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

Percentage Accurate: 99.4% → 99.8%

Time: 12.9s

Alternatives: 14

Speedup: 1.1×

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, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

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

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

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

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

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

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

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

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

   8. *-lowering-*.f64 99.8

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

4. Applied egg-rr 99.8%

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

Alternative 2: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+30) t_1 (if (<= t_1 0.02) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+30) {
		tmp = t_1;
	} else if (t_1 <= 0.02) {
		tmp = 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 - y)) / (z - t)
    if (t_1 <= (-2d+30)) then
        tmp = t_1
    else if (t_1 <= 0.02d0) then
        tmp = 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 - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+30) {
		tmp = t_1;
	} else if (t_1 <= 0.02) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+30:
		tmp = t_1
	elif t_1 <= 0.02:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+30)
		tmp = t_1;
	elseif (t_1 <= 0.02)
		tmp = 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 - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+30)
		tmp = t_1;
	elseif (t_1 <= 0.02)
		tmp = 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[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+30], t$95$1, If[LessEqual[t$95$1, 0.02], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e30 or 0.0200000000000000004 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.0%

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

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

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

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

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

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

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

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

      5. --lowering--.f64 77.0

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

   5. Simplified 77.0%

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

   if -2e30 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 0.0200000000000000004

   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 75.4

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

   5. Simplified 75.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+30}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 0.02:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60}{z - t} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= y -5e+156)
     t_1
     (if (<= y 5.2e+154) (fma 120.0 a (* (/ 60.0 (- z t)) x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (y <= -5e+156) {
		tmp = t_1;
	} else if (y <= 5.2e+154) {
		tmp = fma(120.0, a, ((60.0 / (z - t)) * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (y <= -5e+156)
		tmp = t_1;
	elseif (y <= 5.2e+154)
		tmp = fma(120.0, a, Float64(Float64(60.0 / Float64(z - t)) * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+156], t$95$1, If[LessEqual[y, 5.2e+154], N[(120.0 * a + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999992e156 or 5.19999999999999978e154 < y

   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

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

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

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

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

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

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

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

      5. --lowering--.f64 78.3

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

   5. Simplified 78.3%

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

   if -4.99999999999999992e156 < y < 5.19999999999999978e154

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

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

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 90.8

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

   5. Simplified 90.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+156}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60}{z - t} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 400000000000:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ (- x y) z) (* a 120.0))))
   (if (<= z -2.2e-22)
     t_1
     (if (<= z 400000000000.0) (fma -60.0 (/ (- x y) t) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(60.0, ((x - y) / z), (a * 120.0));
	double tmp;
	if (z <= -2.2e-22) {
		tmp = t_1;
	} else if (z <= 400000000000.0) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0))
	tmp = 0.0
	if (z <= -2.2e-22)
		tmp = t_1;
	elseif (z <= 400000000000.0)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e-22], t$95$1, If[LessEqual[z, 400000000000.0], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e-22 or 4e11 < z

   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

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

      1. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

      4. *-lowering-*.f64 89.4

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

   5. Simplified 89.4%

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

   if -2.2000000000000001e-22 < z < 4e11

   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 0

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

      1. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

      4. *-lowering-*.f64 82.4

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

   5. Simplified 82.4%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 400000000000:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(120, a, \frac{60 \cdot x}{z}\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 430000000000:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 120.0 a (/ (* 60.0 x) z))))
   (if (<= z -1.5e-24)
     t_1
     (if (<= z 430000000000.0) (fma -60.0 (/ (- x y) t) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(120.0, a, ((60.0 * x) / z));
	double tmp;
	if (z <= -1.5e-24) {
		tmp = t_1;
	} else if (z <= 430000000000.0) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(120.0, a, Float64(Float64(60.0 * x) / z))
	tmp = 0.0
	if (z <= -1.5e-24)
		tmp = t_1;
	elseif (z <= 430000000000.0)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(120.0 * a + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e-24], t$95$1, If[LessEqual[z, 430000000000.0], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999998e-24 or 4.3e11 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

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

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 80.0

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

   5. Simplified 80.0%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 74.9

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

   8. Simplified 74.9%

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

   if -1.49999999999999998e-24 < z < 4.3e11

   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 0

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

      1. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

      4. *-lowering-*.f64 82.4

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

   5. Simplified 82.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60 \cdot x}{z}\right)\\ \mathbf{elif}\;z \leq 430000000000:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60 \cdot x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e-127)
   (* a 120.0)
   (if (<= a -1.3e-302)
     (* x (/ -60.0 t))
     (if (<= a 4.3e-120) (/ x (* z 0.016666666666666666)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-127) {
		tmp = a * 120.0;
	} else if (a <= -1.3e-302) {
		tmp = x * (-60.0 / t);
	} else if (a <= 4.3e-120) {
		tmp = x / (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 <= (-4.8d-127)) then
        tmp = a * 120.0d0
    else if (a <= (-1.3d-302)) then
        tmp = x * ((-60.0d0) / t)
    else if (a <= 4.3d-120) then
        tmp = x / (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 <= -4.8e-127) {
		tmp = a * 120.0;
	} else if (a <= -1.3e-302) {
		tmp = x * (-60.0 / t);
	} else if (a <= 4.3e-120) {
		tmp = x / (z * 0.016666666666666666);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e-127:
		tmp = a * 120.0
	elif a <= -1.3e-302:
		tmp = x * (-60.0 / t)
	elif a <= 4.3e-120:
		tmp = x / (z * 0.016666666666666666)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e-127)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.3e-302)
		tmp = Float64(x * Float64(-60.0 / t));
	elseif (a <= 4.3e-120)
		tmp = Float64(x / Float64(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 <= -4.8e-127)
		tmp = a * 120.0;
	elseif (a <= -1.3e-302)
		tmp = x * (-60.0 / t);
	elseif (a <= 4.3e-120)
		tmp = x / (z * 0.016666666666666666);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e-127], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.3e-302], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e-120], N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.79999999999999964e-127 or 4.29999999999999982e-120 < 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 64.4

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

   5. Simplified 64.4%

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

   if -4.79999999999999964e-127 < a < -1.30000000000000006e-302

   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. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 51.6

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

   5. Simplified 51.6%

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

   6. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 39.1

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

   8. Simplified 39.1%

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

   if -1.30000000000000006e-302 < a < 4.29999999999999982e-120

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 50.6

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

   5. Simplified 50.6%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 41.4

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

   8. Simplified 41.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. div-inv N/A

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

      6. metadata-eval N/A

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

      7. *-lowering-*.f64 41.4

         \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} \]

   10. Applied egg-rr 41.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e-127)
   (* a 120.0)
   (if (<= a -8.5e-307)
     (* x (/ -60.0 t))
     (if (<= a 2.9e-120) (* x (/ 60.0 z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e-127) {
		tmp = a * 120.0;
	} else if (a <= -8.5e-307) {
		tmp = x * (-60.0 / t);
	} else if (a <= 2.9e-120) {
		tmp = x * (60.0 / 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 <= (-3.8d-127)) then
        tmp = a * 120.0d0
    else if (a <= (-8.5d-307)) then
        tmp = x * ((-60.0d0) / t)
    else if (a <= 2.9d-120) then
        tmp = x * (60.0d0 / 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 <= -3.8e-127) {
		tmp = a * 120.0;
	} else if (a <= -8.5e-307) {
		tmp = x * (-60.0 / t);
	} else if (a <= 2.9e-120) {
		tmp = x * (60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e-127:
		tmp = a * 120.0
	elif a <= -8.5e-307:
		tmp = x * (-60.0 / t)
	elif a <= 2.9e-120:
		tmp = x * (60.0 / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e-127)
		tmp = Float64(a * 120.0);
	elseif (a <= -8.5e-307)
		tmp = Float64(x * Float64(-60.0 / t));
	elseif (a <= 2.9e-120)
		tmp = Float64(x * Float64(60.0 / 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 <= -3.8e-127)
		tmp = a * 120.0;
	elseif (a <= -8.5e-307)
		tmp = x * (-60.0 / t);
	elseif (a <= 2.9e-120)
		tmp = x * (60.0 / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e-127], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -8.5e-307], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-120], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.80000000000000003e-127 or 2.9e-120 < 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 64.4

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

   5. Simplified 64.4%

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

   if -3.80000000000000003e-127 < a < -8.4999999999999995e-307

   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. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 51.6

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

   5. Simplified 51.6%

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

   6. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 39.1

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

   8. Simplified 39.1%

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

   if -8.4999999999999995e-307 < a < 2.9e-120

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 50.6

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

   5. Simplified 50.6%

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

   6. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 41.4

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

   8. Simplified 41.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60 \cdot x}{z}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.1e-45)
   (fma 120.0 a (/ (* 60.0 x) z))
   (if (<= a 2.8e-17) (/ (* 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 <= -5.1e-45) {
		tmp = fma(120.0, a, ((60.0 * x) / z));
	} else if (a <= 2.8e-17) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.1e-45)
		tmp = fma(120.0, a, Float64(Float64(60.0 * x) / z));
	elseif (a <= 2.8e-17)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.1e-45], N[(120.0 * a + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-17], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.0999999999999997e-45

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

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

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 81.3

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

   5. Simplified 81.3%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 66.8

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

   8. Simplified 66.8%

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

   if -5.0999999999999997e-45 < a < 2.7999999999999999e-17

   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

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

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

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

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

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

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

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

      5. --lowering--.f64 80.3

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

   5. Simplified 80.3%

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

   if 2.7999999999999999e-17 < a

   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 79.6

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

   5. Simplified 79.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60 \cdot x}{z}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+155}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+142}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.45e+155)
   (* -60.0 (/ y (- z t)))
   (if (<= y 2e+142) (* a 120.0) (/ (* y -60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.45e+155) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= 2e+142) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.45d+155)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= 2d+142) then
        tmp = a * 120.0d0
    else
        tmp = (y * (-60.0d0)) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.45e+155) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= 2e+142) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.45e+155:
		tmp = -60.0 * (y / (z - t))
	elif y <= 2e+142:
		tmp = a * 120.0
	else:
		tmp = (y * -60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.45e+155)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= 2e+142)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.45e+155)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= 2e+142)
		tmp = a * 120.0;
	else
		tmp = (y * -60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.45e+155], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+142], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e155

   1. Initial program 99.8%

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

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

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

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

      3. --lowering--.f64 64.3

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

   5. Simplified 64.3%

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

   if -1.45e155 < y < 2.0000000000000001e142

   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 60.3

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

   5. Simplified 60.3%

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

   if 2.0000000000000001e142 < 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. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 99.4

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 70.7

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

   7. Simplified 70.7%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+155}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+142}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+160}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+143}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.6e+160)
   (* -60.0 (/ y (- z t)))
   (if (<= y 1.9e+143) (* a 120.0) (* y (/ 60.0 (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.6e+160) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= 1.9e+143) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / (t - 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 (y <= (-4.6d+160)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= 1.9d+143) then
        tmp = a * 120.0d0
    else
        tmp = y * (60.0d0 / (t - 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 (y <= -4.6e+160) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= 1.9e+143) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.6e+160:
		tmp = -60.0 * (y / (z - t))
	elif y <= 1.9e+143:
		tmp = a * 120.0
	else:
		tmp = y * (60.0 / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.6e+160)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= 1.9e+143)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y * Float64(60.0 / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.6e+160)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= 1.9e+143)
		tmp = a * 120.0;
	else
		tmp = y * (60.0 / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.6e+160], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+143], N[(a * 120.0), $MachinePrecision], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.59999999999999975e160

   1. Initial program 99.8%

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

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

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

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

      3. --lowering--.f64 64.3

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

   5. Simplified 64.3%

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

   if -4.59999999999999975e160 < y < 1.9e143

   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 60.3

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

   5. Simplified 60.3%

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

   if 1.9e143 < 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. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 99.4

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 70.7

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

   7. Simplified 70.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. frac-2neg N/A

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

      5. metadata-eval N/A

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

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

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

      7. neg-sub0 N/A

         \[\leadsto y \cdot \frac{60}{\color{blue}{0 - \left(z - t\right)}} \]

      8. sub-neg N/A

         \[\leadsto y \cdot \frac{60}{0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)}} \]

      9. +-commutative N/A

         \[\leadsto y \cdot \frac{60}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)}} \]

      10. associate--r+ N/A

          \[\leadsto y \cdot \frac{60}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(t\right)\right)\right) - z}} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 70.6

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

   9. Applied egg-rr 70.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+160}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+143}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+142}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -1.7e+157) t_1 (if (<= y 1.82e+142) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.7e+157) {
		tmp = t_1;
	} else if (y <= 1.82e+142) {
		tmp = 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) * (y / (z - t))
    if (y <= (-1.7d+157)) then
        tmp = t_1
    else if (y <= 1.82d+142) then
        tmp = 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 * (y / (z - t));
	double tmp;
	if (y <= -1.7e+157) {
		tmp = t_1;
	} else if (y <= 1.82e+142) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -1.7e+157:
		tmp = t_1
	elif y <= 1.82e+142:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -1.7e+157)
		tmp = t_1;
	elseif (y <= 1.82e+142)
		tmp = 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 * (y / (z - t));
	tmp = 0.0;
	if (y <= -1.7e+157)
		tmp = t_1;
	elseif (y <= 1.82e+142)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+157], t$95$1, If[LessEqual[y, 1.82e+142], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6999999999999999e157 or 1.8200000000000001e142 < y

   1. Initial program 99.8%

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

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

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

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

      3. --lowering--.f64 67.2

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

   5. Simplified 67.2%

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

   if -1.6999999999999999e157 < y < 1.8200000000000001e142

   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 60.3

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

   5. Simplified 60.3%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+157}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+142}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e-128)
   (* a 120.0)
   (if (<= a 3.2e-204) (* x (/ -60.0 t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e-128) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-204) {
		tmp = x * (-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 <= (-6d-128)) then
        tmp = a * 120.0d0
    else if (a <= 3.2d-204) then
        tmp = x * ((-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 <= -6e-128) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-204) {
		tmp = x * (-60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e-128:
		tmp = a * 120.0
	elif a <= 3.2e-204:
		tmp = x * (-60.0 / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e-128)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.2e-204)
		tmp = Float64(x * Float64(-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 <= -6e-128)
		tmp = a * 120.0;
	elseif (a <= 3.2e-204)
		tmp = x * (-60.0 / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e-128], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.2e-204], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.99999999999999956e-128 or 3.2e-204 < a

   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 60.4

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

   5. Simplified 60.4%

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

   if -5.99999999999999956e-128 < a < 3.2e-204

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 52.6

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

   5. Simplified 52.6%

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

   6. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 35.6

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

   8. Simplified 35.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.32 \cdot 10^{+215}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.32e+215) (* a 120.0) (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.32e+215) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 1.32d+215) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.32e+215) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.32e+215:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.32e+215)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.32e+215)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.32e+215], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.32000000000000005e215

   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 52.8

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

   5. Simplified 52.8%

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

   if 1.32000000000000005e215 < y

   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 0

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

      1. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

      4. *-lowering-*.f64 36.7

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

   5. Simplified 36.7%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 37.6

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

   8. Simplified 37.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 37.4

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

   10. Applied egg-rr 37.4%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.32 \cdot 10^{+215}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.8% accurate, 5.2× 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 49.9

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

5. Simplified 49.9%

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

6. Final simplification 49.9%

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

Developer Target 1: 99.8% accurate, 0.8× 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 2024197 
(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)))