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

Percentage Accurate: 99.4% → 99.8%

Time: 8.4s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. 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 99.4

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

   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. lower-/.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 2: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-132} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-95}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5e-132) (not (<= (* a 120.0) 4e-95)))
   (fma (/ x (- z t)) 60.0 (* 120.0 a))
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -5e-132) || !((a * 120.0) <= 4e-95)) {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -5e-132) || !(Float64(a * 120.0) <= 4e-95))
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-132], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-95]], $MachinePrecision]], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.9999999999999999e-132 or 3.99999999999999996e-95 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.3

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

      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. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   6. 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. lower-*.f64 83.8

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

   7. Applied rewrites 83.8%

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

   if -4.9999999999999999e-132 < (*.f64 a #s(literal 120 binary64)) < 3.99999999999999996e-95

   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 90.8

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

   5. Applied rewrites 90.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-132} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-95}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50 \lor \neg \left(a \cdot 120 \leq 10^{+25}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -50.0) (not (<= (* a 120.0) 1e+25)))
   (* 120.0 a)
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -50.0) || !((a * 120.0) <= 1e+25)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-50.0d0)) .or. (.not. ((a * 120.0d0) <= 1d+25))) then
        tmp = 120.0d0 * a
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -50.0) || !((a * 120.0) <= 1e+25)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -50.0) or not ((a * 120.0) <= 1e+25):
		tmp = 120.0 * a
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -50.0) || !(Float64(a * 120.0) <= 1e+25))
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -50.0) || ~(((a * 120.0) <= 1e+25)))
		tmp = 120.0 * a;
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -50.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+25]], $MachinePrecision]], N[(120.0 * a), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -50 or 1.00000000000000009e25 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 80.2

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

   5. Applied rewrites 80.2%

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

   if -50 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000009e25

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-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 77.5

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

   5. Applied rewrites 77.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50 \lor \neg \left(a \cdot 120 \leq 10^{+25}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50 \lor \neg \left(a \cdot 120 \leq 10^{+25}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -50.0) (not (<= (* a 120.0) 1e+25)))
   (* 120.0 a)
   (* (/ (- x y) (- z t)) 60.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -50.0) || !((a * 120.0) <= 1e+25)) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / (z - 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) :: tmp
    if (((a * 120.0d0) <= (-50.0d0)) .or. (.not. ((a * 120.0d0) <= 1d+25))) then
        tmp = 120.0d0 * a
    else
        tmp = ((x - y) / (z - 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 tmp;
	if (((a * 120.0) <= -50.0) || !((a * 120.0) <= 1e+25)) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / (z - t)) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -50.0) or not ((a * 120.0) <= 1e+25):
		tmp = 120.0 * a
	else:
		tmp = ((x - y) / (z - t)) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -50.0) || !(Float64(a * 120.0) <= 1e+25))
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -50.0) || ~(((a * 120.0) <= 1e+25)))
		tmp = 120.0 * a;
	else
		tmp = ((x - y) / (z - t)) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -50.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+25]], $MachinePrecision]], N[(120.0 * a), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -50 or 1.00000000000000009e25 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 80.2

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

   5. Applied rewrites 80.2%

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

   if -50 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000009e25

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.0

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

      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. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 77.5

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

   7. Applied rewrites 77.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50 \lor \neg \left(a \cdot 120 \leq 10^{+25}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{y}{z - t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.3e+14)
   (fma (/ x (- z t)) 60.0 (* 120.0 a))
   (if (<= x 1.06e+99)
     (fma 120.0 a (* (/ y (- z t)) -60.0))
     (+ (/ (* 60.0 x) (- z t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.3e+14) {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	} else if (x <= 1.06e+99) {
		tmp = fma(120.0, a, ((y / (z - t)) * -60.0));
	} else {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.3e+14)
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	elseif (x <= 1.06e+99)
		tmp = fma(120.0, a, Float64(Float64(y / Float64(z - t)) * -60.0));
	else
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.3e+14], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.06e+99], N[(120.0 * a + N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.3e14

   1. Initial program 99.7%

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

      1. 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 99.7

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

      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. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   6. 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. lower-*.f64 87.7

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

   7. Applied rewrites 87.7%

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

   if -4.3e14 < x < 1.05999999999999999e99

   1. Initial program 99.2%

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

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 96.4

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

   5. Applied rewrites 96.4%

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

   if 1.05999999999999999e99 < 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 x around inf

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

      1. lower-*.f64 96.2

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

   5. Applied rewrites 96.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{y}{z - t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+14} \lor \neg \left(x \leq 1.06 \cdot 10^{+99}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{y}{z - t} \cdot -60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.3e+14) (not (<= x 1.06e+99)))
   (fma (/ x (- z t)) 60.0 (* 120.0 a))
   (fma 120.0 a (* (/ y (- z t)) -60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.3e+14) || !(x <= 1.06e+99)) {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	} else {
		tmp = fma(120.0, a, ((y / (z - t)) * -60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.3e+14) || !(x <= 1.06e+99))
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	else
		tmp = fma(120.0, a, Float64(Float64(y / Float64(z - t)) * -60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.3e+14], N[Not[LessEqual[x, 1.06e+99]], $MachinePrecision]], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(120.0 * a + N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e14 or 1.05999999999999999e99 < x

   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. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   6. 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. lower-*.f64 91.4

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

   7. Applied rewrites 91.4%

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

   if -4.3e14 < x < 1.05999999999999999e99

   1. Initial program 99.2%

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

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 96.4

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

   5. Applied rewrites 96.4%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+14} \lor \neg \left(x \leq 1.06 \cdot 10^{+99}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{y}{z - t} \cdot -60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+118} \lor \neg \left(x \leq 1.4 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -6.8e+118) (not (<= x 1.4e+135)))
   (* x (/ 60.0 (- z t)))
   (* 120.0 a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.8e+118) || !(x <= 1.4e+135)) {
		tmp = x * (60.0 / (z - t));
	} 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 ((x <= (-6.8d+118)) .or. (.not. (x <= 1.4d+135))) then
        tmp = x * (60.0d0 / (z - t))
    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 ((x <= -6.8e+118) || !(x <= 1.4e+135)) {
		tmp = x * (60.0 / (z - t));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -6.8e+118) or not (x <= 1.4e+135):
		tmp = x * (60.0 / (z - t))
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -6.8e+118) || !(x <= 1.4e+135))
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -6.8e+118) || ~((x <= 1.4e+135)))
		tmp = x * (60.0 / (z - t));
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -6.8e+118], N[Not[LessEqual[x, 1.4e+135]], $MachinePrecision]], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.79999999999999973e118 or 1.40000000000000001e135 < 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 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 75.2

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

   5. Applied rewrites 75.2%

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

   7. Applied rewrites 75.3%

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

   if -6.79999999999999973e118 < x < 1.40000000000000001e135

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 62.0

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

   5. Applied rewrites 62.0%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+118} \lor \neg \left(x \leq 1.4 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+135}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e+118)
   (* x (/ 60.0 (- z t)))
   (if (<= x 1.4e+135) (* 120.0 a) (/ (* x 60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+118) {
		tmp = x * (60.0 / (z - t));
	} else if (x <= 1.4e+135) {
		tmp = 120.0 * a;
	} else {
		tmp = (x * 60.0) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.8d+118)) then
        tmp = x * (60.0d0 / (z - t))
    else if (x <= 1.4d+135) then
        tmp = 120.0d0 * a
    else
        tmp = (x * 60.0d0) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+118) {
		tmp = x * (60.0 / (z - t));
	} else if (x <= 1.4e+135) {
		tmp = 120.0 * a;
	} else {
		tmp = (x * 60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e+118:
		tmp = x * (60.0 / (z - t))
	elif x <= 1.4e+135:
		tmp = 120.0 * a
	else:
		tmp = (x * 60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e+118)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (x <= 1.4e+135)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x * 60.0) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e+118)
		tmp = x * (60.0 / (z - t));
	elseif (x <= 1.4e+135)
		tmp = 120.0 * a;
	else
		tmp = (x * 60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e+118], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+135], N[(120.0 * a), $MachinePrecision], N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999973e118

   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 72.4

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

   5. Applied rewrites 72.4%

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

   7. Applied rewrites 72.5%

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

   if -6.79999999999999973e118 < x < 1.40000000000000001e135

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 62.0

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

   5. Applied rewrites 62.0%

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

   if 1.40000000000000001e135 < 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 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 78.0

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

   5. Applied rewrites 78.0%

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

   7. Applied rewrites 78.1%

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

Alternative 9: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+135}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e+118)
   (* x (/ 60.0 (- z t)))
   (if (<= x 1.4e+135) (* 120.0 a) (* (/ x (- z t)) 60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+118) {
		tmp = x * (60.0 / (z - t));
	} else if (x <= 1.4e+135) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / (z - 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) :: tmp
    if (x <= (-6.8d+118)) then
        tmp = x * (60.0d0 / (z - t))
    else if (x <= 1.4d+135) then
        tmp = 120.0d0 * a
    else
        tmp = (x / (z - 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 tmp;
	if (x <= -6.8e+118) {
		tmp = x * (60.0 / (z - t));
	} else if (x <= 1.4e+135) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / (z - t)) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e+118:
		tmp = x * (60.0 / (z - t))
	elif x <= 1.4e+135:
		tmp = 120.0 * a
	else:
		tmp = (x / (z - t)) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e+118)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (x <= 1.4e+135)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e+118)
		tmp = x * (60.0 / (z - t));
	elseif (x <= 1.4e+135)
		tmp = 120.0 * a;
	else
		tmp = (x / (z - t)) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e+118], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+135], N[(120.0 * a), $MachinePrecision], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999973e118

   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 72.4

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

   5. Applied rewrites 72.4%

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

   7. Applied rewrites 72.5%

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

   if -6.79999999999999973e118 < x < 1.40000000000000001e135

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 62.0

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

   5. Applied rewrites 62.0%

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

   if 1.40000000000000001e135 < 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 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 78.0

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

   5. Applied rewrites 78.0%

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

Alternative 10: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+118} \lor \neg \left(x \leq 9.8 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -6.8e+118) (not (<= x 9.8e+154)))
   (* x (/ -60.0 t))
   (* 120.0 a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.8e+118) || !(x <= 9.8e+154)) {
		tmp = x * (-60.0 / t);
	} 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 ((x <= (-6.8d+118)) .or. (.not. (x <= 9.8d+154))) then
        tmp = x * ((-60.0d0) / t)
    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 ((x <= -6.8e+118) || !(x <= 9.8e+154)) {
		tmp = x * (-60.0 / t);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -6.8e+118) or not (x <= 9.8e+154):
		tmp = x * (-60.0 / t)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -6.8e+118) || !(x <= 9.8e+154))
		tmp = Float64(x * Float64(-60.0 / t));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -6.8e+118) || ~((x <= 9.8e+154)))
		tmp = x * (-60.0 / t);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -6.8e+118], N[Not[LessEqual[x, 9.8e+154]], $MachinePrecision]], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.79999999999999973e118 or 9.8000000000000003e154 < 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 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 76.6

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 51.0%

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

   10. Applied rewrites 51.1%

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

   if -6.79999999999999973e118 < x < 9.8000000000000003e154

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 61.8

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

   5. Applied rewrites 61.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+118} \lor \neg \left(x \leq 9.8 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+154}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e+118)
   (* x (/ -60.0 t))
   (if (<= x 9.8e+154) (* 120.0 a) (/ (* -60.0 x) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+118) {
		tmp = x * (-60.0 / t);
	} else if (x <= 9.8e+154) {
		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) :: tmp
    if (x <= (-6.8d+118)) then
        tmp = x * ((-60.0d0) / t)
    else if (x <= 9.8d+154) 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 tmp;
	if (x <= -6.8e+118) {
		tmp = x * (-60.0 / t);
	} else if (x <= 9.8e+154) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * x) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e+118:
		tmp = x * (-60.0 / t)
	elif x <= 9.8e+154:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 * x) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e+118)
		tmp = Float64(x * Float64(-60.0 / t));
	elseif (x <= 9.8e+154)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 * x) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e+118)
		tmp = x * (-60.0 / t);
	elseif (x <= 9.8e+154)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 * x) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e+118], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+154], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 * x), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999973e118

   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 72.4

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

   5. Applied rewrites 72.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 50.3%

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

   10. Applied rewrites 50.5%

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

   if -6.79999999999999973e118 < x < 9.8000000000000003e154

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 61.8

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

   5. Applied rewrites 61.8%

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

   if 9.8000000000000003e154 < x

   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 81.3

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 51.8%

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

   10. Applied rewrites 51.8%

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

Alternative 12: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+154}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e+118)
   (* x (/ -60.0 t))
   (if (<= x 9.8e+154) (* 120.0 a) (* (/ x t) -60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+118) {
		tmp = x * (-60.0 / t);
	} else if (x <= 9.8e+154) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / 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) :: tmp
    if (x <= (-6.8d+118)) then
        tmp = x * ((-60.0d0) / t)
    else if (x <= 9.8d+154) then
        tmp = 120.0d0 * a
    else
        tmp = (x / 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 tmp;
	if (x <= -6.8e+118) {
		tmp = x * (-60.0 / t);
	} else if (x <= 9.8e+154) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e+118:
		tmp = x * (-60.0 / t)
	elif x <= 9.8e+154:
		tmp = 120.0 * a
	else:
		tmp = (x / t) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e+118)
		tmp = Float64(x * Float64(-60.0 / t));
	elseif (x <= 9.8e+154)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / t) * -60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e+118)
		tmp = x * (-60.0 / t);
	elseif (x <= 9.8e+154)
		tmp = 120.0 * a;
	else
		tmp = (x / t) * -60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e+118], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+154], N[(120.0 * a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999973e118

   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 72.4

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

   5. Applied rewrites 72.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 50.3%

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

   10. Applied rewrites 50.5%

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

   if -6.79999999999999973e118 < x < 9.8000000000000003e154

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 61.8

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

   5. Applied rewrites 61.8%

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

   if 9.8000000000000003e154 < x

   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 81.3

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 51.8%

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

Alternative 13: 51.5% 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 99.4%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 51.4

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

5. Applied rewrites 51.4%

   \[\leadsto \color{blue}{120 \cdot a} \]
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 2024326 
(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)))