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

Percentage Accurate: 99.4% → 99.8%

Time: 13.1s

Alternatives: 12

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: 99.4% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

Alternative 2: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t}\\ t_2 := t\_1 \cdot x + a \cdot 120\\ \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-122}:\\ \;\;\;\;t\_1 \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (- z t))) (t_2 (+ (* t_1 x) (* a 120.0))))
   (if (<= (* a 120.0) -4e-38)
     t_2
     (if (<= (* a 120.0) 2e-122) (* t_1 (- x y)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double t_2 = (t_1 * x) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -4e-38) {
		tmp = t_2;
	} else if ((a * 120.0) <= 2e-122) {
		tmp = t_1 * (x - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 / (z - t)
    t_2 = (t_1 * x) + (a * 120.0d0)
    if ((a * 120.0d0) <= (-4d-38)) then
        tmp = t_2
    else if ((a * 120.0d0) <= 2d-122) then
        tmp = t_1 * (x - y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double t_2 = (t_1 * x) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -4e-38) {
		tmp = t_2;
	} else if ((a * 120.0) <= 2e-122) {
		tmp = t_1 * (x - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / (z - t)
	t_2 = (t_1 * x) + (a * 120.0)
	tmp = 0
	if (a * 120.0) <= -4e-38:
		tmp = t_2
	elif (a * 120.0) <= 2e-122:
		tmp = t_1 * (x - y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(z - t))
	t_2 = Float64(Float64(t_1 * x) + Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-38)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= 2e-122)
		tmp = Float64(t_1 * Float64(x - y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / (z - t);
	t_2 = (t_1 * x) + (a * 120.0);
	tmp = 0.0;
	if ((a * 120.0) <= -4e-38)
		tmp = t_2;
	elseif ((a * 120.0) <= 2e-122)
		tmp = t_1 * (x - y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-38], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-122], N[(t$95$1 * N[(x - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -3.9999999999999998e-38 or 2.00000000000000012e-122 < (*.f64 a #s(literal 120 binary64))

   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 99.8%

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

   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 x around inf

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

   7. Simplified 88.4%

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

   if -3.9999999999999998e-38 < (*.f64 a #s(literal 120 binary64)) < 2.00000000000000012e-122

   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 86.0%

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

   5. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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 86.1%

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

   7. Applied egg-rr 86.1%

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

Alternative 3: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-7}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e+14)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-7) (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e+14) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-7) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-1d+14)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-7) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e+14) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-7) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e+14:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-7:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e+14)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-7)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e+14)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-7)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e+14], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-7], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e14 or 9.9999999999999995e-8 < (*.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 z around inf

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

      1. *-lowering-*.f64 79.1%

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

   5. Simplified 79.1%

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

   if -1e14 < (*.f64 a #s(literal 120 binary64)) < 9.9999999999999995e-8

   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 79.6%

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

   5. Simplified 79.6%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 79.7%

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

   7. Applied egg-rr 79.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-7}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-25}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e+14)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-25) (* (/ 60.0 (- z t)) (- x y)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e+14) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-25) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-1d+14)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-25) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e+14) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-25) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e+14:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-25:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e+14)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-25)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e+14)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-25)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e+14], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-25], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e14 or 1.00000000000000004e-25 < (*.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 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 -1e14 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000004e-25

   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 80.0%

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

   5. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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 80.1%

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

   7. Applied egg-rr 80.1%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-25}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{if}\;y \leq -6 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+82}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ 60.0 (/ (- t z) y)) (* a 120.0))))
   (if (<= y -6e+72)
     t_1
     (if (<= y 2.65e+82) (+ (* (/ 60.0 (- z t)) x) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / ((t - z) / y)) + (a * 120.0);
	double tmp;
	if (y <= -6e+72) {
		tmp = t_1;
	} else if (y <= 2.65e+82) {
		tmp = ((60.0 / (z - t)) * x) + (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 / ((t - z) / y)) + (a * 120.0d0)
    if (y <= (-6d+72)) then
        tmp = t_1
    else if (y <= 2.65d+82) then
        tmp = ((60.0d0 / (z - t)) * x) + (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 / ((t - z) / y)) + (a * 120.0);
	double tmp;
	if (y <= -6e+72) {
		tmp = t_1;
	} else if (y <= 2.65e+82) {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / ((t - z) / y)) + (a * 120.0)
	tmp = 0
	if y <= -6e+72:
		tmp = t_1
	elif y <= 2.65e+82:
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(Float64(t - z) / y)) + Float64(a * 120.0))
	tmp = 0.0
	if (y <= -6e+72)
		tmp = t_1;
	elseif (y <= 2.65e+82)
		tmp = Float64(Float64(Float64(60.0 / Float64(z - t)) * x) + 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 / ((t - z) / y)) + (a * 120.0);
	tmp = 0.0;
	if (y <= -6e+72)
		tmp = t_1;
	elseif (y <= 2.65e+82)
		tmp = ((60.0 / (z - t)) * x) + (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[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+72], t$95$1, If[LessEqual[y, 2.65e+82], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000006e72 or 2.64999999999999989e82 < y

   1. Initial program 99.7%

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \color{blue}{\left(-1 \cdot \frac{z - t}{y}\right)}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

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

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. unsub-neg N/A

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

      8. remove-double-neg N/A

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

      9. --lowering--.f64 92.4%

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

   7. Simplified 92.4%

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

   if -6.00000000000000006e72 < y < 2.64999999999999989e82

   1. Initial program 99.7%

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

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

   7. Simplified 91.9%

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

Alternative 6: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e-48)
   (* a 120.0)
   (if (<= a 5.5e-26) (/ (* (- x y) -60.0) t) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e-48) {
		tmp = a * 120.0;
	} else if (a <= 5.5e-26) {
		tmp = ((x - y) * -60.0) / 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 <= (-1.35d-48)) then
        tmp = a * 120.0d0
    else if (a <= 5.5d-26) then
        tmp = ((x - y) * (-60.0d0)) / 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 <= -1.35e-48) {
		tmp = a * 120.0;
	} else if (a <= 5.5e-26) {
		tmp = ((x - y) * -60.0) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e-48:
		tmp = a * 120.0
	elif a <= 5.5e-26:
		tmp = ((x - y) * -60.0) / t
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e-48)
		tmp = Float64(a * 120.0);
	elseif (a <= 5.5e-26)
		tmp = Float64(Float64(Float64(x - y) * -60.0) / 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 <= -1.35e-48)
		tmp = a * 120.0;
	elseif (a <= 5.5e-26)
		tmp = ((x - y) * -60.0) / t;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e-48], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 5.5e-26], N[(N[(N[(x - y), $MachinePrecision] * -60.0), $MachinePrecision] / t), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.35000000000000006e-48 or 5.5000000000000005e-26 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 76.0%

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

   5. Simplified 76.0%

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

   if -1.35000000000000006e-48 < a < 5.5000000000000005e-26

   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 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 51.2%

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

   8. Simplified 51.2%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{-51}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.26e-51)
   (* a 120.0)
   (if (<= a 3.1e-43) (/ x (* (- t z) -0.016666666666666666)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.26e-51) {
		tmp = a * 120.0;
	} else if (a <= 3.1e-43) {
		tmp = x / ((t - z) * -0.016666666666666666);
	} 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 <= (-1.26d-51)) then
        tmp = a * 120.0d0
    else if (a <= 3.1d-43) then
        tmp = x / ((t - z) * (-0.016666666666666666d0))
    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 <= -1.26e-51) {
		tmp = a * 120.0;
	} else if (a <= 3.1e-43) {
		tmp = x / ((t - z) * -0.016666666666666666);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.26e-51:
		tmp = a * 120.0
	elif a <= 3.1e-43:
		tmp = x / ((t - z) * -0.016666666666666666)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.26e-51)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.1e-43)
		tmp = Float64(x / Float64(Float64(t - z) * -0.016666666666666666));
	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 <= -1.26e-51)
		tmp = a * 120.0;
	elseif (a <= 3.1e-43)
		tmp = x / ((t - z) * -0.016666666666666666);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.26e-51], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.1e-43], N[(x / N[(N[(t - z), $MachinePrecision] * -0.016666666666666666), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2600000000000001e-51 or 3.0999999999999999e-43 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 74.4%

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

   5. Simplified 74.4%

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

   if -1.2600000000000001e-51 < a < 3.0999999999999999e-43

   1. Initial program 99.6%

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

      1. flip3-+ N/A

         \[\leadsto \frac{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}{\color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}} \]

      2. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}}}\right)\right) \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{-1}{60} \cdot \frac{t - z}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 49.2%

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

   7. Simplified 49.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{\left(t - z\right) \cdot -0.016666666666666666}{x}}} \]
   8. Step-by-step derivation

      1. clear-num N/A

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

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

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

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

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

      4. --lowering--.f64 49.2%

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

   9. Applied egg-rr 49.2%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot -0.016666666666666666}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{-51}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.4e-50)
   (* a 120.0)
   (if (<= a 7.2e-43) (* (/ 60.0 (- z t)) x) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e-50) {
		tmp = a * 120.0;
	} else if (a <= 7.2e-43) {
		tmp = (60.0 / (z - t)) * x;
	} 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 <= (-1.4d-50)) then
        tmp = a * 120.0d0
    else if (a <= 7.2d-43) then
        tmp = (60.0d0 / (z - t)) * x
    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 <= -1.4e-50) {
		tmp = a * 120.0;
	} else if (a <= 7.2e-43) {
		tmp = (60.0 / (z - t)) * x;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.4e-50:
		tmp = a * 120.0
	elif a <= 7.2e-43:
		tmp = (60.0 / (z - t)) * x
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.4e-50)
		tmp = Float64(a * 120.0);
	elseif (a <= 7.2e-43)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	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 <= -1.4e-50)
		tmp = a * 120.0;
	elseif (a <= 7.2e-43)
		tmp = (60.0 / (z - t)) * x;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.4e-50], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 7.2e-43], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3999999999999999e-50 or 7.1999999999999998e-43 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 74.4%

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

   5. Simplified 74.4%

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

   if -1.3999999999999999e-50 < a < 7.1999999999999998e-43

   1. Initial program 99.6%

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

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   6. 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. *-commutative N/A

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

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

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

      5. --lowering--.f64 49.1%

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

   7. Simplified 49.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 49.2%

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

   9. Applied egg-rr 49.2%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-24}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.2e-42)
   (* a 120.0)
   (if (<= a 2.9e-24) (* -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 <= -4.2e-42) {
		tmp = a * 120.0;
	} else if (a <= 2.9e-24) {
		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 <= (-4.2d-42)) then
        tmp = a * 120.0d0
    else if (a <= 2.9d-24) 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 <= -4.2e-42) {
		tmp = a * 120.0;
	} else if (a <= 2.9e-24) {
		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 <= -4.2e-42:
		tmp = a * 120.0
	elif a <= 2.9e-24:
		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 <= -4.2e-42)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.9e-24)
		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 <= -4.2e-42)
		tmp = a * 120.0;
	elseif (a <= 2.9e-24)
		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, -4.2e-42], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.9e-24], 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 < -4.20000000000000013e-42 or 2.8999999999999999e-24 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 76.4%

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

   5. Simplified 76.4%

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

   if -4.20000000000000013e-42 < a < 2.8999999999999999e-24

   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 39.9%

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

   5. Simplified 39.9%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-24}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-169}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e-169)
   (* a 120.0)
   (if (<= a 6.2e-44) (/ x (* t -0.016666666666666666)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e-169) {
		tmp = a * 120.0;
	} else if (a <= 6.2e-44) {
		tmp = x / (t * -0.016666666666666666);
	} 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 <= (-1.9d-169)) then
        tmp = a * 120.0d0
    else if (a <= 6.2d-44) then
        tmp = x / (t * (-0.016666666666666666d0))
    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 <= -1.9e-169) {
		tmp = a * 120.0;
	} else if (a <= 6.2e-44) {
		tmp = x / (t * -0.016666666666666666);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e-169:
		tmp = a * 120.0
	elif a <= 6.2e-44:
		tmp = x / (t * -0.016666666666666666)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e-169)
		tmp = Float64(a * 120.0);
	elseif (a <= 6.2e-44)
		tmp = Float64(x / Float64(t * -0.016666666666666666));
	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 <= -1.9e-169)
		tmp = a * 120.0;
	elseif (a <= 6.2e-44)
		tmp = x / (t * -0.016666666666666666);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e-169], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 6.2e-44], N[(x / N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e-169 or 6.19999999999999968e-44 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 69.1%

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

   5. Simplified 69.1%

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

   if -1.9e-169 < a < 6.19999999999999968e-44

   1. Initial program 99.5%

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

      1. flip3-+ N/A

         \[\leadsto \frac{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}{\color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}} \]

      2. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}}}\right)\right) \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{-1}{60} \cdot \frac{t - z}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 50.9%

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

   7. Simplified 50.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{\left(t - z\right) \cdot -0.016666666666666666}{x}}} \]
   8. Step-by-step derivation

      1. clear-num N/A

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

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

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

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

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

      4. --lowering--.f64 51.0%

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

   9. Applied egg-rr 51.0%

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

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{-1}{60} \cdot t\right)}\right) \]
   11. Step-by-step derivation

       1. *-commutative N/A

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

       2. *-lowering-*.f64 32.3%

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

   12. Simplified 32.3%

       \[\leadsto \frac{x}{\color{blue}{t \cdot -0.016666666666666666}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-169}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.02 \cdot 10^{+198}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1.02e+198) (* a 120.0) (* x (/ 60.0 z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.02e+198) {
		tmp = a * 120.0;
	} else {
		tmp = 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 (x <= 1.02d+198) then
        tmp = a * 120.0d0
    else
        tmp = 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 (x <= 1.02e+198) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.02e+198:
		tmp = a * 120.0
	else:
		tmp = x * (60.0 / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 1.02e+198)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(60.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 1.02e+198)
		tmp = a * 120.0;
	else
		tmp = x * (60.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 1.02e+198], N[(a * 120.0), $MachinePrecision], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.01999999999999998e198

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 55.1%

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

   5. Simplified 55.1%

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

   if 1.01999999999999998e198 < x

   1. Initial program 99.6%

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

      1. flip3-+ N/A

         \[\leadsto \frac{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}{\color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}} \]

      2. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right)}^{3} + {\left(a \cdot 120\right)}^{3}}{\frac{60 \cdot \left(x - y\right)}{z - t} \cdot \frac{60 \cdot \left(x - y\right)}{z - t} + \left(\left(a \cdot 120\right) \cdot \left(a \cdot 120\right) - \frac{60 \cdot \left(x - y\right)}{z - t} \cdot \left(a \cdot 120\right)\right)}}}\right)\right) \]

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{-1}{60} \cdot \frac{t - z}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 69.4%

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

   7. Simplified 69.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{\left(t - z\right) \cdot -0.016666666666666666}{x}}} \]
   8. Step-by-step derivation

      1. clear-num N/A

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

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

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

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

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

      4. --lowering--.f64 69.4%

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

   9. Applied egg-rr 69.4%

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

   10. Taylor expanded in t around 0

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

          \[\leadsto \frac{x \cdot 60}{z} \]

       3. associate-*r/ N/A

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

       4. metadata-eval N/A

          \[\leadsto x \cdot \frac{60 \cdot 1}{z} \]

       5. associate-*r/ N/A

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

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

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

       7. associate-*r/ N/A

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

       8. metadata-eval N/A

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

       9. /-lowering-/.f64 45.8%

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

   12. Simplified 45.8%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.02 \cdot 10^{+198}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.4% 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 99.7%

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

3. Taylor expanded in z around inf

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

   1. *-lowering-*.f64 51.6%

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

5. Simplified 51.6%

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

6. Final simplification 51.6%

   \[\leadsto a \cdot 120 \]
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 2024192 
(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)))