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

Percentage Accurate: 99.5% → 99.8%

Time: 14.7s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{x - y}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{1}{\frac{z - t}{x - y}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{\frac{z - t}{x - y}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \left(\frac{z - t}{x - y}\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\left(z - t\right), \left(x - y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(x - y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. --lowering--.f64 99.8%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(x, y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

4. Applied egg-rr 99.8%

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

Alternative 2: 76.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-60}{t} + a \cdot 120\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-25}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-57}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z} + a \cdot 120\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+62}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* x (/ -60.0 t)) (* a 120.0))))
   (if (<= t -3.8e+84)
     t_1
     (if (<= t -1.22e-25)
       (* (- x y) (/ 60.0 (- z t)))
       (if (<= t 5.5e-57)
         (+ (* (- x y) (/ 60.0 z)) (* a 120.0))
         (if (<= t 1.25e+62) (/ (- x y) (/ (- z t) 60.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * (-60.0 / t)) + (a * 120.0);
	double tmp;
	if (t <= -3.8e+84) {
		tmp = t_1;
	} else if (t <= -1.22e-25) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (t <= 5.5e-57) {
		tmp = ((x - y) * (60.0 / z)) + (a * 120.0);
	} else if (t <= 1.25e+62) {
		tmp = (x - y) / ((z - t) / 60.0);
	} else {
		tmp = t_1;
	}
	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 = (x * ((-60.0d0) / t)) + (a * 120.0d0)
    if (t <= (-3.8d+84)) then
        tmp = t_1
    else if (t <= (-1.22d-25)) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if (t <= 5.5d-57) then
        tmp = ((x - y) * (60.0d0 / z)) + (a * 120.0d0)
    else if (t <= 1.25d+62) then
        tmp = (x - y) / ((z - t) / 60.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * (-60.0 / t)) + (a * 120.0);
	double tmp;
	if (t <= -3.8e+84) {
		tmp = t_1;
	} else if (t <= -1.22e-25) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (t <= 5.5e-57) {
		tmp = ((x - y) * (60.0 / z)) + (a * 120.0);
	} else if (t <= 1.25e+62) {
		tmp = (x - y) / ((z - t) / 60.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * (-60.0 / t)) + (a * 120.0)
	tmp = 0
	if t <= -3.8e+84:
		tmp = t_1
	elif t <= -1.22e-25:
		tmp = (x - y) * (60.0 / (z - t))
	elif t <= 5.5e-57:
		tmp = ((x - y) * (60.0 / z)) + (a * 120.0)
	elif t <= 1.25e+62:
		tmp = (x - y) / ((z - t) / 60.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * Float64(-60.0 / t)) + Float64(a * 120.0))
	tmp = 0.0
	if (t <= -3.8e+84)
		tmp = t_1;
	elseif (t <= -1.22e-25)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (t <= 5.5e-57)
		tmp = Float64(Float64(Float64(x - y) * Float64(60.0 / z)) + Float64(a * 120.0));
	elseif (t <= 1.25e+62)
		tmp = Float64(Float64(x - y) / Float64(Float64(z - t) / 60.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * (-60.0 / t)) + (a * 120.0);
	tmp = 0.0;
	if (t <= -3.8e+84)
		tmp = t_1;
	elseif (t <= -1.22e-25)
		tmp = (x - y) * (60.0 / (z - t));
	elseif (t <= 5.5e-57)
		tmp = ((x - y) * (60.0 / z)) + (a * 120.0);
	elseif (t <= 1.25e+62)
		tmp = (x - y) / ((z - t) / 60.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+84], t$95$1, If[LessEqual[t, -1.22e-25], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-57], N[(N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+62], N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.8000000000000001e84 or 1.25000000000000007e62 < t

   1. Initial program 98.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{x - y}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{1}{\frac{z - t}{x - y}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{\frac{z - t}{x - y}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \left(\frac{z - t}{x - y}\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\left(z - t\right), \left(x - y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(x - y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(x, y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(60 \cdot \frac{x}{z - t}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot x}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot x\right), \left(z - t\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 60\right), \left(z - t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 60\right), \left(z - t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. --lowering--.f64 86.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 60\right), \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 86.7%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-60 \cdot \frac{x}{t}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-60 \cdot x}{t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x \cdot -60}{t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{-60}{t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-60}{t}\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 83.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   10. Simplified 83.7%

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

   if -3.8000000000000001e84 < t < -1.21999999999999999e-25

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 75.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 75.9%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \color{blue}{\left(x - y\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(\color{blue}{x} - y\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right) \]

      5. --lowering--.f64 76.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 76.0%

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

   if -1.21999999999999999e-25 < t < 5.50000000000000011e-57

   1. Initial program 99.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \color{blue}{z}\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 90.3%

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

   if 5.50000000000000011e-57 < t < 1.25000000000000007e62

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 74.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 74.5%

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

      1. associate-*l/ N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - y\right), \color{blue}{\left(\frac{z - t}{60}\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(\frac{\color{blue}{z - t}}{60}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(z - t\right), \color{blue}{60}\right)\right) \]

      8. --lowering--.f64 74.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), 60\right)\right) \]

   7. Applied egg-rr 74.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{-60}{t} + a \cdot 120\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-25}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-57}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z} + a \cdot 120\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+62}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-23}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-47}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e-23)
   (+ (/ (* y -60.0) (- z t)) (* a 120.0))
   (if (<= (* a 120.0) 2e-47)
     (/ 60.0 (/ (- z t) (- x y)))
     (+ (* (- x y) (/ 60.0 z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-23) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else if ((a * 120.0) <= 2e-47) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = ((x - y) * (60.0 / z)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-5d-23)) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else if ((a * 120.0d0) <= 2d-47) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = ((x - y) * (60.0d0 / z)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-23) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else if ((a * 120.0) <= 2e-47) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = ((x - y) * (60.0 / z)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e-23:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	elif (a * 120.0) <= 2e-47:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = ((x - y) * (60.0 / z)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-23)
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	elseif (Float64(a * 120.0) <= 2e-47)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(Float64(x - y) * Float64(60.0 / z)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e-23)
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	elseif ((a * 120.0) <= 2e-47)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = ((x - y) * (60.0 / z)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-23], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-47], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000002e-23

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(-60 \cdot y\right)}, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 89.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, y\right), \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   5. Simplified 89.2%

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

   if -5.0000000000000002e-23 < (*.f64 a #s(literal 120 binary64)) < 1.9999999999999999e-47

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 82.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 82.3%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(60, \color{blue}{\left(\frac{z - t}{x - y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\left(z - t\right), \color{blue}{\left(x - y\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\color{blue}{x} - y\right)\right)\right) \]

      6. --lowering--.f64 82.4%

         \[\leadsto \mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Applied egg-rr 82.4%

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

   if 1.9999999999999999e-47 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \color{blue}{z}\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 80.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-23}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-47}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+67}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+29)
   (* a 120.0)
   (if (<= (* a 120.0) 1e+67)
     (/ 60.0 (/ (- z t) (- x y)))
     (+ (* a 120.0) (/ (* y -60.0) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+29) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+67) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / 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) <= (-2d+29)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d+67) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / 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) <= -2e+29) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+67) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+29:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e+67:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+29)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e+67)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+29)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e+67)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (a * 120.0) + ((y * -60.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+29], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+67], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999983e29

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 79.0%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 79.0%

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

   if -1.99999999999999983e29 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999983e66

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 76.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 76.4%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(60, \color{blue}{\left(\frac{z - t}{x - y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\left(z - t\right), \color{blue}{\left(x - y\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\color{blue}{x} - y\right)\right)\right) \]

      6. --lowering--.f64 76.4%

         \[\leadsto \mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Applied egg-rr 76.4%

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

   if 9.99999999999999983e66 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(-60 \cdot y\right)}, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 89.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, y\right), \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   5. Simplified 89.4%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-60 \cdot \frac{y}{z}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-60 \cdot y}{z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-60 \cdot y\right), z\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-lowering-*.f64 82.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, y\right), z\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   8. Simplified 82.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+67}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+67}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+42)
   (* a 120.0)
   (if (<= (* a 120.0) 1e+67)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (/ (* y -60.0) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+42) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+67) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / 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) <= (-5d+42)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d+67) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / 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) <= -5e+42) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+67) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e+42:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e+67:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+42)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e+67)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e+42)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e+67)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + ((y * -60.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+42], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+67], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000007e42

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 80.0%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 80.0%

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

   if -5.00000000000000007e42 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999983e66

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 76.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 76.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x - y}{z - t}\right), \color{blue}{60}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), \left(z - t\right)\right), 60\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(z - t\right)\right), 60\right) \]

      6. --lowering--.f64 76.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, t\right)\right), 60\right) \]

   7. Applied egg-rr 76.0%

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

   if 9.99999999999999983e66 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(-60 \cdot y\right)}, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 89.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, y\right), \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   5. Simplified 89.4%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-60 \cdot \frac{y}{z}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-60 \cdot y}{z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-60 \cdot y\right), z\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-lowering-*.f64 82.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, y\right), z\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   8. Simplified 82.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+67}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+42)
   (* a 120.0)
   (if (<= (* a 120.0) 5e+16)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* x (/ 60.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+42) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e+16) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / 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) <= (-5d+42)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d+16) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (x * (60.0d0 / 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) <= -5e+42) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e+16) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e+42:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e+16:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (x * (60.0 / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+42)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e+16)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e+42)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e+16)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (x * (60.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+42], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+16], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000007e42

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 80.0%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 80.0%

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

   if -5.00000000000000007e42 < (*.f64 a #s(literal 120 binary64)) < 5e16

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 77.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 77.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x - y}{z - t}\right), \color{blue}{60}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), \left(z - t\right)\right), 60\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(z - t\right)\right), 60\right) \]

      6. --lowering--.f64 77.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, t\right)\right), 60\right) \]

   7. Applied egg-rr 77.9%

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

   if 5e16 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{x - y}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{1}{\frac{z - t}{x - y}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{\frac{z - t}{x - y}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \left(\frac{z - t}{x - y}\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\left(z - t\right), \left(x - y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(x - y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(x, y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(60 \cdot \frac{x}{z - t}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot x}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot x\right), \left(z - t\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 60\right), \left(z - t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 60\right), \left(z - t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. --lowering--.f64 89.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 60\right), \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 89.3%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 60\right), \color{blue}{z}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 75.1%

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

       1. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{60}{z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z} \cdot x\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z}\right), x\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

       4. /-lowering-/.f64 75.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, z\right), x\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   12. Applied egg-rr 75.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 6 \cdot 10^{+66}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+42)
   (* a 120.0)
   (if (<= (* a 120.0) 6e+66) (* 60.0 (/ (- x y) (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+42) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 6e+66) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-5d+42)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 6d+66) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+42) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 6e+66) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e+42:
		tmp = a * 120.0
	elif (a * 120.0) <= 6e+66:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+42)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 6e+66)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e+42)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 6e+66)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+42], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 6e+66], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000007e42 or 6.00000000000000005e66 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 78.7%

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

   if -5.00000000000000007e42 < (*.f64 a #s(literal 120 binary64)) < 6.00000000000000005e66

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 76.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 76.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x - y}{z - t}\right), \color{blue}{60}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), \left(z - t\right)\right), 60\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(z - t\right)\right), 60\right) \]

      6. --lowering--.f64 76.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, t\right)\right), 60\right) \]

   7. Applied egg-rr 76.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 6 \cdot 10^{+66}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-261}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e+39)
   (* a 120.0)
   (if (<= a 1.35e-261)
     (* -60.0 (/ y (- z t)))
     (if (<= a 5e+64) (/ (* 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 <= -8.5e+39) {
		tmp = a * 120.0;
	} else if (a <= 1.35e-261) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 5e+64) {
		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 <= (-8.5d+39)) then
        tmp = a * 120.0d0
    else if (a <= 1.35d-261) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 5d+64) 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 <= -8.5e+39) {
		tmp = a * 120.0;
	} else if (a <= 1.35e-261) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 5e+64) {
		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 <= -8.5e+39:
		tmp = a * 120.0
	elif a <= 1.35e-261:
		tmp = -60.0 * (y / (z - t))
	elif a <= 5e+64:
		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 <= -8.5e+39)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.35e-261)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 5e+64)
		tmp = Float64(Float64(60.0 * 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 <= -8.5e+39)
		tmp = a * 120.0;
	elseif (a <= 1.35e-261)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 5e+64)
		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, -8.5e+39], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.35e-261], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+64], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.49999999999999971e39 or 5e64 < a

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 78.7%

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

   if -8.49999999999999971e39 < a < 1.3499999999999999e-261

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 54.4%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 54.4%

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

   if 1.3499999999999999e-261 < a < 5e64

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot x\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, x\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 52.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, x\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 52.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-261}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-263}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.2e+40)
   (* a 120.0)
   (if (<= a 3.5e-263)
     (* -60.0 (/ y (- z t)))
     (if (<= a 5e+64) (/ x (/ (- z t) 60.0)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.2e+40) {
		tmp = a * 120.0;
	} else if (a <= 3.5e-263) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 5e+64) {
		tmp = x / ((z - t) / 60.0);
	} 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 <= (-2.2d+40)) then
        tmp = a * 120.0d0
    else if (a <= 3.5d-263) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 5d+64) then
        tmp = x / ((z - t) / 60.0d0)
    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 <= -2.2e+40) {
		tmp = a * 120.0;
	} else if (a <= 3.5e-263) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 5e+64) {
		tmp = x / ((z - t) / 60.0);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.2e+40:
		tmp = a * 120.0
	elif a <= 3.5e-263:
		tmp = -60.0 * (y / (z - t))
	elif a <= 5e+64:
		tmp = x / ((z - t) / 60.0)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.2e+40)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.5e-263)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 5e+64)
		tmp = Float64(x / Float64(Float64(z - t) / 60.0));
	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 <= -2.2e+40)
		tmp = a * 120.0;
	elseif (a <= 3.5e-263)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 5e+64)
		tmp = x / ((z - t) / 60.0);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.2e+40], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.5e-263], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+64], N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1999999999999999e40 or 5e64 < a

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 78.7%

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

   if -2.1999999999999999e40 < a < 3.49999999999999969e-263

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 54.4%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 54.4%

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

   if 3.49999999999999969e-263 < a < 5e64

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 71.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 71.1%

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

      1. associate-*l/ N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - y\right), \color{blue}{\left(\frac{z - t}{60}\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(\frac{\color{blue}{z - t}}{60}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(z - t\right), \color{blue}{60}\right)\right) \]

      8. --lowering--.f64 71.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), 60\right)\right) \]

   7. Applied egg-rr 71.0%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), 60\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 52.7%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-263}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-262}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e+39)
   (* a 120.0)
   (if (<= a 6.2e-262)
     (* -60.0 (/ y (- z t)))
     (if (<= a 5e+64) (* x (/ 60.0 (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+39) {
		tmp = a * 120.0;
	} else if (a <= 6.2e-262) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 5e+64) {
		tmp = x * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.5d+39)) then
        tmp = a * 120.0d0
    else if (a <= 6.2d-262) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 5d+64) then
        tmp = x * (60.0d0 / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+39) {
		tmp = a * 120.0;
	} else if (a <= 6.2e-262) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 5e+64) {
		tmp = x * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e+39:
		tmp = a * 120.0
	elif a <= 6.2e-262:
		tmp = -60.0 * (y / (z - t))
	elif a <= 5e+64:
		tmp = x * (60.0 / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e+39)
		tmp = Float64(a * 120.0);
	elseif (a <= 6.2e-262)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 5e+64)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e+39)
		tmp = a * 120.0;
	elseif (a <= 6.2e-262)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 5e+64)
		tmp = x * (60.0 / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e+39], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 6.2e-262], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+64], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.49999999999999971e39 or 5e64 < a

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 78.7%

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

   if -8.49999999999999971e39 < a < 6.1999999999999997e-262

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 54.4%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 54.4%

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

   if 6.1999999999999997e-262 < a < 5e64

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 71.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 71.1%

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

      1. associate-*l/ N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - y\right), \color{blue}{\left(\frac{z - t}{60}\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(\frac{\color{blue}{z - t}}{60}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(z - t\right), \color{blue}{60}\right)\right) \]

      8. --lowering--.f64 71.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), 60\right)\right) \]

   7. Applied egg-rr 71.0%

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

      1. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(\frac{z}{60} - \color{blue}{\frac{t}{60}}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\frac{z}{60}\right), \color{blue}{\left(\frac{t}{60}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(z, 60\right), \left(\frac{\color{blue}{t}}{60}\right)\right)\right) \]

      4. /-lowering-/.f64 71.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(z, 60\right), \mathsf{/.f64}\left(t, \color{blue}{60}\right)\right)\right) \]

   9. Applied egg-rr 71.0%

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

   10. Taylor expanded in x around inf

       \[\leadsto \color{blue}{\frac{x}{\frac{1}{60} \cdot z - \frac{1}{60} \cdot t}} \]
   11. Step-by-step derivation

       1. *-rgt-identity N/A

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

       2. associate-*r/ N/A

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

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{\frac{1}{60} \cdot z - \frac{1}{60} \cdot t}\right)}\right) \]

       4. distribute-lft-out-- N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{\frac{1}{60} \cdot \color{blue}{\left(z - t\right)}}\right)\right) \]

       5. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{\frac{1}{60}}}{\color{blue}{z - t}}\right)\right) \]

       6. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{60}{\color{blue}{z} - t}\right)\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(60, \color{blue}{\left(z - t\right)}\right)\right) \]

       8. --lowering--.f64 52.6%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   12. Simplified 52.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-262}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10^{-32}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (* 60.0 x) (- z t)) (* a 120.0))))
   (if (<= x -1.25e+101)
     t_1
     (if (<= x 1e-32) (+ (/ (* y -60.0) (- z t)) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((60.0 * x) / (z - t)) + (a * 120.0);
	double tmp;
	if (x <= -1.25e+101) {
		tmp = t_1;
	} else if (x <= 1e-32) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    if (x <= (-1.25d+101)) then
        tmp = t_1
    else if (x <= 1d-32) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = t_1
    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)) + (a * 120.0);
	double tmp;
	if (x <= -1.25e+101) {
		tmp = t_1;
	} else if (x <= 1e-32) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((60.0 * x) / (z - t)) + (a * 120.0)
	tmp = 0
	if x <= -1.25e+101:
		tmp = t_1
	elif x <= 1e-32:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0))
	tmp = 0.0
	if (x <= -1.25e+101)
		tmp = t_1;
	elseif (x <= 1e-32)
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((60.0 * x) / (z - t)) + (a * 120.0);
	tmp = 0.0;
	if (x <= -1.25e+101)
		tmp = t_1;
	elseif (x <= 1e-32)
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e+101], t$95$1, If[LessEqual[x, 1e-32], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999997e101 or 1.00000000000000006e-32 < x

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(60 \cdot \frac{x}{z - t}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot x}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot x\right), \left(z - t\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, x\right), \left(z - t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      4. --lowering--.f64 92.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, x\right), \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   5. Simplified 92.2%

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

   if -1.24999999999999997e101 < x < 1.00000000000000006e-32

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(-60 \cdot y\right)}, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 92.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, y\right), \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   5. Simplified 92.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq 10^{-32}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-37}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-270}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-229}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.75e-37)
   (* a 120.0)
   (if (<= a 1.15e-270)
     (* -60.0 (/ y z))
     (if (<= a 1.2e-229) (/ (* 60.0 x) z) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.75e-37) {
		tmp = a * 120.0;
	} else if (a <= 1.15e-270) {
		tmp = -60.0 * (y / z);
	} else if (a <= 1.2e-229) {
		tmp = (60.0 * x) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.75d-37)) then
        tmp = a * 120.0d0
    else if (a <= 1.15d-270) then
        tmp = (-60.0d0) * (y / z)
    else if (a <= 1.2d-229) then
        tmp = (60.0d0 * x) / z
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.75e-37) {
		tmp = a * 120.0;
	} else if (a <= 1.15e-270) {
		tmp = -60.0 * (y / z);
	} else if (a <= 1.2e-229) {
		tmp = (60.0 * x) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.75e-37:
		tmp = a * 120.0
	elif a <= 1.15e-270:
		tmp = -60.0 * (y / z)
	elif a <= 1.2e-229:
		tmp = (60.0 * x) / z
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.75e-37)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.15e-270)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (a <= 1.2e-229)
		tmp = Float64(Float64(60.0 * x) / z);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.75e-37)
		tmp = a * 120.0;
	elseif (a <= 1.15e-270)
		tmp = -60.0 * (y / z);
	elseif (a <= 1.2e-229)
		tmp = (60.0 * x) / z;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.75e-37], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.15e-270], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-229], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7499999999999999e-37 or 1.2e-229 < a

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 60.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 60.2%

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

   if -2.7499999999999999e-37 < a < 1.1500000000000001e-270

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 55.1%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 55.1%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 37.8%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 37.8%

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

   if 1.1500000000000001e-270 < a < 1.2e-229

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 96.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 96.0%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(x - y\right) \cdot 60\right), z\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(x - y\right), 60\right), z\right) \]

      5. --lowering--.f64 58.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, y\right), 60\right), z\right) \]

   8. Simplified 58.6%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\color{blue}{x}, 60\right), z\right) \]
   10. Step-by-step derivation

   11. Simplified 50.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-37}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-270}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-229}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e+40)
   (* a 120.0)
   (if (<= a 5e+64) (* (- x y) (/ 60.0 (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e+40) {
		tmp = a * 120.0;
	} else if (a <= 5e+64) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.95d+40)) then
        tmp = a * 120.0d0
    else if (a <= 5d+64) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e+40) {
		tmp = a * 120.0;
	} else if (a <= 5e+64) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.95e+40:
		tmp = a * 120.0
	elif a <= 5e+64:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e+40)
		tmp = Float64(a * 120.0);
	elseif (a <= 5e+64)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.95e+40)
		tmp = a * 120.0;
	elseif (a <= 5e+64)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e+40], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 5e+64], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.95e40 or 5e64 < a

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 78.7%

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

   if -1.95e40 < a < 5e64

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 76.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 76.6%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \color{blue}{\left(x - y\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(\color{blue}{x} - y\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right) \]

      5. --lowering--.f64 76.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 76.4%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-133}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e+39)
   (* a 120.0)
   (if (<= a 6.5e-133) (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+39) {
		tmp = a * 120.0;
	} else if (a <= 6.5e-133) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.5d+39)) then
        tmp = a * 120.0d0
    else if (a <= 6.5d-133) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+39) {
		tmp = a * 120.0;
	} else if (a <= 6.5e-133) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e+39:
		tmp = a * 120.0
	elif a <= 6.5e-133:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e+39)
		tmp = Float64(a * 120.0);
	elseif (a <= 6.5e-133)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e+39)
		tmp = a * 120.0;
	elseif (a <= 6.5e-133)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e+39], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 6.5e-133], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.49999999999999971e39 or 6.5000000000000002e-133 < a

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 67.3%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 67.3%

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

   if -8.49999999999999971e39 < a < 6.5000000000000002e-133

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 45.9%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 45.9%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-133}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-37}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-248}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.9e-37)
   (* a 120.0)
   (if (<= a 3.4e-248) (* -60.0 (/ y z)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e-37) {
		tmp = a * 120.0;
	} else if (a <= 3.4e-248) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.9d-37)) then
        tmp = a * 120.0d0
    else if (a <= 3.4d-248) then
        tmp = (-60.0d0) * (y / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e-37) {
		tmp = a * 120.0;
	} else if (a <= 3.4e-248) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.9e-37:
		tmp = a * 120.0
	elif a <= 3.4e-248:
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.9e-37)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.4e-248)
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.9e-37)
		tmp = a * 120.0;
	elseif (a <= 3.4e-248)
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.9e-37], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.4e-248], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.90000000000000005e-37 or 3.3999999999999998e-248 < a

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 58.1%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 58.1%

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

   if -2.90000000000000005e-37 < a < 3.3999999999999998e-248

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 52.6%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 52.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 35.5%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 35.5%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-37}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-248}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((x - y) * (60.0 / (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 = ((x - y) * (60.0d0 / (z - t))) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   2. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. --lowering--.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

4. Applied egg-rr 99.7%

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

5. Final simplification 99.7%

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

Alternative 17: 50.3% 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 99.4%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 46.9%

      \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

5. Simplified 46.9%

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

6. Final simplification 46.9%

   \[\leadsto a \cdot 120 \]
7. Add Preprocessing

Developer Target 1: 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 2024191 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

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