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

Percentage Accurate: 99.4% → 99.8%

Time: 9.5s

Alternatives: 13

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.8

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

   5. lift-/.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-/l* N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. frac-2neg N/A

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

   12. lower-/.f64 N/A

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

   13. metadata-eval N/A

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

   14. neg-sub0 N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{0 - \left(z - t\right)}} \cdot \left(x - y\right)\right) \]

   15. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{0 - \color{blue}{\left(z - t\right)}} \cdot \left(x - y\right)\right) \]

   16. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)}} \cdot \left(x - y\right)\right) \]

   17. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)}} \cdot \left(x - y\right)\right) \]

   18. associate--r+ N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(t\right)\right)\right) - z}} \cdot \left(x - y\right)\right) \]

   19. neg-sub0 N/A

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

   20. remove-double-neg N/A

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

   21. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 58.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot x\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+41}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_2 \leq 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{z - t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) x)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+30)
     t_1
     (if (<= t_2 5e+41)
       (* 120.0 a)
       (if (<= t_2 1e+229) t_1 (* (/ -60.0 (- z t)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * x;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+30) {
		tmp = t_1;
	} else if (t_2 <= 5e+41) {
		tmp = 120.0 * a;
	} else if (t_2 <= 1e+229) {
		tmp = t_1;
	} else {
		tmp = (-60.0 / (z - t)) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / (z - t)) * x
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+30)) then
        tmp = t_1
    else if (t_2 <= 5d+41) then
        tmp = 120.0d0 * a
    else if (t_2 <= 1d+229) then
        tmp = t_1
    else
        tmp = ((-60.0d0) / (z - t)) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * x;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+30) {
		tmp = t_1;
	} else if (t_2 <= 5e+41) {
		tmp = 120.0 * a;
	} else if (t_2 <= 1e+229) {
		tmp = t_1;
	} else {
		tmp = (-60.0 / (z - t)) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / (z - t)) * x
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+30:
		tmp = t_1
	elif t_2 <= 5e+41:
		tmp = 120.0 * a
	elif t_2 <= 1e+229:
		tmp = t_1
	else:
		tmp = (-60.0 / (z - t)) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(z - t)) * x)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+30)
		tmp = t_1;
	elseif (t_2 <= 5e+41)
		tmp = Float64(120.0 * a);
	elseif (t_2 <= 1e+229)
		tmp = t_1;
	else
		tmp = Float64(Float64(-60.0 / Float64(z - t)) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 / (z - t)) * x;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+30)
		tmp = t_1;
	elseif (t_2 <= 5e+41)
		tmp = 120.0 * a;
	elseif (t_2 <= 1e+229)
		tmp = t_1;
	else
		tmp = (-60.0 / (z - t)) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+30], t$95$1, If[LessEqual[t$95$2, 5e+41], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$2, 1e+229], t$95$1, N[(N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999998e30 or 5.00000000000000022e41 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999999e228

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 55.2

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

   5. Applied rewrites 55.2%

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

   7. Applied rewrites 55.4%

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

   if -4.9999999999999998e30 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000022e41

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if 9.9999999999999999e228 < (/.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 y around inf

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 82.1

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

   5. Applied rewrites 82.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+41}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+229}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{z - t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot x\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+41}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+189}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) x)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+30)
     t_1
     (if (<= t_2 5e+41)
       (* 120.0 a)
       (if (<= t_2 5e+189) t_1 (* (/ (- x y) t) -60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * x;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+30) {
		tmp = t_1;
	} else if (t_2 <= 5e+41) {
		tmp = 120.0 * a;
	} else if (t_2 <= 5e+189) {
		tmp = t_1;
	} else {
		tmp = ((x - y) / t) * -60.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / (z - t)) * x
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+30)) then
        tmp = t_1
    else if (t_2 <= 5d+41) then
        tmp = 120.0d0 * a
    else if (t_2 <= 5d+189) then
        tmp = t_1
    else
        tmp = ((x - y) / t) * (-60.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * x;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+30) {
		tmp = t_1;
	} else if (t_2 <= 5e+41) {
		tmp = 120.0 * a;
	} else if (t_2 <= 5e+189) {
		tmp = t_1;
	} else {
		tmp = ((x - y) / t) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / (z - t)) * x
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+30:
		tmp = t_1
	elif t_2 <= 5e+41:
		tmp = 120.0 * a
	elif t_2 <= 5e+189:
		tmp = t_1
	else:
		tmp = ((x - y) / t) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(z - t)) * x)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+30)
		tmp = t_1;
	elseif (t_2 <= 5e+41)
		tmp = Float64(120.0 * a);
	elseif (t_2 <= 5e+189)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 / (z - t)) * x;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+30)
		tmp = t_1;
	elseif (t_2 <= 5e+41)
		tmp = 120.0 * a;
	elseif (t_2 <= 5e+189)
		tmp = t_1;
	else
		tmp = ((x - y) / t) * -60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+30], t$95$1, If[LessEqual[t$95$2, 5e+41], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$2, 5e+189], t$95$1, N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999998e30 or 5.00000000000000022e41 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000004e189

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 55.9

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

   5. Applied rewrites 55.9%

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

   7. Applied rewrites 56.0%

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

   if -4.9999999999999998e30 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000022e41

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if 5.0000000000000004e189 < (/.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 t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 62.9

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

   5. Applied rewrites 62.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 57.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+41}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+189}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z} \cdot x\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+172}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_2 \leq 10^{+234}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 z) x)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+30)
     t_1
     (if (<= t_2 4e+172)
       (* 120.0 a)
       (if (<= t_2 1e+234) t_1 (* (/ 60.0 t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / z) * x;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+30) {
		tmp = t_1;
	} else if (t_2 <= 4e+172) {
		tmp = 120.0 * a;
	} else if (t_2 <= 1e+234) {
		tmp = t_1;
	} else {
		tmp = (60.0 / t) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / z) * x
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+30)) then
        tmp = t_1
    else if (t_2 <= 4d+172) then
        tmp = 120.0d0 * a
    else if (t_2 <= 1d+234) then
        tmp = t_1
    else
        tmp = (60.0d0 / t) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / z) * x;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+30) {
		tmp = t_1;
	} else if (t_2 <= 4e+172) {
		tmp = 120.0 * a;
	} else if (t_2 <= 1e+234) {
		tmp = t_1;
	} else {
		tmp = (60.0 / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / z) * x
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+30:
		tmp = t_1
	elif t_2 <= 4e+172:
		tmp = 120.0 * a
	elif t_2 <= 1e+234:
		tmp = t_1
	else:
		tmp = (60.0 / t) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / z) * x)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+30)
		tmp = t_1;
	elseif (t_2 <= 4e+172)
		tmp = Float64(120.0 * a);
	elseif (t_2 <= 1e+234)
		tmp = t_1;
	else
		tmp = Float64(Float64(60.0 / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 / z) * x;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+30)
		tmp = t_1;
	elseif (t_2 <= 4e+172)
		tmp = 120.0 * a;
	elseif (t_2 <= 1e+234)
		tmp = t_1;
	else
		tmp = (60.0 / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / z), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+30], t$95$1, If[LessEqual[t$95$2, 4e+172], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$2, 1e+234], t$95$1, N[(N[(60.0 / t), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999998e30 or 4.0000000000000003e172 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000002e234

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 56.0

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

   5. Applied rewrites 56.0%

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

   7. Applied rewrites 56.2%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 36.6%

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

   if -4.9999999999999998e30 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.0000000000000003e172

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   if 1.00000000000000002e234 < (/.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 t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 65.9

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 59.5%

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

   10. Applied rewrites 59.6%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;\frac{60}{z} \cdot x\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{+172}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+234}:\\ \;\;\;\;\frac{60}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -4e+67)
     t_1
     (if (<= t_2 4e+172) (fma (/ x (- z t)) 60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -4e+67) {
		tmp = t_1;
	} else if (t_2 <= 4e+172) {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -4e+67)
		tmp = t_1;
	elseif (t_2 <= 4e+172)
		tmp = fma(Float64(x / Float64(z - t)), 60.0, 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[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $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, -4e+67], t$95$1, If[LessEqual[t$95$2, 4e+172], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + 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)) < -3.99999999999999993e67 or 4.0000000000000003e172 < (/.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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 89.9

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

   5. Applied rewrites 89.9%

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

   if -3.99999999999999993e67 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.0000000000000003e172

   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. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 87.5

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

   5. Applied rewrites 87.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -4 \cdot 10^{+67}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+41}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -0.05) t_1 (if (<= t_2 5e+41) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -0.05) {
		tmp = t_1;
	} else if (t_2 <= 5e+41) {
		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 / (z - t)) * (x - y)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-0.05d0)) then
        tmp = t_1
    else if (t_2 <= 5d+41) 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 / (z - t)) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -0.05) {
		tmp = t_1;
	} else if (t_2 <= 5e+41) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / (z - t)) * (x - y)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -0.05:
		tmp = t_1
	elif t_2 <= 5e+41:
		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(z - t)) * Float64(x - y))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -0.05)
		tmp = t_1;
	elseif (t_2 <= 5e+41)
		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 / (z - t)) * (x - y);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -0.05)
		tmp = t_1;
	elseif (t_2 <= 5e+41)
		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[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $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, -0.05], t$95$1, If[LessEqual[t$95$2, 5e+41], 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)) < -0.050000000000000003 or 5.00000000000000022e41 < (/.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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 79.7

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

   5. Applied rewrites 79.7%

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

   if -0.050000000000000003 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000022e41

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 77.6

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

   5. Applied rewrites 77.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -0.05:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+41}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+172}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+61)
     (* (/ x t) -60.0)
     (if (<= t_1 4e+172) (* 120.0 a) (* (/ 60.0 t) y)))))

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 <= -5e+61) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 4e+172) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 / t) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+61)) then
        tmp = (x / t) * (-60.0d0)
    else if (t_1 <= 4d+172) then
        tmp = 120.0d0 * a
    else
        tmp = (60.0d0 / t) * y
    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 <= -5e+61) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 4e+172) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+61:
		tmp = (x / t) * -60.0
	elif t_1 <= 4e+172:
		tmp = 120.0 * a
	else:
		tmp = (60.0 / t) * y
	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 <= -5e+61)
		tmp = Float64(Float64(x / t) * -60.0);
	elseif (t_1 <= 4e+172)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(60.0 / t) * y);
	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 <= -5e+61)
		tmp = (x / t) * -60.0;
	elseif (t_1 <= 4e+172)
		tmp = 120.0 * a;
	else
		tmp = (60.0 / t) * y;
	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, -5e+61], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 4e+172], N[(120.0 * a), $MachinePrecision], N[(N[(60.0 / t), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000018e61

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 29.7%

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

   if -5.00000000000000018e61 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.0000000000000003e172

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 65.9

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

   5. Applied rewrites 65.9%

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

   if 4.0000000000000003e172 < (/.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 t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 52.0

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

   5. Applied rewrites 52.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 42.0%

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

   10. Applied rewrites 42.0%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{+172}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{t} \cdot y\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+172}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 t) y)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+116) t_1 (if (<= t_2 4e+172) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / t) * y;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+116) {
		tmp = t_1;
	} else if (t_2 <= 4e+172) {
		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 / t) * y
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+116)) then
        tmp = t_1
    else if (t_2 <= 4d+172) 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 / t) * y;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+116) {
		tmp = t_1;
	} else if (t_2 <= 4e+172) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / t) * y
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+116:
		tmp = t_1
	elif t_2 <= 4e+172:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / t) * y)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+116)
		tmp = t_1;
	elseif (t_2 <= 4e+172)
		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 / t) * y;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+116)
		tmp = t_1;
	elseif (t_2 <= 4e+172)
		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 / t), $MachinePrecision] * y), $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+116], t$95$1, If[LessEqual[t$95$2, 4e+172], 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)) < -2.00000000000000003e116 or 4.0000000000000003e172 < (/.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 t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 51.1

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

   5. Applied rewrites 51.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 34.6%

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

   10. Applied rewrites 34.6%

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

   if -2.00000000000000003e116 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.0000000000000003e172

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 62.6

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

   5. Applied rewrites 62.6%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+116}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{+172}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 500000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e-23)
   (fma (/ x z) 60.0 (* 120.0 a))
   (if (<= (* 120.0 a) 500000.0) (* (/ 60.0 (- z t)) (- x y)) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e-23) {
		tmp = fma((x / z), 60.0, (120.0 * a));
	} else if ((120.0 * a) <= 500000.0) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e-23)
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= 500000.0)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e-23], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 500000.0], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.9%

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

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.7

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

   5. Applied rewrites 93.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.6%

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

   if -5.0000000000000002e-23 < (*.f64 a #s(literal 120 binary64)) < 5e5

   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 81.5

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

   5. Applied rewrites 81.5%

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

   if 5e5 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 77.2

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

   5. Applied rewrites 77.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 500000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -3.7 \cdot 10^{-30}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 8 \cdot 10^{-32}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -3.7e-30)
   (* 120.0 a)
   (if (<= (* 120.0 a) 8e-32) (* (/ (- x y) t) -60.0) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -3.7e-30) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 8e-32) {
		tmp = ((x - y) / t) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	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 ((120.0d0 * a) <= (-3.7d-30)) then
        tmp = 120.0d0 * a
    else if ((120.0d0 * a) <= 8d-32) then
        tmp = ((x - y) / t) * (-60.0d0)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -3.7e-30) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 8e-32) {
		tmp = ((x - y) / t) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (120.0 * a) <= -3.7e-30:
		tmp = 120.0 * a
	elif (120.0 * a) <= 8e-32:
		tmp = ((x - y) / t) * -60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -3.7e-30)
		tmp = Float64(120.0 * a);
	elseif (Float64(120.0 * a) <= 8e-32)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((120.0 * a) <= -3.7e-30)
		tmp = 120.0 * a;
	elseif ((120.0 * a) <= 8e-32)
		tmp = ((x - y) / t) * -60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -3.7e-30], N[(120.0 * a), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 8e-32], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -3.7000000000000003e-30 or 8.00000000000000045e-32 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.8

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

   5. Applied rewrites 71.8%

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

   if -3.7000000000000003e-30 < (*.f64 a #s(literal 120 binary64)) < 8.00000000000000045e-32

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 59.2

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

   5. Applied rewrites 59.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 47.5%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -3.7 \cdot 10^{-30}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 8 \cdot 10^{-32}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 120 \cdot a + \frac{60 \cdot x}{z - t}\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-142}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* 120.0 a) (/ (* 60.0 x) (- z t)))))
   (if (<= x -6.8e+59)
     t_1
     (if (<= x 2.8e-142) (fma (/ y (- z t)) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (120.0 * a) + ((60.0 * x) / (z - t));
	double tmp;
	if (x <= -6.8e+59) {
		tmp = t_1;
	} else if (x <= 2.8e-142) {
		tmp = fma((y / (z - t)), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(120.0 * a) + Float64(Float64(60.0 * x) / Float64(z - t)))
	tmp = 0.0
	if (x <= -6.8e+59)
		tmp = t_1;
	elseif (x <= 2.8e-142)
		tmp = fma(Float64(y / Float64(z - t)), -60.0, 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[(120.0 * a), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+59], t$95$1, If[LessEqual[x, 2.8e-142], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.80000000000000012e59 or 2.80000000000000004e-142 < 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

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

      1. *-commutative N/A

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

      2. lower-*.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -6.80000000000000012e59 < x < 2.80000000000000004e-142

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 95.4

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

   5. Applied rewrites 95.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+59}:\\ \;\;\;\;120 \cdot a + \frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-142}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a + \frac{60 \cdot x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-142}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x (- z t)) 60.0 (* 120.0 a))))
   (if (<= x -6.8e+59)
     t_1
     (if (<= x 2.8e-142) (fma (/ y (- z t)) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / (z - t)), 60.0, (120.0 * a));
	double tmp;
	if (x <= -6.8e+59) {
		tmp = t_1;
	} else if (x <= 2.8e-142) {
		tmp = fma((y / (z - t)), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (x <= -6.8e+59)
		tmp = t_1;
	elseif (x <= 2.8e-142)
		tmp = fma(Float64(y / Float64(z - t)), -60.0, 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[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+59], t$95$1, If[LessEqual[x, 2.8e-142], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.80000000000000012e59 or 2.80000000000000004e-142 < 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. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -6.80000000000000012e59 < x < 2.80000000000000004e-142

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 95.4

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

   5. Applied rewrites 95.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-142}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.8% 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 a around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 48.8

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

5. Applied rewrites 48.8%

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

6. Final simplification 48.8%

   \[\leadsto 120 \cdot a \]
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 2024253 
(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)))