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

Percentage Accurate: 99.3% → 99.8%

Time: 14.2s

Alternatives: 18

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $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. +-commutative 99.8%

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

   2. fma-def 99.8%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-37}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{-z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+36)
   (+ (* a 120.0) (/ 60.0 (/ t y)))
   (if (<= (* a 120.0) -2e-57)
     (+ (* a 120.0) (/ (* y -60.0) z))
     (if (<= (* a 120.0) 1e-37)
       (* (/ 60.0 (- z t)) (- x y))
       (+ (* a 120.0) (/ 60.0 (/ (- z) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+36) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= -2e-57) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else if ((a * 120.0) <= 1e-37) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = (a * 120.0) + (60.0 / (-z / y));
	}
	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+36)) then
        tmp = (a * 120.0d0) + (60.0d0 / (t / y))
    else if ((a * 120.0d0) <= (-2d-57)) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / z)
    else if ((a * 120.0d0) <= 1d-37) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else
        tmp = (a * 120.0d0) + (60.0d0 / (-z / y))
    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+36) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= -2e-57) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else if ((a * 120.0) <= 1e-37) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = (a * 120.0) + (60.0 / (-z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+36:
		tmp = (a * 120.0) + (60.0 / (t / y))
	elif (a * 120.0) <= -2e-57:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	elif (a * 120.0) <= 1e-37:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = (a * 120.0) + (60.0 / (-z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+36)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(t / y)));
	elseif (Float64(a * 120.0) <= -2e-57)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	elseif (Float64(a * 120.0) <= 1e-37)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(-z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e+36)
		tmp = (a * 120.0) + (60.0 / (t / y));
	elseif ((a * 120.0) <= -2e-57)
		tmp = (a * 120.0) + ((y * -60.0) / z);
	elseif ((a * 120.0) <= 1e-37)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = (a * 120.0) + (60.0 / (-z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+36], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-57], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-37], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[((-z) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -4.00000000000000017e36

   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 0 77.8%

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

      1. neg-mul-1 77.8%

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

      2. distribute-neg-frac 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in x around 0 75.6%

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

   if -4.00000000000000017e36 < (*.f64 a 120) < -1.99999999999999991e-57

   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. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-/r/ 99.7%

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

      2. div-inv 99.6%

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

      3. associate-/r* 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in x around 0 94.4%

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

   9. Taylor expanded in z around inf 81.9%

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

       1. *-commutative 81.9%

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

       2. associate-*l/ 81.9%

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

   11. Simplified 81.9%

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

   if -1.99999999999999991e-57 < (*.f64 a 120) < 1.00000000000000007e-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* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-*l/ 81.0%

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

   8. Simplified 81.0%

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

      1. clear-num 81.0%

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

      2. *-un-lft-identity 81.0%

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

      3. times-frac 80.9%

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

      4. clear-num 80.8%

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

      5. div-inv 80.8%

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

      6. clear-num 80.9%

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

      7. associate-/r/ 81.1%

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

      8. clear-num 81.0%

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

      9. clear-num 81.0%

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

      10. clear-num 81.1%

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

   10. Applied egg-rr 81.1%

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

   if 1.00000000000000007e-37 < (*.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 80.5%

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

   5. Taylor expanded in x around 0 81.2%

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

      1. associate-*r/ 81.2%

         \[\leadsto \frac{60}{\color{blue}{\frac{-1 \cdot z}{y}}} + a \cdot 120 \]

      2. mul-1-neg 81.2%

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

   7. Simplified 81.2%

      \[\leadsto \frac{60}{\color{blue}{\frac{-z}{y}}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-37}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{-z}{y}}\\ \end{array} \]

Alternative 3: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-57} \lor \neg \left(a \cdot 120 \leq 10^{-37}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+36)
   (+ (* a 120.0) (/ 60.0 (/ t y)))
   (if (or (<= (* a 120.0) -2e-57) (not (<= (* a 120.0) 1e-37)))
     (+ (* a 120.0) (* -60.0 (/ y z)))
     (* (/ 60.0 (- z t)) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+36) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if (((a * 120.0) <= -2e-57) || !((a * 120.0) <= 1e-37)) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	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+36)) then
        tmp = (a * 120.0d0) + (60.0d0 / (t / y))
    else if (((a * 120.0d0) <= (-2d-57)) .or. (.not. ((a * 120.0d0) <= 1d-37))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else
        tmp = (60.0d0 / (z - t)) * (x - y)
    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+36) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if (((a * 120.0) <= -2e-57) || !((a * 120.0) <= 1e-37)) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+36:
		tmp = (a * 120.0) + (60.0 / (t / y))
	elif ((a * 120.0) <= -2e-57) or not ((a * 120.0) <= 1e-37):
		tmp = (a * 120.0) + (-60.0 * (y / z))
	else:
		tmp = (60.0 / (z - t)) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+36)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(t / y)));
	elseif ((Float64(a * 120.0) <= -2e-57) || !(Float64(a * 120.0) <= 1e-37))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e+36)
		tmp = (a * 120.0) + (60.0 / (t / y));
	elseif (((a * 120.0) <= -2e-57) || ~(((a * 120.0) <= 1e-37)))
		tmp = (a * 120.0) + (-60.0 * (y / z));
	else
		tmp = (60.0 / (z - t)) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+36], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-57], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-37]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -4.00000000000000017e36

   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 0 77.8%

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

      1. neg-mul-1 77.8%

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

      2. distribute-neg-frac 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in x around 0 75.6%

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

   if -4.00000000000000017e36 < (*.f64 a 120) < -1.99999999999999991e-57 or 1.00000000000000007e-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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 79.6%

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

   5. Taylor expanded in x around 0 81.3%

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

   if -1.99999999999999991e-57 < (*.f64 a 120) < 1.00000000000000007e-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* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-*l/ 81.0%

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

   8. Simplified 81.0%

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

      1. clear-num 81.0%

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

      2. *-un-lft-identity 81.0%

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

      3. times-frac 80.9%

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

      4. clear-num 80.8%

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

      5. div-inv 80.8%

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

      6. clear-num 80.9%

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

      7. associate-/r/ 81.1%

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

      8. clear-num 81.0%

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

      9. clear-num 81.0%

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

      10. clear-num 81.1%

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

   10. Applied egg-rr 81.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-57} \lor \neg \left(a \cdot 120 \leq 10^{-37}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 4: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-37}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+36)
   (+ (* a 120.0) (/ 60.0 (/ t y)))
   (if (<= (* a 120.0) -2e-57)
     (+ (* a 120.0) (/ (* y -60.0) z))
     (if (<= (* a 120.0) 1e-37)
       (* (/ 60.0 (- z t)) (- x y))
       (+ (* a 120.0) (* -60.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+36) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= -2e-57) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else if ((a * 120.0) <= 1e-37) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	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+36)) then
        tmp = (a * 120.0d0) + (60.0d0 / (t / y))
    else if ((a * 120.0d0) <= (-2d-57)) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / z)
    else if ((a * 120.0d0) <= 1d-37) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    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+36) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= -2e-57) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else if ((a * 120.0) <= 1e-37) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+36:
		tmp = (a * 120.0) + (60.0 / (t / y))
	elif (a * 120.0) <= -2e-57:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	elif (a * 120.0) <= 1e-37:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+36)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(t / y)));
	elseif (Float64(a * 120.0) <= -2e-57)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	elseif (Float64(a * 120.0) <= 1e-37)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e+36)
		tmp = (a * 120.0) + (60.0 / (t / y));
	elseif ((a * 120.0) <= -2e-57)
		tmp = (a * 120.0) + ((y * -60.0) / z);
	elseif ((a * 120.0) <= 1e-37)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = (a * 120.0) + (-60.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+36], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-57], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-37], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -4.00000000000000017e36

   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 0 77.8%

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

      1. neg-mul-1 77.8%

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

      2. distribute-neg-frac 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in x around 0 75.6%

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

   if -4.00000000000000017e36 < (*.f64 a 120) < -1.99999999999999991e-57

   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. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-/r/ 99.7%

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

      2. div-inv 99.6%

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

      3. associate-/r* 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in x around 0 94.4%

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

   9. Taylor expanded in z around inf 81.9%

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

       1. *-commutative 81.9%

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

       2. associate-*l/ 81.9%

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

   11. Simplified 81.9%

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

   if -1.99999999999999991e-57 < (*.f64 a 120) < 1.00000000000000007e-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* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-*l/ 81.0%

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

   8. Simplified 81.0%

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

      1. clear-num 81.0%

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

      2. *-un-lft-identity 81.0%

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

      3. times-frac 80.9%

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

      4. clear-num 80.8%

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

      5. div-inv 80.8%

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

      6. clear-num 80.9%

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

      7. associate-/r/ 81.1%

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

      8. clear-num 81.0%

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

      9. clear-num 81.0%

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

      10. clear-num 81.1%

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

   10. Applied egg-rr 81.1%

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

   if 1.00000000000000007e-37 < (*.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 80.5%

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

   5. Taylor expanded in x around 0 81.2%

      \[\leadsto \color{blue}{120 \cdot a + -60 \cdot \frac{y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-37}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 5: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+251}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+188}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t_1 \cdot \left(x - y\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+141}:\\ \;\;\;\;a \cdot 120 + t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (- z t))))
   (if (<= y -5.6e+251)
     (* -60.0 (/ y (- z t)))
     (if (<= y -2.6e+188)
       (+ (* a 120.0) (* -60.0 (/ y z)))
       (if (<= y -7.2e+19)
         (* t_1 (- x y))
         (if (<= y 3.2e+141)
           (+ (* a 120.0) (* t_1 x))
           (/ (* 60.0 (- x y)) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if (y <= -5.6e+251) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -2.6e+188) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (y <= -7.2e+19) {
		tmp = t_1 * (x - y);
	} else if (y <= 3.2e+141) {
		tmp = (a * 120.0) + (t_1 * x);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 / (z - t)
    if (y <= (-5.6d+251)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= (-2.6d+188)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (y <= (-7.2d+19)) then
        tmp = t_1 * (x - y)
    else if (y <= 3.2d+141) then
        tmp = (a * 120.0d0) + (t_1 * x)
    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 t_1 = 60.0 / (z - t);
	double tmp;
	if (y <= -5.6e+251) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -2.6e+188) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (y <= -7.2e+19) {
		tmp = t_1 * (x - y);
	} else if (y <= 3.2e+141) {
		tmp = (a * 120.0) + (t_1 * x);
	} else {
		tmp = (60.0 * (x - y)) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / (z - t)
	tmp = 0
	if y <= -5.6e+251:
		tmp = -60.0 * (y / (z - t))
	elif y <= -2.6e+188:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif y <= -7.2e+19:
		tmp = t_1 * (x - y)
	elif y <= 3.2e+141:
		tmp = (a * 120.0) + (t_1 * x)
	else:
		tmp = (60.0 * (x - y)) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(z - t))
	tmp = 0.0
	if (y <= -5.6e+251)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= -2.6e+188)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (y <= -7.2e+19)
		tmp = Float64(t_1 * Float64(x - y));
	elseif (y <= 3.2e+141)
		tmp = Float64(Float64(a * 120.0) + Float64(t_1 * x));
	else
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / (z - t);
	tmp = 0.0;
	if (y <= -5.6e+251)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= -2.6e+188)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (y <= -7.2e+19)
		tmp = t_1 * (x - y);
	elseif (y <= 3.2e+141)
		tmp = (a * 120.0) + (t_1 * x);
	else
		tmp = (60.0 * (x - y)) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+251], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e+188], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e+19], N[(t$95$1 * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+141], N[(N[(a * 120.0), $MachinePrecision] + N[(t$95$1 * x), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.6000000000000001e251

   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. Step-by-step derivation

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 100.0%

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

   if -5.6000000000000001e251 < y < -2.59999999999999987e188

   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 86.3%

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

   5. Taylor expanded in x around 0 86.3%

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

   if -2.59999999999999987e188 < y < -7.2e19

   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. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around 0 74.9%

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

      1. *-commutative 74.9%

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

      2. associate-*l/ 74.9%

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

   8. Simplified 74.9%

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

      1. clear-num 74.8%

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

      2. *-un-lft-identity 74.8%

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

      3. times-frac 74.7%

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

      4. clear-num 74.7%

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

      5. div-inv 74.7%

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

      6. clear-num 74.8%

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

      7. associate-/r/ 75.0%

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

      8. clear-num 74.8%

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

      9. clear-num 74.8%

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

      10. clear-num 75.0%

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

   10. Applied egg-rr 75.0%

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

   if -7.2e19 < y < 3.20000000000000019e141

   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. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 93.4%

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

      1. associate-*r/ 93.4%

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

      2. associate-*l/ 93.4%

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

      3. *-commutative 93.4%

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

   8. Simplified 93.4%

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

   if 3.20000000000000019e141 < y

   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. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 71.6%

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

   8. Simplified 71.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+251}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+188}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+141}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]

Alternative 6: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{-68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))) (t_2 (* -60.0 (/ y (- z t)))))
   (if (<= a -7.2e-68)
     (* a 120.0)
     (if (<= a -5.3e-173)
       t_2
       (if (<= a 1.25e-245)
         t_1
         (if (<= a 4.2e-236) t_2 (if (<= a 5e-56) t_1 (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -7.2e-68) {
		tmp = a * 120.0;
	} else if (a <= -5.3e-173) {
		tmp = t_2;
	} else if (a <= 1.25e-245) {
		tmp = t_1;
	} else if (a <= 4.2e-236) {
		tmp = t_2;
	} else if (a <= 5e-56) {
		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) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    t_2 = (-60.0d0) * (y / (z - t))
    if (a <= (-7.2d-68)) then
        tmp = a * 120.0d0
    else if (a <= (-5.3d-173)) then
        tmp = t_2
    else if (a <= 1.25d-245) then
        tmp = t_1
    else if (a <= 4.2d-236) then
        tmp = t_2
    else if (a <= 5d-56) 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 / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -7.2e-68) {
		tmp = a * 120.0;
	} else if (a <= -5.3e-173) {
		tmp = t_2;
	} else if (a <= 1.25e-245) {
		tmp = t_1;
	} else if (a <= 4.2e-236) {
		tmp = t_2;
	} else if (a <= 5e-56) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	t_2 = -60.0 * (y / (z - t))
	tmp = 0
	if a <= -7.2e-68:
		tmp = a * 120.0
	elif a <= -5.3e-173:
		tmp = t_2
	elif a <= 1.25e-245:
		tmp = t_1
	elif a <= 4.2e-236:
		tmp = t_2
	elif a <= 5e-56:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	t_2 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (a <= -7.2e-68)
		tmp = Float64(a * 120.0);
	elseif (a <= -5.3e-173)
		tmp = t_2;
	elseif (a <= 1.25e-245)
		tmp = t_1;
	elseif (a <= 4.2e-236)
		tmp = t_2;
	elseif (a <= 5e-56)
		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 / (z - t));
	t_2 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (a <= -7.2e-68)
		tmp = a * 120.0;
	elseif (a <= -5.3e-173)
		tmp = t_2;
	elseif (a <= 1.25e-245)
		tmp = t_1;
	elseif (a <= 4.2e-236)
		tmp = t_2;
	elseif (a <= 5e-56)
		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[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e-68], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -5.3e-173], t$95$2, If[LessEqual[a, 1.25e-245], t$95$1, If[LessEqual[a, 4.2e-236], t$95$2, If[LessEqual[a, 5e-56], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.20000000000000015e-68 or 4.99999999999999997e-56 < a

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 71.9%

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

   if -7.20000000000000015e-68 < a < -5.29999999999999964e-173 or 1.2499999999999999e-245 < a < 4.19999999999999958e-236

   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. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 60.5%

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

   if -5.29999999999999964e-173 < a < 1.2499999999999999e-245 or 4.19999999999999958e-236 < a < 4.99999999999999997e-56

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 57.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-173}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-245}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-236}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-56}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-245}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-56}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= a -2.5e-69)
     (* a 120.0)
     (if (<= a -1.75e-172)
       t_1
       (if (<= a 4e-245)
         (* (/ 60.0 (- z t)) x)
         (if (<= a 3.3e-235)
           t_1
           (if (<= a 4.5e-56) (* 60.0 (/ x (- z t))) (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -2.5e-69) {
		tmp = a * 120.0;
	} else if (a <= -1.75e-172) {
		tmp = t_1;
	} else if (a <= 4e-245) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 3.3e-235) {
		tmp = t_1;
	} else if (a <= 4.5e-56) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (a <= (-2.5d-69)) then
        tmp = a * 120.0d0
    else if (a <= (-1.75d-172)) then
        tmp = t_1
    else if (a <= 4d-245) then
        tmp = (60.0d0 / (z - t)) * x
    else if (a <= 3.3d-235) then
        tmp = t_1
    else if (a <= 4.5d-56) 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 t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -2.5e-69) {
		tmp = a * 120.0;
	} else if (a <= -1.75e-172) {
		tmp = t_1;
	} else if (a <= 4e-245) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 3.3e-235) {
		tmp = t_1;
	} else if (a <= 4.5e-56) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if a <= -2.5e-69:
		tmp = a * 120.0
	elif a <= -1.75e-172:
		tmp = t_1
	elif a <= 4e-245:
		tmp = (60.0 / (z - t)) * x
	elif a <= 3.3e-235:
		tmp = t_1
	elif a <= 4.5e-56:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (a <= -2.5e-69)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.75e-172)
		tmp = t_1;
	elseif (a <= 4e-245)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (a <= 3.3e-235)
		tmp = t_1;
	elseif (a <= 4.5e-56)
		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)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (a <= -2.5e-69)
		tmp = a * 120.0;
	elseif (a <= -1.75e-172)
		tmp = t_1;
	elseif (a <= 4e-245)
		tmp = (60.0 / (z - t)) * x;
	elseif (a <= 3.3e-235)
		tmp = t_1;
	elseif (a <= 4.5e-56)
		tmp = 60.0 * (x / (z - t));
	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[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e-69], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.75e-172], t$95$1, If[LessEqual[a, 4e-245], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 3.3e-235], t$95$1, If[LessEqual[a, 4.5e-56], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.50000000000000017e-69 or 4.5000000000000001e-56 < a

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 71.9%

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

   if -2.50000000000000017e-69 < a < -1.75000000000000014e-172 or 3.9999999999999997e-245 < a < 3.30000000000000028e-235

   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. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 60.5%

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

   if -1.75000000000000014e-172 < a < 3.9999999999999997e-245

   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. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*l/ 92.6%

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

   8. Simplified 92.6%

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

   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%

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

   12. Taylor expanded in x around 0 65.2%

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

       1. *-commutative 65.2%

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

       2. associate-*l/ 65.2%

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

       3. associate-*r/ 65.3%

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

   14. Simplified 65.3%

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

   if 3.30000000000000028e-235 < a < 4.5000000000000001e-56

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 47.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-172}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-245}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-235}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-56}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{\frac{z - t}{-60}}\\ \mathbf{elif}\;a \leq 10^{-245}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-237}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-55}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-63)
   (* a 120.0)
   (if (<= a -2.9e-175)
     (/ y (/ (- z t) -60.0))
     (if (<= a 1e-245)
       (* (/ 60.0 (- z t)) x)
       (if (<= a 3.2e-237)
         (* -60.0 (/ y (- z t)))
         (if (<= a 2.5e-55) (* 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 <= -2.4e-63) {
		tmp = a * 120.0;
	} else if (a <= -2.9e-175) {
		tmp = y / ((z - t) / -60.0);
	} else if (a <= 1e-245) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 3.2e-237) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 2.5e-55) {
		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 (a <= (-2.4d-63)) then
        tmp = a * 120.0d0
    else if (a <= (-2.9d-175)) then
        tmp = y / ((z - t) / (-60.0d0))
    else if (a <= 1d-245) then
        tmp = (60.0d0 / (z - t)) * x
    else if (a <= 3.2d-237) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 2.5d-55) 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 (a <= -2.4e-63) {
		tmp = a * 120.0;
	} else if (a <= -2.9e-175) {
		tmp = y / ((z - t) / -60.0);
	} else if (a <= 1e-245) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 3.2e-237) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 2.5e-55) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e-63:
		tmp = a * 120.0
	elif a <= -2.9e-175:
		tmp = y / ((z - t) / -60.0)
	elif a <= 1e-245:
		tmp = (60.0 / (z - t)) * x
	elif a <= 3.2e-237:
		tmp = -60.0 * (y / (z - t))
	elif a <= 2.5e-55:
		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 (a <= -2.4e-63)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.9e-175)
		tmp = Float64(y / Float64(Float64(z - t) / -60.0));
	elseif (a <= 1e-245)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (a <= 3.2e-237)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 2.5e-55)
		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 (a <= -2.4e-63)
		tmp = a * 120.0;
	elseif (a <= -2.9e-175)
		tmp = y / ((z - t) / -60.0);
	elseif (a <= 1e-245)
		tmp = (60.0 / (z - t)) * x;
	elseif (a <= 3.2e-237)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 2.5e-55)
		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[a, -2.4e-63], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.9e-175], N[(y / N[(N[(z - t), $MachinePrecision] / -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-245], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 3.2e-237], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-55], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.4000000000000001e-63 or 2.5000000000000001e-55 < a

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 71.9%

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

   if -2.4000000000000001e-63 < a < -2.89999999999999999e-175

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 53.5%

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

      1. associate-*r/ 53.6%

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

      2. *-commutative 53.6%

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

      3. associate-/l* 53.7%

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

   8. Simplified 53.7%

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

   if -2.89999999999999999e-175 < a < 9.9999999999999993e-246

   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. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*l/ 92.6%

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

   8. Simplified 92.6%

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

   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%

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

   12. Taylor expanded in x around 0 65.2%

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

       1. *-commutative 65.2%

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

       2. associate-*l/ 65.2%

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

       3. associate-*r/ 65.3%

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

   14. Simplified 65.3%

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

   if 9.9999999999999993e-246 < a < 3.2e-237

   1. Initial program 100.0%

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

      1. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 86.5%

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

   if 3.2e-237 < a < 2.5000000000000001e-55

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 47.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{\frac{z - t}{-60}}\\ \mathbf{elif}\;a \leq 10^{-245}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-237}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-55}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 81.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-121} \lor \neg \left(t \leq 5.7 \cdot 10^{-28}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.25e-121) (not (<= t 5.7e-28)))
   (+ (* a 120.0) (* (/ 60.0 (- z t)) x))
   (+ (* a 120.0) (/ 60.0 (/ z (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e-121) || !(t <= 5.7e-28)) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	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 ((t <= (-1.25d-121)) .or. (.not. (t <= 5.7d-28))) then
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    else
        tmp = (a * 120.0d0) + (60.0d0 / (z / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e-121) || !(t <= 5.7e-28)) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.25e-121) or not (t <= 5.7e-28):
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	else:
		tmp = (a * 120.0) + (60.0 / (z / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.25e-121) || !(t <= 5.7e-28))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.25e-121) || ~((t <= 5.7e-28)))
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	else
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.25e-121], N[Not[LessEqual[t, 5.7e-28]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999997e-121 or 5.7000000000000004e-28 < 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* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 82.8%

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

      1. associate-*r/ 82.9%

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

      2. associate-*l/ 82.9%

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

      3. *-commutative 82.9%

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

   8. Simplified 82.9%

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

   if -1.24999999999999997e-121 < t < 5.7000000000000004e-28

   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 inf 88.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-121} \lor \neg \left(t \leq 5.7 \cdot 10^{-28}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 10: 87.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+172}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.6e+172)
   (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
   (if (<= x 1.25e+26)
     (+ (* a 120.0) (/ (* y -60.0) (- z t)))
     (+ (* a 120.0) (* (/ 60.0 (- z t)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.6e+172) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else if (x <= 1.25e+26) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	}
	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 <= (-8.6d+172)) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    else if (x <= 1.25d+26) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    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 <= -8.6e+172) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else if (x <= 1.25e+26) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.6e+172:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	elif x <= 1.25e+26:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.6e+172)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	elseif (x <= 1.25e+26)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8.6e+172)
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	elseif (x <= 1.25e+26)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.6e+172], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+26], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.6000000000000005e172

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 88.7%

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

   if -8.6000000000000005e172 < x < 1.25e26

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 94.1%

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

   if 1.25e26 < x

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 92.3%

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

      1. associate-*r/ 92.4%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

   8. Simplified 92.4%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+172}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \end{array} \]

Alternative 11: 87.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+172}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+25}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9.2e+172)
   (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
   (if (<= x 6e+25)
     (+ (* a 120.0) (/ (* y -60.0) (- 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 (x <= -9.2e+172) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else if (x <= 6e+25) {
		tmp = (a * 120.0) + ((y * -60.0) / (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 (x <= (-9.2d+172)) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    else if (x <= 6d+25) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (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 (x <= -9.2e+172) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else if (x <= 6e+25) {
		tmp = (a * 120.0) + ((y * -60.0) / (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 x <= -9.2e+172:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	elif x <= 6e+25:
		tmp = (a * 120.0) + ((y * -60.0) / (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 (x <= -9.2e+172)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	elseif (x <= 6e+25)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / 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 (x <= -9.2e+172)
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	elseif (x <= 6e+25)
		tmp = (a * 120.0) + ((y * -60.0) / (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[LessEqual[x, -9.2e+172], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+25], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $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 3 regimes

2. if x < -9.2000000000000003e172

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 88.7%

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

   if -9.2000000000000003e172 < x < 6.00000000000000011e25

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 94.1%

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

   if 6.00000000000000011e25 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 92.4%

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

      1. *-commutative 92.4%

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

   4. Simplified 92.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+172}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+25}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]

Alternative 12: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-59}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-14}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-59)
   (* a 120.0)
   (if (<= a 1.35e-14) (* 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 <= -2.4e-59) {
		tmp = a * 120.0;
	} else if (a <= 1.35e-14) {
		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 <= (-2.4d-59)) then
        tmp = a * 120.0d0
    else if (a <= 1.35d-14) 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 <= -2.4e-59) {
		tmp = a * 120.0;
	} else if (a <= 1.35e-14) {
		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 <= -2.4e-59:
		tmp = a * 120.0
	elif a <= 1.35e-14:
		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 (a <= -2.4e-59)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.35e-14)
		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 <= -2.4e-59)
		tmp = a * 120.0;
	elseif (a <= 1.35e-14)
		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[a, -2.4e-59], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.35e-14], 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 a < -2.40000000000000015e-59 or 1.3499999999999999e-14 < a

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 73.7%

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

   if -2.40000000000000015e-59 < a < 1.3499999999999999e-14

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 81.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-59}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-14}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-59}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-20}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e-59)
   (* a 120.0)
   (if (<= a 5.3e-20) (* (/ 60.0 (- z t)) (- x y)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-59) {
		tmp = a * 120.0;
	} else if (a <= 5.3e-20) {
		tmp = (60.0 / (z - t)) * (x - y);
	} 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 <= (-3.2d-59)) then
        tmp = a * 120.0d0
    else if (a <= 5.3d-20) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    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 <= -3.2e-59) {
		tmp = a * 120.0;
	} else if (a <= 5.3e-20) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e-59:
		tmp = a * 120.0
	elif a <= 5.3e-20:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e-59)
		tmp = Float64(a * 120.0);
	elseif (a <= 5.3e-20)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	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 <= -3.2e-59)
		tmp = a * 120.0;
	elseif (a <= 5.3e-20)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e-59], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 5.3e-20], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1999999999999999e-59 or 5.3000000000000002e-20 < a

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 73.7%

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

   if -3.1999999999999999e-59 < a < 5.3000000000000002e-20

   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. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*l/ 81.4%

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

   8. Simplified 81.4%

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

      1. clear-num 81.3%

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

      2. *-un-lft-identity 81.3%

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

      3. times-frac 81.2%

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

      4. clear-num 81.1%

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

      5. div-inv 81.2%

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

      6. clear-num 81.2%

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

      7. associate-/r/ 81.4%

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

      8. clear-num 81.3%

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

      9. clear-num 81.3%

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

      10. clear-num 81.4%

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

   10. Applied egg-rr 81.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-59}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-20}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-59}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-32}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e-59)
   (* a 120.0)
   (if (<= a 1.95e-32)
     (* (/ 60.0 (- z t)) (- x y))
     (+ (* a 120.0) (* -60.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-59) {
		tmp = a * 120.0;
	} else if (a <= 1.95e-32) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	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 <= (-3.2d-59)) then
        tmp = a * 120.0d0
    else if (a <= 1.95d-32) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    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 <= -3.2e-59) {
		tmp = a * 120.0;
	} else if (a <= 1.95e-32) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e-59:
		tmp = a * 120.0
	elif a <= 1.95e-32:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e-59)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.95e-32)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e-59)
		tmp = a * 120.0;
	elseif (a <= 1.95e-32)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = (a * 120.0) + (-60.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e-59], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.95e-32], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1999999999999999e-59

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 70.7%

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

   if -3.1999999999999999e-59 < a < 1.9500000000000001e-32

   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. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-*l/ 81.0%

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

   8. Simplified 81.0%

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

      1. clear-num 81.0%

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

      2. *-un-lft-identity 81.0%

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

      3. times-frac 80.9%

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

      4. clear-num 80.8%

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

      5. div-inv 80.8%

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

      6. clear-num 80.9%

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

      7. associate-/r/ 81.1%

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

      8. clear-num 81.0%

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

      9. clear-num 81.0%

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

      10. clear-num 81.1%

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

   10. Applied egg-rr 81.1%

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

   if 1.9500000000000001e-32 < 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 80.5%

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

   5. Taylor expanded in x around 0 81.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-59}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-32}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 15: 99.7% accurate, 1.0× speedup

Math

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

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(Float64(60.0 / 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[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $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. 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. Step-by-step derivation

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 16: 56.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+19} \lor \neg \left(y \leq 10^{+141}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7.2e+19) (not (<= y 1e+141)))
   (* -60.0 (/ y (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.2e+19) || !(y <= 1e+141)) {
		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 ((y <= (-7.2d+19)) .or. (.not. (y <= 1d+141))) 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 ((y <= -7.2e+19) || !(y <= 1e+141)) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7.2e+19) or not (y <= 1e+141):
		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 ((y <= -7.2e+19) || !(y <= 1e+141))
		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 ((y <= -7.2e+19) || ~((y <= 1e+141)))
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7.2e+19], N[Not[LessEqual[y, 1e+141]], $MachinePrecision]], 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 y < -7.2e19 or 1.00000000000000002e141 < y

   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. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 59.0%

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

   if -7.2e19 < y < 1.00000000000000002e141

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

      3. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 62.3%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+19} \lor \neg \left(y \leq 10^{+141}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17: 52.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 10^{-172}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e-173)
   (* a 120.0)
   (if (<= a 1e-172) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e-173) {
		tmp = a * 120.0;
	} else if (a <= 1e-172) {
		tmp = -60.0 * (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 (a <= (-3.7d-173)) then
        tmp = a * 120.0d0
    else if (a <= 1d-172) then
        tmp = (-60.0d0) * (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 (a <= -3.7e-173) {
		tmp = a * 120.0;
	} else if (a <= 1e-172) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e-173:
		tmp = a * 120.0
	elif a <= 1e-172:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e-173)
		tmp = Float64(a * 120.0);
	elseif (a <= 1e-172)
		tmp = Float64(-60.0 * Float64(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 (a <= -3.7e-173)
		tmp = a * 120.0;
	elseif (a <= 1e-172)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e-173], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1e-172], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7e-173 or 1e-172 < a

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 62.1%

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

   if -3.7e-173 < a < 1e-172

   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 z around 0 63.5%

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

      1. neg-mul-1 63.5%

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

      2. distribute-neg-frac 63.5%

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

   6. Simplified 63.5%

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

   7. Taylor expanded in y around 0 41.9%

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

   8. Taylor expanded in a around 0 39.6%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 10^{-172}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18: 51.3% 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. +-commutative 99.8%

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

   2. fma-def 99.8%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in a around inf 49.2%

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

5. Final simplification 49.2%

   \[\leadsto a \cdot 120 \]

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 2023221 
(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)))