left(x + \left(-y\right)\right)}}{t} + a \cdot 120 \]

      12. sub-neg 83.3%

          \[\leadsto \frac{-60 \cdot \color{blue}{\left(x - y\right)}}{t} + a \cdot 120 \]

      13. *-commutative 83.3%

          \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot -60}}{t} + a \cdot 120 \]

      14. associate-*r/ 83.2%

          \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{-60}{t}} + a \cdot 120 \]

   5. Simplified 83.2%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{-60}{t}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+179}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+100}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-25} \lor \neg \left(z \leq 3 \cdot 10^{+19}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \]

Alternative 9: 56.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -2 \cdot 10^{-170}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{-62}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -5e+17)
   (* a 120.0)
   (if (<= (- z t) -2e-170)
     (* 60.0 (/ (- x y) z))
     (if (<= (- z t) 5e-62) (* 60.0 (/ (- y x) t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+17) {
		tmp = a * 120.0;
	} else if ((z - t) <= -2e-170) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((z - t) <= 5e-62) {
		tmp = 60.0 * ((y - x) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z - t) <= (-5d+17)) then
        tmp = a * 120.0d0
    else if ((z - t) <= (-2d-170)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if ((z - t) <= 5d-62) then
        tmp = 60.0d0 * ((y - x) / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+17) {
		tmp = a * 120.0;
	} else if ((z - t) <= -2e-170) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((z - t) <= 5e-62) {
		tmp = 60.0 * ((y - x) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -5e+17:
		tmp = a * 120.0
	elif (z - t) <= -2e-170:
		tmp = 60.0 * ((x - y) / z)
	elif (z - t) <= 5e-62:
		tmp = 60.0 * ((y - x) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -5e+17)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= -2e-170)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (Float64(z - t) <= 5e-62)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -5e+17)
		tmp = a * 120.0;
	elseif ((z - t) <= -2e-170)
		tmp = 60.0 * ((x - y) / z);
	elseif ((z - t) <= 5e-62)
		tmp = 60.0 * ((y - x) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -5e+17], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], -2e-170], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 5e-62], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 z t) < -5e17 or 5.0000000000000002e-62 < (-.f64 z t)

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 59.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -5e17 < (-.f64 z t) < -1.99999999999999997e-170

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 80.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around inf 60.0%

      \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z}} \]

   if -1.99999999999999997e-170 < (-.f64 z t) < 5.0000000000000002e-62

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 95.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0 74.9%

      \[\leadsto 60 \cdot \color{blue}{\left(-1 \cdot \frac{x - y}{t}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.9%

         \[\leadsto 60 \cdot \color{blue}{\frac{-1 \cdot \left(x - y\right)}{t}} \]

      2. neg-mul-1 74.9%

         \[\leadsto 60 \cdot \frac{\color{blue}{-\left(x - y\right)}}{t} \]

   7. Simplified 74.9%

      \[\leadsto 60 \cdot \color{blue}{\frac{-\left(x - y\right)}{t}} \]

   8. Taylor expanded in t around 0 74.9%

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -2 \cdot 10^{-170}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{-62}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-26} \lor \neg \left(z \leq 6200000000000\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.45e-26) (not (<= z 6200000000000.0)))
   (+ (* a 120.0) (/ 60.0 (/ z (- x y))))
   (+ (* a 120.0) (* (- x y) (/ -60.0 t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.45e-26) || !(z <= 6200000000000.0)) {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	} else {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.45d-26)) .or. (.not. (z <= 6200000000000.0d0))) then
        tmp = (a * 120.0d0) + (60.0d0 / (z / (x - y)))
    else
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.45e-26) || !(z <= 6200000000000.0)) {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	} else {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.45e-26) or not (z <= 6200000000000.0):
		tmp = (a * 120.0) + (60.0 / (z / (x - y)))
	else:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.45e-26) || !(z <= 6200000000000.0))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / Float64(x - y))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.45e-26) || ~((z <= 6200000000000.0)))
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	else
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.45e-26], N[Not[LessEqual[z, 6200000000000.0]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45e-26 or 6.2e12 < z

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 90.3%

      \[\leadsto \frac{60}{\color{blue}{\frac{z}{x - y}}} + a \cdot 120 \]

   if -2.45e-26 < z < 6.2e12

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0 99.8%

      \[\leadsto \frac{\color{blue}{-60 \cdot y + 60 \cdot x}}{z - t} + a \cdot 120 \]

   3. Taylor expanded in z around 0 83.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{-60 \cdot y + 60 \cdot x}{t}} + a \cdot 120 \]
   4. Step-by-step derivation

      1. fma-def 83.8%

         \[\leadsto -1 \cdot \frac{\color{blue}{\mathsf{fma}\left(-60, y, 60 \cdot x\right)}}{t} + a \cdot 120 \]

      2. associate-*r/ 83.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot \mathsf{fma}\left(-60, y, 60 \cdot x\right)}{t}} + a \cdot 120 \]

      3. fma-def 83.8%

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(-60 \cdot y + 60 \cdot x\right)}}{t} + a \cdot 120 \]

      4. +-commutative 83.8%

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(60 \cdot x + -60 \cdot y\right)}}{t} + a \cdot 120 \]

      5. distribute-lft-in 83.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(60 \cdot x\right) + -1 \cdot \left(-60 \cdot y\right)}}{t} + a \cdot 120 \]

      6. neg-mul-1 83.8%

         \[\leadsto \frac{\color{blue}{\left(-60 \cdot x\right)} + -1 \cdot \left(-60 \cdot y\right)}{t} + a \cdot 120 \]

      7. distribute-lft-neg-in 83.8%

         \[\leadsto \frac{\color{blue}{\left(-60\right) \cdot x} + -1 \cdot \left(-60 \cdot y\right)}{t} + a \cdot 120 \]

      8. metadata-eval 83.8%

         \[\leadsto \frac{\color{blue}{-60} \cdot x + -1 \cdot \left(-60 \cdot y\right)}{t} + a \cdot 120 \]

      9. neg-mul-1 83.8%

         \[\leadsto \frac{-60 \cdot x + \color{blue}{\left(--60 \cdot y\right)}}{t} + a \cdot 120 \]

      10. distribute-rgt-neg-in 83.8%

          \[\leadsto \frac{-60 \cdot x + \color{blue}{-60 \cdot \left(-y\right)}}{t} + a \cdot 120 \]

      11. distribute-lft-in 83.8%

          \[\leadsto \frac{\color{blue}{-60 \cdot \left(x + \left(-y\right)\right)}}{t} + a \cdot 120 \]

      12. sub-neg 83.8%

          \[\leadsto \frac{-60 \cdot \color{blue}{\left(x - y\right)}}{t} + a \cdot 120 \]

      13. *-commutative 83.8%

          \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot -60}}{t} + a \cdot 120 \]

      14. associate-*r/ 83.7%

          \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{-60}{t}} + a \cdot 120 \]

   5. Simplified 83.7%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{-60}{t}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-26} \lor \neg \left(z \leq 6200000000000\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \]

Alternative 11: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -19000000 \lor \neg \left(y \leq 8 \cdot 10^{+54}\right):\\ \;\;\;\;a \cdot 120 + \frac{-60 \cdot y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -19000000.0) (not (<= y 8e+54)))
   (+ (* a 120.0) (/ (* -60.0 y) (- z t)))
   (+ (* a 120.0) (/ (* 60.0 x) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -19000000.0) || !(y <= 8e+54)) {
		tmp = (a * 120.0) + ((-60.0 * y) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-19000000.0d0)) .or. (.not. (y <= 8d+54))) then
        tmp = (a * 120.0d0) + (((-60.0d0) * y) / (z - t))
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -19000000.0) || !(y <= 8e+54)) {
		tmp = (a * 120.0) + ((-60.0 * y) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -19000000.0) or not (y <= 8e+54):
		tmp = (a * 120.0) + ((-60.0 * y) / (z - t))
	else:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -19000000.0) || !(y <= 8e+54))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(-60.0 * y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -19000000.0) || ~((y <= 8e+54)))
		tmp = (a * 120.0) + ((-60.0 * y) / (z - t));
	else
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -19000000.0], N[Not[LessEqual[y, 8e+54]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e7 or 8.0000000000000006e54 < y

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0 86.1%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]

   if -1.9e7 < y < 8.0000000000000006e54

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in x around inf 94.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. associate-*r/ 94.5%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} + a \cdot 120 \]

      2. *-commutative 94.5%

         \[\leadsto \frac{\color{blue}{x \cdot 60}}{z - t} + a \cdot 120 \]

   6. Simplified 94.5%

      \[\leadsto \color{blue}{\frac{x \cdot 60}{z - t}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -19000000 \lor \neg \left(y \leq 8 \cdot 10^{+54}\right):\\ \;\;\;\;a \cdot 120 + \frac{-60 \cdot y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]

Alternative 12: 55.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -100000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{+15}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -100000000.0)
   (* a 120.0)
   (if (<= (- z t) 2e+15) (* 60.0 (/ x (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -100000000.0) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e+15) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z - t) <= (-100000000.0d0)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 2d+15) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -100000000.0) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e+15) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -100000000.0:
		tmp = a * 120.0
	elif (z - t) <= 2e+15:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -100000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 2e+15)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -100000000.0)
		tmp = a * 120.0;
	elseif ((z - t) <= 2e+15)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -100000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 2e+15], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -1e8 or 2e15 < (-.f64 z t)

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 61.6%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1e8 < (-.f64 z t) < 2e15

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 85.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in x around inf 52.3%

      \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -100000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{+15}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{-14}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -5e+17)
   (* a 120.0)
   (if (<= (- z t) 2e-14) (* 60.0 (/ (- x y) z)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+17) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e-14) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z - t) <= (-5d+17)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 2d-14) then
        tmp = 60.0d0 * ((x - y) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+17) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e-14) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -5e+17:
		tmp = a * 120.0
	elif (z - t) <= 2e-14:
		tmp = 60.0 * ((x - y) / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -5e+17)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 2e-14)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -5e+17)
		tmp = a * 120.0;
	elseif ((z - t) <= 2e-14)
		tmp = 60.0 * ((x - y) / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -5e+17], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 2e-14], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -5e17 or 2e-14 < (-.f64 z t)

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 61.2%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -5e17 < (-.f64 z t) < 2e-14

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 86.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around inf 54.0%

      \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{-14}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 + \frac{60}{\frac{z - t}{x - y}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* a 120.0) (/ 60.0 (/ (- z t) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + (60.0 / ((z - t) / (x - y)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (a * 120.0d0) + (60.0d0 / ((z - t) / (x - y)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + (60.0 / ((z - t) / (x - y)));
}

Python

def code(x, y, z, t, a):
	return (a * 120.0) + (60.0 / ((z - t) / (x - y)))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / Float64(x - y))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (a * 120.0) + (60.0 / ((z - t) / (x - y)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

4. Final simplification 99.8%

   \[\leadsto a \cdot 120 + \frac{60}{\frac{z - t}{x - y}} \]

Alternative 15: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* a 120.0) (/ (* 60.0 (- x y)) (- z t))))

C

double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + ((60.0 * (x - y)) / (z - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (a * 120.0d0) + ((60.0d0 * (x - y)) / (z - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + ((60.0 * (x - y)) / (z - t));
}

Python

def code(x, y, z, t, a):
	return (a * 120.0) + ((60.0 * (x - y)) / (z - t))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(a * 120.0) + Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (a * 120.0) + ((60.0 * (x - y)) / (z - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

2. Final simplification 99.8%

   \[\leadsto a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t} \]

Alternative 16: 53.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-146}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-152}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.6e-146)
   (* a 120.0)
   (if (<= a 5.6e-152) (* 60.0 (/ x z)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e-146) {
		tmp = a * 120.0;
	} else if (a <= 5.6e-152) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.6d-146)) then
        tmp = a * 120.0d0
    else if (a <= 5.6d-152) then
        tmp = 60.0d0 * (x / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e-146) {
		tmp = a * 120.0;
	} else if (a <= 5.6e-152) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.6e-146:
		tmp = a * 120.0
	elif a <= 5.6e-152:
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.6e-146)
		tmp = Float64(a * 120.0);
	elseif (a <= 5.6e-152)
		tmp = Float64(60.0 * Float64(x / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.6e-146)
		tmp = a * 120.0;
	elseif (a <= 5.6e-152)
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.6e-146], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 5.6e-152], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.6000000000000001e-146 or 5.59999999999999969e-152 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 65.1%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -4.6000000000000001e-146 < a < 5.59999999999999969e-152

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 93.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in x around inf 54.1%

      \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

   6. Taylor expanded in z around inf 39.6%

      \[\leadsto 60 \cdot \color{blue}{\frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-146}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-152}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17: 50.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* a 120.0))

C

double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = a * 120.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Python

def code(x, y, z, t, a):
	return a * 120.0

Julia

function code(x, y, z, t, a)
	return Float64(a * 120.0)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = a * 120.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

4. Taylor expanded in z around inf 50.1%

   \[\leadsto \color{blue}{120 \cdot a} \]

5. Final simplification 50.1%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (60.0d0 / ((z - t) / (x - y))) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(60.0 / Float64(Float64(z - t) / Float64(x - y))) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (60.0 / ((z - t) / (x - y))) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))