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

Percentage Accurate: 99.3% → 99.8%

Time: 18.0s

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: 99.3% 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: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. fma-def 99.4%

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

   3. associate-*l/ 99.8%

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

   4. *-commutative 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-33} \lor \neg \left(a \cdot 120 \leq -5 \cdot 10^{-96}\right) \land a \cdot 120 \leq 5 \cdot 10^{+39}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+27)
   (* a 120.0)
   (if (or (<= (* a 120.0) -4e-33)
           (and (not (<= (* a 120.0) -5e-96)) (<= (* a 120.0) 5e+39)))
     (* 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) <= -5e+27) {
		tmp = a * 120.0;
	} else if (((a * 120.0) <= -4e-33) || (!((a * 120.0) <= -5e-96) && ((a * 120.0) <= 5e+39))) {
		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) <= (-5d+27)) then
        tmp = a * 120.0d0
    else if (((a * 120.0d0) <= (-4d-33)) .or. (.not. ((a * 120.0d0) <= (-5d-96))) .and. ((a * 120.0d0) <= 5d+39)) 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) <= -5e+27) {
		tmp = a * 120.0;
	} else if (((a * 120.0) <= -4e-33) || (!((a * 120.0) <= -5e-96) && ((a * 120.0) <= 5e+39))) {
		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) <= -5e+27:
		tmp = a * 120.0
	elif ((a * 120.0) <= -4e-33) or (not ((a * 120.0) <= -5e-96) and ((a * 120.0) <= 5e+39)):
		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) <= -5e+27)
		tmp = Float64(a * 120.0);
	elseif ((Float64(a * 120.0) <= -4e-33) || (!(Float64(a * 120.0) <= -5e-96) && (Float64(a * 120.0) <= 5e+39)))
		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) <= -5e+27)
		tmp = a * 120.0;
	elseif (((a * 120.0) <= -4e-33) || (~(((a * 120.0) <= -5e-96)) && ((a * 120.0) <= 5e+39)))
		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], -5e+27], N[(a * 120.0), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-33], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-96]], $MachinePrecision], LessEqual[N[(a * 120.0), $MachinePrecision], 5e+39]]], 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) < -4.99999999999999979e27 or -4.0000000000000002e-33 < (*.f64 a 120) < -4.99999999999999995e-96 or 5.00000000000000015e39 < (*.f64 a 120)

   1. Initial program 99.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 82.4%

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

   if -4.99999999999999979e27 < (*.f64 a 120) < -4.0000000000000002e-33 or -4.99999999999999995e-96 < (*.f64 a 120) < 5.00000000000000015e39

   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 80.5%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-33} \lor \neg \left(a \cdot 120 \leq -5 \cdot 10^{-96}\right) \land a \cdot 120 \leq 5 \cdot 10^{+39}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-75}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+39}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+27)
   (* a 120.0)
   (if (<= (* a 120.0) -5e-75)
     (+ (* a 120.0) (/ 60.0 (/ t y)))
     (if (<= (* a 120.0) 5e+39) (* 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) <= -5e+27) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e-75) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= 5e+39) {
		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) <= (-5d+27)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-5d-75)) then
        tmp = (a * 120.0d0) + (60.0d0 / (t / y))
    else if ((a * 120.0d0) <= 5d+39) 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) <= -5e+27) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e-75) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= 5e+39) {
		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) <= -5e+27:
		tmp = a * 120.0
	elif (a * 120.0) <= -5e-75:
		tmp = (a * 120.0) + (60.0 / (t / y))
	elif (a * 120.0) <= 5e+39:
		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) <= -5e+27)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -5e-75)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(t / y)));
	elseif (Float64(a * 120.0) <= 5e+39)
		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) <= -5e+27)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -5e-75)
		tmp = (a * 120.0) + (60.0 / (t / y));
	elseif ((a * 120.0) <= 5e+39)
		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], -5e+27], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-75], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+39], 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) < -4.99999999999999979e27 or 5.00000000000000015e39 < (*.f64 a 120)

   1. Initial program 99.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 84.3%

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

   if -4.99999999999999979e27 < (*.f64 a 120) < -4.99999999999999979e-75

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 83.0%

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

   3. Taylor expanded in z around 0 74.6%

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

      1. associate-*r/ 74.5%

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

      2. associate-/l* 74.5%

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

   5. Simplified 74.5%

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

   if -4.99999999999999979e-75 < (*.f64 a 120) < 5.00000000000000015e39

   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 80.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-75}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+39}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-75}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+27)
   (* a 120.0)
   (if (<= (* a 120.0) -5e-75)
     (+ (* a 120.0) (/ 60.0 (/ t y)))
     (if (<= (* a 120.0) 5e+39) (/ (* (- x y) 60.0) (- z t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+27) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e-75) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= 5e+39) {
		tmp = ((x - y) * 60.0) / (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) <= (-5d+27)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-5d-75)) then
        tmp = (a * 120.0d0) + (60.0d0 / (t / y))
    else if ((a * 120.0d0) <= 5d+39) then
        tmp = ((x - y) * 60.0d0) / (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) <= -5e+27) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e-75) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= 5e+39) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e+27:
		tmp = a * 120.0
	elif (a * 120.0) <= -5e-75:
		tmp = (a * 120.0) + (60.0 / (t / y))
	elif (a * 120.0) <= 5e+39:
		tmp = ((x - y) * 60.0) / (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) <= -5e+27)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -5e-75)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(t / y)));
	elseif (Float64(a * 120.0) <= 5e+39)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / 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) <= -5e+27)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -5e-75)
		tmp = (a * 120.0) + (60.0 / (t / y));
	elseif ((a * 120.0) <= 5e+39)
		tmp = ((x - y) * 60.0) / (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], -5e+27], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-75], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+39], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -4.99999999999999979e27 or 5.00000000000000015e39 < (*.f64 a 120)

   1. Initial program 99.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 84.3%

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

   if -4.99999999999999979e27 < (*.f64 a 120) < -4.99999999999999979e-75

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 83.0%

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

   3. Taylor expanded in z around 0 74.6%

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

      1. associate-*r/ 74.5%

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

      2. associate-/l* 74.5%

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

   5. Simplified 74.5%

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

   if -4.99999999999999979e-75 < (*.f64 a 120) < 5.00000000000000015e39

   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 80.7%

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

      1. associate-*r/ 80.7%

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

   6. Applied egg-rr 80.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-75}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+55} \lor \neg \left(x \leq -3.8 \cdot 10^{+18}\right) \land x \leq 9.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.6e+98)
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))
   (if (or (<= x -3e+55) (and (not (<= x -3.8e+18)) (<= x 9.2e+98)))
     (+ (/ (* y -60.0) (- z t)) (* a 120.0))
     (+ (* 60.0 (/ x (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.6e+98) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else if ((x <= -3e+55) || (!(x <= -3.8e+18) && (x <= 9.2e+98))) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (60.0 * (x / (z - t))) + (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 (x <= (-3.6d+98)) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else if ((x <= (-3d+55)) .or. (.not. (x <= (-3.8d+18))) .and. (x <= 9.2d+98)) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = (60.0d0 * (x / (z - t))) + (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 (x <= -3.6e+98) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else if ((x <= -3e+55) || (!(x <= -3.8e+18) && (x <= 9.2e+98))) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.6e+98:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	elif (x <= -3e+55) or (not (x <= -3.8e+18) and (x <= 9.2e+98)):
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.6e+98)
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	elseif ((x <= -3e+55) || (!(x <= -3.8e+18) && (x <= 9.2e+98)))
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.6e+98)
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	elseif ((x <= -3e+55) || (~((x <= -3.8e+18)) && (x <= 9.2e+98)))
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.6e+98], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3e+55], And[N[Not[LessEqual[x, -3.8e+18]], $MachinePrecision], LessEqual[x, 9.2e+98]]], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.59999999999999981e98

   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 x around inf 94.3%

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

      1. associate-*r/ 94.5%

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

      2. associate-*l/ 94.5%

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

      3. *-commutative 94.5%

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

   6. Simplified 94.5%

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

   if -3.59999999999999981e98 < x < -3.00000000000000017e55 or -3.8e18 < x < 9.20000000000000053e98

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 92.2%

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

   if -3.00000000000000017e55 < x < -3.8e18 or 9.20000000000000053e98 < x

   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 x around inf 94.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+55} \lor \neg \left(x \leq -3.8 \cdot 10^{+18}\right) \land x \leq 9.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 6: 89.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{+51} \lor \neg \left(x \leq -5.7 \cdot 10^{+18}\right) \land x \leq 7.6 \cdot 10^{+99}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.8e+98)
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))
   (if (or (<= x -1.28e+51) (and (not (<= x -5.7e+18)) (<= x 7.6e+99)))
     (+ (/ 60.0 (/ (- t z) y)) (* a 120.0))
     (+ (* 60.0 (/ x (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.8e+98) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else if ((x <= -1.28e+51) || (!(x <= -5.7e+18) && (x <= 7.6e+99))) {
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 * (x / (z - t))) + (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 (x <= (-3.8d+98)) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else if ((x <= (-1.28d+51)) .or. (.not. (x <= (-5.7d+18))) .and. (x <= 7.6d+99)) then
        tmp = (60.0d0 / ((t - z) / y)) + (a * 120.0d0)
    else
        tmp = (60.0d0 * (x / (z - t))) + (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 (x <= -3.8e+98) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else if ((x <= -1.28e+51) || (!(x <= -5.7e+18) && (x <= 7.6e+99))) {
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.8e+98:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	elif (x <= -1.28e+51) or (not (x <= -5.7e+18) and (x <= 7.6e+99)):
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0)
	else:
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.8e+98)
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	elseif ((x <= -1.28e+51) || (!(x <= -5.7e+18) && (x <= 7.6e+99)))
		tmp = Float64(Float64(60.0 / Float64(Float64(t - z) / y)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.8e+98)
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	elseif ((x <= -1.28e+51) || (~((x <= -5.7e+18)) && (x <= 7.6e+99)))
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	else
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.8e+98], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.28e+51], And[N[Not[LessEqual[x, -5.7e+18]], $MachinePrecision], LessEqual[x, 7.6e+99]]], N[(N[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999999e98

   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 x around inf 94.3%

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

      1. associate-*r/ 94.5%

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

      2. associate-*l/ 94.5%

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

      3. *-commutative 94.5%

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

   6. Simplified 94.5%

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

   if -3.7999999999999999e98 < x < -1.27999999999999993e51 or -5.7e18 < x < 7.6e99

   1. Initial program 99.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 0 92.8%

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

      1. associate-*r/ 92.8%

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

      2. neg-mul-1 92.8%

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

   6. Simplified 92.8%

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

   if -1.27999999999999993e51 < x < -5.7e18 or 7.6e99 < x

   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 x around inf 94.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{+51} \lor \neg \left(x \leq -5.7 \cdot 10^{+18}\right) \land x \leq 7.6 \cdot 10^{+99}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 7: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-217} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-37}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -4e-217) (not (<= (* a 120.0) 2e-37)))
   (+ (* 60.0 (/ x (- z t))) (* a 120.0))
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -4e-217) || !((a * 120.0) <= 2e-37)) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = 60.0 * ((x - y) / (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 (((a * 120.0d0) <= (-4d-217)) .or. (.not. ((a * 120.0d0) <= 2d-37))) then
        tmp = (60.0d0 * (x / (z - t))) + (a * 120.0d0)
    else
        tmp = 60.0d0 * ((x - y) / (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 (((a * 120.0) <= -4e-217) || !((a * 120.0) <= 2e-37)) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -4e-217) or not ((a * 120.0) <= 2e-37):
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -4e-217) || !(Float64(a * 120.0) <= 2e-37))
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -4e-217) || ~(((a * 120.0) <= 2e-37)))
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-217], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-37]], $MachinePrecision]], N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -4.00000000000000033e-217 or 2.00000000000000013e-37 < (*.f64 a 120)

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 x around inf 85.7%

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

   if -4.00000000000000033e-217 < (*.f64 a 120) < 2.00000000000000013e-37

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 85.6%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-217} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-37}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 8: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-37}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-217)
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))
   (if (<= (* a 120.0) 2e-37)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* 60.0 (/ x (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e-217) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else if ((a * 120.0) <= 2e-37) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (60.0 * (x / (z - t))) + (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) <= (-4d-217)) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else if ((a * 120.0d0) <= 2d-37) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (60.0d0 * (x / (z - t))) + (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) <= -4e-217) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else if ((a * 120.0) <= 2e-37) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e-217:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	elif (a * 120.0) <= 2e-37:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-217)
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	elseif (Float64(a * 120.0) <= 2e-37)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + 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) <= -4e-217)
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	elseif ((a * 120.0) <= 2e-37)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-217], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-37], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -4.00000000000000033e-217

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 83.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*l/ 83.6%

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

      3. *-commutative 83.6%

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

   6. Simplified 83.6%

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

   if -4.00000000000000033e-217 < (*.f64 a 120) < 2.00000000000000013e-37

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 85.6%

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

   if 2.00000000000000013e-37 < (*.f64 a 120)

   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 x around inf 89.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-37}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 9: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-37}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-217)
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))
   (if (<= (* a 120.0) 2e-37)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (/ x (* (- z t) 0.016666666666666666)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e-217) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else if ((a * 120.0) <= 2e-37) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (x / ((z - t) * 0.016666666666666666)) + (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) <= (-4d-217)) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else if ((a * 120.0d0) <= 2d-37) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (x / ((z - t) * 0.016666666666666666d0)) + (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) <= -4e-217) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else if ((a * 120.0) <= 2e-37) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (x / ((z - t) * 0.016666666666666666)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e-217:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	elif (a * 120.0) <= 2e-37:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (x / ((z - t) * 0.016666666666666666)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-217)
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	elseif (Float64(a * 120.0) <= 2e-37)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(x / Float64(Float64(z - t) * 0.016666666666666666)) + 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) <= -4e-217)
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	elseif ((a * 120.0) <= 2e-37)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (x / ((z - t) * 0.016666666666666666)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-217], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-37], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -4.00000000000000033e-217

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 83.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*l/ 83.6%

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

      3. *-commutative 83.6%

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

   6. Simplified 83.6%

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

   if -4.00000000000000033e-217 < (*.f64 a 120) < 2.00000000000000013e-37

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 85.6%

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

   if 2.00000000000000013e-37 < (*.f64 a 120)

   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 x around inf 89.8%

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

      1. associate-*r/ 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-/l* 89.8%

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

      4. div-inv 89.8%

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

      5. metadata-eval 89.8%

         \[\leadsto \frac{x}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   6. Applied egg-rr 89.8%

      \[\leadsto \color{blue}{\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-37}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120\\ \end{array} \]

Alternative 10: 53.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+188}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+176}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-19}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+188)
   (* a 120.0)
   (if (<= z -8.8e+176)
     (* 60.0 (/ x (- z t)))
     (if (<= z -1.4e-207)
       (* a 120.0)
       (if (<= z 1.05e-19) (* -60.0 (/ (- x y) t)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+188) {
		tmp = a * 120.0;
	} else if (z <= -8.8e+176) {
		tmp = 60.0 * (x / (z - t));
	} else if (z <= -1.4e-207) {
		tmp = a * 120.0;
	} else if (z <= 1.05e-19) {
		tmp = -60.0 * ((x - y) / 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 <= (-9d+188)) then
        tmp = a * 120.0d0
    else if (z <= (-8.8d+176)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (z <= (-1.4d-207)) then
        tmp = a * 120.0d0
    else if (z <= 1.05d-19) then
        tmp = (-60.0d0) * ((x - y) / 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 <= -9e+188) {
		tmp = a * 120.0;
	} else if (z <= -8.8e+176) {
		tmp = 60.0 * (x / (z - t));
	} else if (z <= -1.4e-207) {
		tmp = a * 120.0;
	} else if (z <= 1.05e-19) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+188:
		tmp = a * 120.0
	elif z <= -8.8e+176:
		tmp = 60.0 * (x / (z - t))
	elif z <= -1.4e-207:
		tmp = a * 120.0
	elif z <= 1.05e-19:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+188)
		tmp = Float64(a * 120.0);
	elseif (z <= -8.8e+176)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (z <= -1.4e-207)
		tmp = Float64(a * 120.0);
	elseif (z <= 1.05e-19)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 <= -9e+188)
		tmp = a * 120.0;
	elseif (z <= -8.8e+176)
		tmp = 60.0 * (x / (z - t));
	elseif (z <= -1.4e-207)
		tmp = a * 120.0;
	elseif (z <= 1.05e-19)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+188], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, -8.8e+176], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4e-207], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, 1.05e-19], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.00000000000000021e188 or -8.80000000000000029e176 < z < -1.39999999999999996e-207 or 1.0499999999999999e-19 < z

   1. Initial program 99.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 67.4%

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

   if -9.00000000000000021e188 < z < -8.80000000000000029e176

   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* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around 0 99.4%

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

   5. Taylor expanded in x around inf 99.4%

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

   if -1.39999999999999996e-207 < z < 1.0499999999999999e-19

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 73.6%

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

   5. Taylor expanded in z around 0 62.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+188}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+176}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-19}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+176}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-19}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+190)
   (* a 120.0)
   (if (<= z -8.8e+176)
     (* (- x y) (/ 60.0 z))
     (if (<= z -3.6e-207)
       (* a 120.0)
       (if (<= z 1.5e-19) (* -60.0 (/ (- x y) t)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+190) {
		tmp = a * 120.0;
	} else if (z <= -8.8e+176) {
		tmp = (x - y) * (60.0 / z);
	} else if (z <= -3.6e-207) {
		tmp = a * 120.0;
	} else if (z <= 1.5e-19) {
		tmp = -60.0 * ((x - y) / 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 <= (-1d+190)) then
        tmp = a * 120.0d0
    else if (z <= (-8.8d+176)) then
        tmp = (x - y) * (60.0d0 / z)
    else if (z <= (-3.6d-207)) then
        tmp = a * 120.0d0
    else if (z <= 1.5d-19) then
        tmp = (-60.0d0) * ((x - y) / 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 <= -1e+190) {
		tmp = a * 120.0;
	} else if (z <= -8.8e+176) {
		tmp = (x - y) * (60.0 / z);
	} else if (z <= -3.6e-207) {
		tmp = a * 120.0;
	} else if (z <= 1.5e-19) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+190:
		tmp = a * 120.0
	elif z <= -8.8e+176:
		tmp = (x - y) * (60.0 / z)
	elif z <= -3.6e-207:
		tmp = a * 120.0
	elif z <= 1.5e-19:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+190)
		tmp = Float64(a * 120.0);
	elseif (z <= -8.8e+176)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	elseif (z <= -3.6e-207)
		tmp = Float64(a * 120.0);
	elseif (z <= 1.5e-19)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 <= -1e+190)
		tmp = a * 120.0;
	elseif (z <= -8.8e+176)
		tmp = (x - y) * (60.0 / z);
	elseif (z <= -3.6e-207)
		tmp = a * 120.0;
	elseif (z <= 1.5e-19)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+190], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, -8.8e+176], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-207], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, 1.5e-19], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0000000000000001e190 or -8.80000000000000029e176 < z < -3.5999999999999997e-207 or 1.49999999999999996e-19 < z

   1. Initial program 99.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 67.8%

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

   if -1.0000000000000001e190 < z < -8.80000000000000029e176

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 99.2%

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

   5. Taylor expanded in z around inf 84.7%

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

      1. associate-*r/ 84.9%

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

      2. associate-*l/ 84.4%

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

      3. *-commutative 84.4%

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

   7. Simplified 84.4%

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

   if -3.5999999999999997e-207 < z < 1.49999999999999996e-19

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 73.6%

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

   5. Taylor expanded in z around 0 62.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+176}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-19}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12: 53.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+176}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-208}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-19}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+190)
   (* a 120.0)
   (if (<= z -8.8e+176)
     (/ (* (- x y) 60.0) z)
     (if (<= z -6.5e-208)
       (* a 120.0)
       (if (<= z 2.6e-19) (* -60.0 (/ (- x y) t)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+190) {
		tmp = a * 120.0;
	} else if (z <= -8.8e+176) {
		tmp = ((x - y) * 60.0) / z;
	} else if (z <= -6.5e-208) {
		tmp = a * 120.0;
	} else if (z <= 2.6e-19) {
		tmp = -60.0 * ((x - y) / 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 <= (-1d+190)) then
        tmp = a * 120.0d0
    else if (z <= (-8.8d+176)) then
        tmp = ((x - y) * 60.0d0) / z
    else if (z <= (-6.5d-208)) then
        tmp = a * 120.0d0
    else if (z <= 2.6d-19) then
        tmp = (-60.0d0) * ((x - y) / 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 <= -1e+190) {
		tmp = a * 120.0;
	} else if (z <= -8.8e+176) {
		tmp = ((x - y) * 60.0) / z;
	} else if (z <= -6.5e-208) {
		tmp = a * 120.0;
	} else if (z <= 2.6e-19) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+190:
		tmp = a * 120.0
	elif z <= -8.8e+176:
		tmp = ((x - y) * 60.0) / z
	elif z <= -6.5e-208:
		tmp = a * 120.0
	elif z <= 2.6e-19:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+190)
		tmp = Float64(a * 120.0);
	elseif (z <= -8.8e+176)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / z);
	elseif (z <= -6.5e-208)
		tmp = Float64(a * 120.0);
	elseif (z <= 2.6e-19)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 <= -1e+190)
		tmp = a * 120.0;
	elseif (z <= -8.8e+176)
		tmp = ((x - y) * 60.0) / z;
	elseif (z <= -6.5e-208)
		tmp = a * 120.0;
	elseif (z <= 2.6e-19)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+190], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, -8.8e+176], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -6.5e-208], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, 2.6e-19], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0000000000000001e190 or -8.80000000000000029e176 < z < -6.4999999999999998e-208 or 2.60000000000000013e-19 < z

   1. Initial program 99.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 67.8%

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

   if -1.0000000000000001e190 < z < -8.80000000000000029e176

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 99.2%

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

   5. Taylor expanded in z around inf 84.7%

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

      1. associate-*r/ 84.9%

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

   7. Simplified 84.9%

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

   if -6.4999999999999998e-208 < z < 2.60000000000000013e-19

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 73.6%

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

   5. Taylor expanded in z around 0 62.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+176}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-208}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-19}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 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]

Derivation

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* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 14: 58.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-147}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-23}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e-147)
   (* a 120.0)
   (if (<= a 3.7e-23) (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e-147) {
		tmp = a * 120.0;
	} else if (a <= 3.7e-23) {
		tmp = -60.0 * (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 <= (-1d-147)) then
        tmp = a * 120.0d0
    else if (a <= 3.7d-23) then
        tmp = (-60.0d0) * (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 <= -1e-147) {
		tmp = a * 120.0;
	} else if (a <= 3.7e-23) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e-147:
		tmp = a * 120.0
	elif a <= 3.7e-23:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e-147)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.7e-23)
		tmp = Float64(-60.0 * Float64(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 <= -1e-147)
		tmp = a * 120.0;
	elseif (a <= 3.7e-23)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e-147], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.7e-23], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.9999999999999997e-148 or 3.7000000000000003e-23 < a

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 71.1%

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

   if -9.9999999999999997e-148 < a < 3.7000000000000003e-23

   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 83.2%

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

   5. Taylor expanded in x around 0 44.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-147}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-23}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15: 54.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-19}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e-207)
   (* a 120.0)
   (if (<= z 1.05e-19) (* -60.0 (/ (- x y) t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-207) {
		tmp = a * 120.0;
	} else if (z <= 1.05e-19) {
		tmp = -60.0 * ((x - y) / 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 <= (-1.15d-207)) then
        tmp = a * 120.0d0
    else if (z <= 1.05d-19) then
        tmp = (-60.0d0) * ((x - y) / 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 <= -1.15e-207) {
		tmp = a * 120.0;
	} else if (z <= 1.05e-19) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e-207:
		tmp = a * 120.0
	elif z <= 1.05e-19:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e-207)
		tmp = Float64(a * 120.0);
	elseif (z <= 1.05e-19)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 <= -1.15e-207)
		tmp = a * 120.0;
	elseif (z <= 1.05e-19)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e-207], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, 1.05e-19], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e-207 or 1.0499999999999999e-19 < z

   1. Initial program 99.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 65.5%

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

   if -1.15e-207 < z < 1.0499999999999999e-19

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 73.6%

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

   5. Taylor expanded in z around 0 62.4%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-19}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16: 53.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-259}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-154}:\\ \;\;\;\;-60 \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.75e-259)
   (* a 120.0)
   (if (<= a 3.8e-154) (* -60.0 (/ (- y) t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.75e-259) {
		tmp = a * 120.0;
	} else if (a <= 3.8e-154) {
		tmp = -60.0 * (-y / 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 <= (-1.75d-259)) then
        tmp = a * 120.0d0
    else if (a <= 3.8d-154) then
        tmp = (-60.0d0) * (-y / 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 <= -1.75e-259) {
		tmp = a * 120.0;
	} else if (a <= 3.8e-154) {
		tmp = -60.0 * (-y / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.75e-259:
		tmp = a * 120.0
	elif a <= 3.8e-154:
		tmp = -60.0 * (-y / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.75e-259)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.8e-154)
		tmp = Float64(-60.0 * Float64(Float64(-y) / 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 <= -1.75e-259)
		tmp = a * 120.0;
	elseif (a <= 3.8e-154)
		tmp = -60.0 * (-y / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.75e-259], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.8e-154], N[(-60.0 * N[((-y) / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7500000000000001e-259 or 3.8000000000000001e-154 < a

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 61.3%

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

   if -1.7500000000000001e-259 < a < 3.8000000000000001e-154

   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* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around 0 91.6%

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

   5. Taylor expanded in x around 0 53.0%

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

   6. Taylor expanded in z around 0 40.6%

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

      1. associate-*r/ 40.6%

         \[\leadsto -60 \cdot \color{blue}{\frac{-1 \cdot y}{t}} \]

      2. neg-mul-1 40.6%

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

   8. Simplified 40.6%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-259}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-154}:\\ \;\;\;\;-60 \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17: 51.6% 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 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 52.6%

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

5. Final simplification 52.6%

   \[\leadsto a \cdot 120 \]

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 2023279 
(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)))