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

Percentage Accurate: 99.5% → 99.8%

Time: 12.5s

Alternatives: 15

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: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. metadata-eval N/A

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

   4. times-frac N/A

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

   5. metadata-eval N/A

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

   6. associate-*r* N/A

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

   7. times-frac N/A

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

   8. metadata-eval N/A

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

   9. neg-mul-1 N/A

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

   10. distribute-neg-frac N/A

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

   11. distribute-lft-in N/A

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

   12. sub-neg N/A

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

   13. div-sub N/A

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

   14. lower-fma.f64 N/A

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

5. Simplified 99.8%

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

Alternative 2: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-136}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{-x}{t}, 120 \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+57}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+51)
     t_1
     (if (<= t_1 -5e-136)
       (fma 60.0 (/ (- x) t) (* 120.0 a))
       (if (<= t_1 2e+57) (* 120.0 a) 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+51) {
		tmp = t_1;
	} else if (t_1 <= -5e-136) {
		tmp = fma(60.0, (-x / t), (120.0 * a));
	} else if (t_1 <= 2e+57) {
		tmp = 120.0 * a;
	} 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+51)
		tmp = t_1;
	elseif (t_1 <= -5e-136)
		tmp = fma(60.0, Float64(Float64(-x) / t), Float64(120.0 * a));
	elseif (t_1 <= 2e+57)
		tmp = Float64(120.0 * a);
	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[t$95$1, -2e+51], t$95$1, If[LessEqual[t$95$1, -5e-136], N[(60.0 * N[((-x) / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+57], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e51 or 2.0000000000000001e57 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 85.7

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

   5. Simplified 85.7%

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

   if -2e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000002e-136

   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 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 82.0

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{-1 \cdot t}}, 120 \cdot a\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 75.5

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

   8. Simplified 75.5%

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

   if -5.0000000000000002e-136 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e57

   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. lower-*.f64 80.9

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

   5. Simplified 80.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+51}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{-136}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{-x}{t}, 120 \cdot a\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+57}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-136}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{x \cdot -60}{t}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+57}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+51)
     t_1
     (if (<= t_1 -5e-136)
       (fma 120.0 a (/ (* x -60.0) t))
       (if (<= t_1 2e+57) (* 120.0 a) 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+51) {
		tmp = t_1;
	} else if (t_1 <= -5e-136) {
		tmp = fma(120.0, a, ((x * -60.0) / t));
	} else if (t_1 <= 2e+57) {
		tmp = 120.0 * a;
	} 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+51)
		tmp = t_1;
	elseif (t_1 <= -5e-136)
		tmp = fma(120.0, a, Float64(Float64(x * -60.0) / t));
	elseif (t_1 <= 2e+57)
		tmp = Float64(120.0 * a);
	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[t$95$1, -2e+51], t$95$1, If[LessEqual[t$95$1, -5e-136], N[(120.0 * a + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+57], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e51 or 2.0000000000000001e57 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 85.7

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

   5. Simplified 85.7%

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

   if -2e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000002e-136

   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 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 82.0

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 75.5

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

   8. Simplified 75.5%

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

   if -5.0000000000000002e-136 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e57

   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. lower-*.f64 80.9

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

   5. Simplified 80.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+51}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{-136}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{x \cdot -60}{t}\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+57}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;t\_2 \leq 10^{+159}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ (- x y) t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+241)
     t_1
     (if (<= t_2 -2e+51)
       (* y (/ -60.0 (- z t)))
       (if (<= t_2 1e+159) (* 120.0 a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+241) {
		tmp = t_1;
	} else if (t_2 <= -2e+51) {
		tmp = y * (-60.0 / (z - t));
	} else if (t_2 <= 1e+159) {
		tmp = 120.0 * a;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * ((x - y) / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+241)) then
        tmp = t_1
    else if (t_2 <= (-2d+51)) then
        tmp = y * ((-60.0d0) / (z - t))
    else if (t_2 <= 1d+159) then
        tmp = 120.0d0 * a
    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) / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+241) {
		tmp = t_1;
	} else if (t_2 <= -2e+51) {
		tmp = y * (-60.0 / (z - t));
	} else if (t_2 <= 1e+159) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * ((x - y) / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+241:
		tmp = t_1
	elif t_2 <= -2e+51:
		tmp = y * (-60.0 / (z - t))
	elif t_2 <= 1e+159:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(Float64(x - y) / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+241)
		tmp = t_1;
	elseif (t_2 <= -2e+51)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	elseif (t_2 <= 1e+159)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * ((x - y) / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+241)
		tmp = t_1;
	elseif (t_2 <= -2e+51)
		tmp = y * (-60.0 / (z - t));
	elseif (t_2 <= 1e+159)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+241], t$95$1, If[LessEqual[t$95$2, -2e+51], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+159], N[(120.0 * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e241 or 9.9999999999999993e158 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 94.4

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

   5. Simplified 94.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 66.4

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

   8. Simplified 66.4%

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

   if -2.0000000000000001e241 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e51

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r* N/A

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

      7. times-frac N/A

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

      8. metadata-eval N/A

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

      9. neg-mul-1 N/A

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

      10. distribute-neg-frac N/A

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

      11. distribute-lft-in N/A

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

      12. sub-neg N/A

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

      13. div-sub N/A

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

      14. lower-fma.f64 N/A

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

   5. Simplified 99.6%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 99.5

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

   8. Simplified 99.5%

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

   9. Taylor expanded in a around inf

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

       1. lower-*.f64 N/A

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

       2. +-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-/.f64 N/A

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

       5. lower--.f64 N/A

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

       6. *-commutative N/A

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

       7. lower-*.f64 N/A

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

       8. lower--.f64 89.8

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

   11. Simplified 89.8%

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

   12. Taylor expanded in y around inf

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

       4. metadata-eval N/A

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

       5. distribute-neg-frac N/A

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

       6. metadata-eval N/A

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

       7. associate-*r/ N/A

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

       8. lower-*.f64 N/A

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

       9. associate-*r/ N/A

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

       10. metadata-eval N/A

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

       11. distribute-neg-frac N/A

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

       12. metadata-eval N/A

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

       13. lower-/.f64 N/A

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

       14. lower--.f64 52.7

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

   14. Simplified 52.7%

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

   if -2e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999993e158

   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. lower-*.f64 71.5

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

   5. Simplified 71.5%

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

Alternative 5: 83.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+62)
     t_1
     (if (<= t_1 5e+118) (fma -60.0 (/ y (- z t)) (* 120.0 a)) 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+62) {
		tmp = t_1;
	} else if (t_1 <= 5e+118) {
		tmp = fma(-60.0, (y / (z - t)), (120.0 * a));
	} 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+62)
		tmp = t_1;
	elseif (t_1 <= 5e+118)
		tmp = fma(-60.0, Float64(y / Float64(z - t)), Float64(120.0 * a));
	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[t$95$1, -2e+62], t$95$1, If[LessEqual[t$95$1, 5e+118], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $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)) < -2.00000000000000007e62 or 4.99999999999999972e118 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 90.1

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

   5. Simplified 90.1%

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

   if -2.00000000000000007e62 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999972e118

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 85.4

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

   5. Simplified 85.4%

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

Alternative 6: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+57}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+51) t_1 (if (<= t_1 2e+57) (* 120.0 a) 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+51) {
		tmp = t_1;
	} else if (t_1 <= 2e+57) {
		tmp = 120.0 * a;
	} 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+51)) then
        tmp = t_1
    else if (t_1 <= 2d+57) then
        tmp = 120.0d0 * a
    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+51) {
		tmp = t_1;
	} else if (t_1 <= 2e+57) {
		tmp = 120.0 * a;
	} 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+51:
		tmp = t_1
	elif t_1 <= 2e+57:
		tmp = 120.0 * a
	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+51)
		tmp = t_1;
	elseif (t_1 <= 2e+57)
		tmp = Float64(120.0 * a);
	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+51)
		tmp = t_1;
	elseif (t_1 <= 2e+57)
		tmp = 120.0 * a;
	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+51], t$95$1, If[LessEqual[t$95$1, 2e+57], N[(120.0 * a), $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)) < -2e51 or 2.0000000000000001e57 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 85.7

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

   5. Simplified 85.7%

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

   if -2e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e57

   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. lower-*.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. Add Preprocessing

Alternative 7: 60.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+64}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+159}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -4e+64)
     (* 60.0 (/ (- x y) z))
     (if (<= t_1 1e+159) (* 120.0 a) (* -60.0 (/ (- x y) t))))))

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 <= -4e+64) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t_1 <= 1e+159) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * ((x - 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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-4d+64)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (t_1 <= 1d+159) then
        tmp = 120.0d0 * a
    else
        tmp = (-60.0d0) * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -4e+64) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t_1 <= 1e+159) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -4e+64:
		tmp = 60.0 * ((x - y) / z)
	elif t_1 <= 1e+159:
		tmp = 120.0 * a
	else:
		tmp = -60.0 * ((x - y) / t)
	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 <= -4e+64)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (t_1 <= 1e+159)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	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 <= -4e+64)
		tmp = 60.0 * ((x - y) / z);
	elseif (t_1 <= 1e+159)
		tmp = 120.0 * a;
	else
		tmp = -60.0 * ((x - y) / t);
	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, -4e+64], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+159], N[(120.0 * a), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.00000000000000009e64

   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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 91.6

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

   5. Simplified 91.6%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 50.0

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

   8. Simplified 50.0%

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

   if -4.00000000000000009e64 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999993e158

   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. lower-*.f64 70.1

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

   5. Simplified 70.1%

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

   if 9.9999999999999993e158 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 92.4

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

   5. Simplified 92.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 64.9

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

   8. Simplified 64.9%

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

Alternative 8: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+159}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ (- x y) t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+51) t_1 (if (<= t_2 1e+159) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+51) {
		tmp = t_1;
	} else if (t_2 <= 1e+159) {
		tmp = 120.0 * a;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * ((x - y) / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+51)) then
        tmp = t_1
    else if (t_2 <= 1d+159) then
        tmp = 120.0d0 * a
    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) / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+51) {
		tmp = t_1;
	} else if (t_2 <= 1e+159) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * ((x - y) / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+51:
		tmp = t_1
	elif t_2 <= 1e+159:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(Float64(x - y) / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+51)
		tmp = t_1;
	elseif (t_2 <= 1e+159)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * ((x - y) / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+51)
		tmp = t_1;
	elseif (t_2 <= 1e+159)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+51], t$95$1, If[LessEqual[t$95$2, 1e+159], N[(120.0 * a), $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)) < -2e51 or 9.9999999999999993e158 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 91.2

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

   5. Simplified 91.2%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 54.6

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

   8. Simplified 54.6%

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

   if -2e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999993e158

   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. lower-*.f64 71.5

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

   5. Simplified 71.5%

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

Alternative 9: 53.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+193}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -4e+65)
     (/ (* 60.0 x) z)
     (if (<= t_1 1e+193) (* 120.0 a) (/ (* 60.0 y) t)))))

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 <= -4e+65) {
		tmp = (60.0 * x) / z;
	} else if (t_1 <= 1e+193) {
		tmp = 120.0 * a;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-4d+65)) then
        tmp = (60.0d0 * x) / z
    else if (t_1 <= 1d+193) then
        tmp = 120.0d0 * a
    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 t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -4e+65) {
		tmp = (60.0 * x) / z;
	} else if (t_1 <= 1e+193) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -4e+65:
		tmp = (60.0 * x) / z
	elif t_1 <= 1e+193:
		tmp = 120.0 * a
	else:
		tmp = (60.0 * y) / t
	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 <= -4e+65)
		tmp = Float64(Float64(60.0 * x) / z);
	elseif (t_1 <= 1e+193)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(60.0 * y) / t);
	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 <= -4e+65)
		tmp = (60.0 * x) / z;
	elseif (t_1 <= 1e+193)
		tmp = 120.0 * a;
	else
		tmp = (60.0 * y) / t;
	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, -4e+65], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+193], N[(120.0 * a), $MachinePrecision], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4e65

   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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 91.3

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

   5. Simplified 91.3%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 48.6

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

   8. Simplified 48.6%

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

   9. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 31.1

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

   11. Simplified 31.1%

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

   if -4e65 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000007e193

   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. lower-*.f64 67.9

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

   5. Simplified 67.9%

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

   if 1.00000000000000007e193 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 94.0

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

   5. Simplified 94.0%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 70.0

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

   8. Simplified 70.0%

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

   9. Taylor expanded in x around 0

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

       1. associate-*r/ N/A

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

       2. metadata-eval N/A

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

       3. associate-*r* N/A

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

       4. lower-/.f64 N/A

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

       5. associate-*r* N/A

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

       6. metadata-eval N/A

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

       7. *-commutative N/A

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

       8. lower-*.f64 50.9

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

   11. Simplified 50.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -4 \cdot 10^{+65}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+193}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -4e+65)
     (/ (* 60.0 x) z)
     (if (<= t_1 2e+219) (* 120.0 a) (/ (* y -60.0) z)))))

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 <= -4e+65) {
		tmp = (60.0 * x) / z;
	} else if (t_1 <= 2e+219) {
		tmp = 120.0 * a;
	} else {
		tmp = (y * -60.0) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-4d+65)) then
        tmp = (60.0d0 * x) / z
    else if (t_1 <= 2d+219) then
        tmp = 120.0d0 * a
    else
        tmp = (y * (-60.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -4e+65) {
		tmp = (60.0 * x) / z;
	} else if (t_1 <= 2e+219) {
		tmp = 120.0 * a;
	} else {
		tmp = (y * -60.0) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -4e+65:
		tmp = (60.0 * x) / z
	elif t_1 <= 2e+219:
		tmp = 120.0 * a
	else:
		tmp = (y * -60.0) / z
	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 <= -4e+65)
		tmp = Float64(Float64(60.0 * x) / z);
	elseif (t_1 <= 2e+219)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(y * -60.0) / z);
	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 <= -4e+65)
		tmp = (60.0 * x) / z;
	elseif (t_1 <= 2e+219)
		tmp = 120.0 * a;
	else
		tmp = (y * -60.0) / z;
	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, -4e+65], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2e+219], N[(120.0 * a), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4e65

   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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 91.3

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

   5. Simplified 91.3%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 48.6

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

   8. Simplified 48.6%

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

   9. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 31.1

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

   11. Simplified 31.1%

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

   if -4e65 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.99999999999999993e219

   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. lower-*.f64 67.4

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

   5. Simplified 67.4%

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

   if 1.99999999999999993e219 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 99.8

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 50.8

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

   8. Simplified 50.8%

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

   9. Taylor expanded in x around 0

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 34.7

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

   11. Simplified 34.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -4 \cdot 10^{+65}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+219}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+159}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -4e+65)
     (/ (* 60.0 x) z)
     (if (<= t_1 1e+159) (* 120.0 a) (* -60.0 (/ x t))))))

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 <= -4e+65) {
		tmp = (60.0 * x) / z;
	} else if (t_1 <= 1e+159) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-4d+65)) then
        tmp = (60.0d0 * x) / z
    else if (t_1 <= 1d+159) then
        tmp = 120.0d0 * a
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -4e+65) {
		tmp = (60.0 * x) / z;
	} else if (t_1 <= 1e+159) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -4e+65:
		tmp = (60.0 * x) / z
	elif t_1 <= 1e+159:
		tmp = 120.0 * a
	else:
		tmp = -60.0 * (x / t)
	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 <= -4e+65)
		tmp = Float64(Float64(60.0 * x) / z);
	elseif (t_1 <= 1e+159)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	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 <= -4e+65)
		tmp = (60.0 * x) / z;
	elseif (t_1 <= 1e+159)
		tmp = 120.0 * a;
	else
		tmp = -60.0 * (x / t);
	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, -4e+65], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+159], N[(120.0 * a), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4e65

   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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 91.3

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

   5. Simplified 91.3%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 48.6

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

   8. Simplified 48.6%

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

   9. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 31.1

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

   11. Simplified 31.1%

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

   if -4e65 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999993e158

   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. lower-*.f64 69.8

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

   5. Simplified 69.8%

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

   if 9.9999999999999993e158 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 92.4

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

   5. Simplified 92.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 64.9

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

   8. Simplified 64.9%

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

   9. Taylor expanded in x around inf

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

       1. lower-/.f64 29.7

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

   11. Simplified 29.7%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -4 \cdot 10^{+65}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+159}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+159}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -4e+65)
     (* 60.0 (/ x z))
     (if (<= t_1 1e+159) (* 120.0 a) (* -60.0 (/ x t))))))

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 <= -4e+65) {
		tmp = 60.0 * (x / z);
	} else if (t_1 <= 1e+159) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-4d+65)) then
        tmp = 60.0d0 * (x / z)
    else if (t_1 <= 1d+159) then
        tmp = 120.0d0 * a
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -4e+65) {
		tmp = 60.0 * (x / z);
	} else if (t_1 <= 1e+159) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -4e+65:
		tmp = 60.0 * (x / z)
	elif t_1 <= 1e+159:
		tmp = 120.0 * a
	else:
		tmp = -60.0 * (x / t)
	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 <= -4e+65)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (t_1 <= 1e+159)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	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 <= -4e+65)
		tmp = 60.0 * (x / z);
	elseif (t_1 <= 1e+159)
		tmp = 120.0 * a;
	else
		tmp = -60.0 * (x / t);
	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, -4e+65], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+159], N[(120.0 * a), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4e65

   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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 91.3

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

   5. Simplified 91.3%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 48.6

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

   8. Simplified 48.6%

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

   9. Taylor expanded in x around inf

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

       1. lower-/.f64 31.0

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

   11. Simplified 31.0%

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

   if -4e65 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999993e158

   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. lower-*.f64 69.8

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

   5. Simplified 69.8%

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

   if 9.9999999999999993e158 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 92.4

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

   5. Simplified 92.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 64.9

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

   8. Simplified 64.9%

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

   9. Taylor expanded in x around inf

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

       1. lower-/.f64 29.7

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

   11. Simplified 29.7%

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

Alternative 13: 54.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+159}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+182) t_1 (if (<= t_2 1e+159) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+182) {
		tmp = t_1;
	} else if (t_2 <= 1e+159) {
		tmp = 120.0 * a;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+182)) then
        tmp = t_1
    else if (t_2 <= 1d+159) then
        tmp = 120.0d0 * a
    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 / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+182) {
		tmp = t_1;
	} else if (t_2 <= 1e+159) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+182:
		tmp = t_1
	elif t_2 <= 1e+159:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+182)
		tmp = t_1;
	elseif (t_2 <= 1e+159)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+182)
		tmp = t_1;
	elseif (t_2 <= 1e+159)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+182], t$95$1, If[LessEqual[t$95$2, 1e+159], N[(120.0 * a), $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)) < -1.0000000000000001e182 or 9.9999999999999993e158 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 94.4

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

   5. Simplified 94.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 64.9

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

   8. Simplified 64.9%

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

   9. Taylor expanded in x around inf

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

       1. lower-/.f64 32.9

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

   11. Simplified 32.9%

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

   if -1.0000000000000001e182 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999993e158

   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. lower-*.f64 64.6

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

   5. Simplified 64.6%

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

Alternative 14: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-40}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ x (- z t)) (* 120.0 a))))
   (if (<= x -1.05e+73)
     t_1
     (if (<= x 6.6e-40) (fma -60.0 (/ y (- z t)) (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(60.0, (x / (z - t)), (120.0 * a));
	double tmp;
	if (x <= -1.05e+73) {
		tmp = t_1;
	} else if (x <= 6.6e-40) {
		tmp = fma(-60.0, (y / (z - t)), (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(x / Float64(z - t)), Float64(120.0 * a))
	tmp = 0.0
	if (x <= -1.05e+73)
		tmp = t_1;
	elseif (x <= 6.6e-40)
		tmp = fma(-60.0, Float64(y / Float64(z - t)), Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+73], t$95$1, If[LessEqual[x, 6.6e-40], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0500000000000001e73 or 6.59999999999999986e-40 < x

   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 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 90.0

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

   5. Simplified 90.0%

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

   if -1.0500000000000001e73 < x < 6.59999999999999986e-40

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 95.6

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

   5. Simplified 95.6%

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

Alternative 15: 50.2% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ 120 \cdot a \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* 120.0 a))

C

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

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 = 120.0d0 * a
end function

Java

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

Python

def code(x, y, z, t, a):
	return 120.0 * a

Julia

function code(x, y, z, t, a)
	return Float64(120.0 * a)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(120.0 * a), $MachinePrecision]

Derivation

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. lower-*.f64 53.3

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

5. Simplified 53.3%

   \[\leadsto \color{blue}{120 \cdot a} \]
6. 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 2024215 
(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)))