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

Percentage Accurate: 99.4% → 99.8%

Time: 7.8s

Alternatives: 18

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. lift-+.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 99.9

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 60.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+142}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;t\_1 \leq 6 \cdot 10^{-15}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-60}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+142)
     (* (- x y) (/ 60.0 z))
     (if (<= t_1 6e-15)
       (* 120.0 a)
       (if (<= t_1 2e+113)
         (fma y (/ -60.0 z) (* a 120.0))
         (* (- x y) (/ -60.0 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+142) {
		tmp = (x - y) * (60.0 / z);
	} else if (t_1 <= 6e-15) {
		tmp = 120.0 * a;
	} else if (t_1 <= 2e+113) {
		tmp = fma(y, (-60.0 / z), (a * 120.0));
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+142)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	elseif (t_1 <= 6e-15)
		tmp = Float64(120.0 * a);
	elseif (t_1 <= 2e+113)
		tmp = fma(y, Float64(-60.0 / z), Float64(a * 120.0));
	else
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+142], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 6e-15], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$1, 2e+113], N[(y * N[(-60.0 / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e142

   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%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 62.2%

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

   if -2.0000000000000001e142 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 6e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 70.1

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

   5. Applied rewrites 70.1%

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

   if 6e-15 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e113

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 62.8

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

   5. Applied rewrites 62.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 55.9%

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

   10. Applied rewrites 56.0%

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

   if 2e113 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 94.3

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 58.1%

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

Alternative 3: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+142}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+113}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+142)
     (* (- x y) (/ 60.0 z))
     (if (<= t_1 2e+113) (* 120.0 a) (* (- x y) (/ -60.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+142) {
		tmp = (x - y) * (60.0 / z);
	} else if (t_1 <= 2e+113) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+142)) then
        tmp = (x - y) * (60.0d0 / z)
    else if (t_1 <= 2d+113) then
        tmp = 120.0d0 * a
    else
        tmp = (x - y) * ((-60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+142) {
		tmp = (x - y) * (60.0 / z);
	} else if (t_1 <= 2e+113) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+142:
		tmp = (x - y) * (60.0 / z)
	elif t_1 <= 2e+113:
		tmp = 120.0 * a
	else:
		tmp = (x - y) * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+142)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	elseif (t_1 <= 2e+113)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+142)
		tmp = (x - y) * (60.0 / z);
	elseif (t_1 <= 2e+113)
		tmp = 120.0 * a;
	else
		tmp = (x - y) * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+142], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+113], N[(120.0 * a), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e142

   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%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 62.2%

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

   if -2.0000000000000001e142 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e113

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 65.5

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

   5. Applied rewrites 65.5%

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

   if 2e113 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 94.3

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 58.1%

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

Alternative 4: 53.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+137}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+199)
     (* x (/ 60.0 z))
     (if (<= t_1 5e+137) (* 120.0 a) (* (- y) (/ -60.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+199) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= 5e+137) {
		tmp = 120.0 * a;
	} else {
		tmp = -y * (-60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+199)) then
        tmp = x * (60.0d0 / z)
    else if (t_1 <= 5d+137) then
        tmp = 120.0d0 * a
    else
        tmp = -y * ((-60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+199) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= 5e+137) {
		tmp = 120.0 * a;
	} else {
		tmp = -y * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+199:
		tmp = x * (60.0 / z)
	elif t_1 <= 5e+137:
		tmp = 120.0 * a
	else:
		tmp = -y * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+199)
		tmp = Float64(x * Float64(60.0 / z));
	elseif (t_1 <= 5e+137)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-y) * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+199)
		tmp = x * (60.0 / z);
	elseif (t_1 <= 5e+137)
		tmp = 120.0 * a;
	else
		tmp = -y * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+199], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+137], N[(120.0 * a), $MachinePrecision], N[((-y) * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999998e199

   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

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 41.4%

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

   10. Applied rewrites 41.5%

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

   if -4.9999999999999998e199 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000002e137

   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 63.1

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

   5. Applied rewrites 63.1%

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

   if 5.0000000000000002e137 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 96.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 93.7

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

   5. Applied rewrites 93.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 59.3%

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

   9. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot y\right) \cdot \frac{\color{blue}{-60}}{t} \]
   10. Step-by-step derivation

   11. Applied rewrites 38.9%

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

Alternative 5: 53.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+199} \lor \neg \left(t\_1 \leq 10^{+111}\right):\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (or (<= t_1 -5e+199) (not (<= t_1 1e+111)))
     (* x (/ 60.0 z))
     (* 120.0 a))))

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+199) || !(t_1 <= 1e+111)) {
		tmp = x * (60.0 / z);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if ((t_1 <= (-5d+199)) .or. (.not. (t_1 <= 1d+111))) then
        tmp = x * (60.0d0 / z)
    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 t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e+199) || !(t_1 <= 1e+111)) {
		tmp = x * (60.0 / z);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if (t_1 <= -5e+199) or not (t_1 <= 1e+111):
		tmp = x * (60.0 / z)
	else:
		tmp = 120.0 * a
	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+199) || !(t_1 <= 1e+111))
		tmp = Float64(x * Float64(60.0 / z));
	else
		tmp = Float64(120.0 * a);
	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+199) || ~((t_1 <= 1e+111)))
		tmp = x * (60.0 / z);
	else
		tmp = 120.0 * a;
	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[Or[LessEqual[t$95$1, -5e+199], N[Not[LessEqual[t$95$1, 1e+111]], $MachinePrecision]], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999998e199 or 9.99999999999999957e110 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 32.2%

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

   10. Applied rewrites 32.2%

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

   if -4.9999999999999998e199 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999957e110

   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 65.0

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

   5. Applied rewrites 65.0%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+199} \lor \neg \left(\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+111}\right):\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+111}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+199)
     (* x (/ 60.0 z))
     (if (<= t_1 1e+111) (* 120.0 a) (* (/ y z) -60.0)))))

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+199) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= 1e+111) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / z) * -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) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+199)) then
        tmp = x * (60.0d0 / z)
    else if (t_1 <= 1d+111) then
        tmp = 120.0d0 * a
    else
        tmp = (y / z) * (-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 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+199) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= 1e+111) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / z) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+199:
		tmp = x * (60.0 / z)
	elif t_1 <= 1e+111:
		tmp = 120.0 * a
	else:
		tmp = (y / z) * -60.0
	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+199)
		tmp = Float64(x * Float64(60.0 / z));
	elseif (t_1 <= 1e+111)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(y / z) * -60.0);
	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+199)
		tmp = x * (60.0 / z);
	elseif (t_1 <= 1e+111)
		tmp = 120.0 * a;
	else
		tmp = (y / z) * -60.0;
	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+199], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+111], N[(120.0 * a), $MachinePrecision], N[(N[(y / z), $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)) < -4.9999999999999998e199

   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

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 41.4%

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

   10. Applied rewrites 41.5%

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

   if -4.9999999999999998e199 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999957e110

   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 65.0

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

   5. Applied rewrites 65.0%

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

   if 9.99999999999999957e110 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 50.3

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

   5. Applied rewrites 50.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 30.6%

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

Alternative 7: 53.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+111}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+199)
     (* x (/ 60.0 z))
     (if (<= t_1 1e+111) (* 120.0 a) (* (/ x z) 60.0)))))

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+199) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= 1e+111) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / z) * 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) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+199)) then
        tmp = x * (60.0d0 / z)
    else if (t_1 <= 1d+111) then
        tmp = 120.0d0 * a
    else
        tmp = (x / z) * 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 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+199) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= 1e+111) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+199:
		tmp = x * (60.0 / z)
	elif t_1 <= 1e+111:
		tmp = 120.0 * a
	else:
		tmp = (x / z) * 60.0
	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+199)
		tmp = Float64(x * Float64(60.0 / z));
	elseif (t_1 <= 1e+111)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / z) * 60.0);
	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+199)
		tmp = x * (60.0 / z);
	elseif (t_1 <= 1e+111)
		tmp = 120.0 * a;
	else
		tmp = (x / z) * 60.0;
	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+199], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+111], N[(120.0 * a), $MachinePrecision], N[(N[(x / z), $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)) < -4.9999999999999998e199

   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

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 41.4%

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

   10. Applied rewrites 41.5%

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

   if -4.9999999999999998e199 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999957e110

   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 65.0

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

   5. Applied rewrites 65.0%

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

   if 9.99999999999999957e110 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 50.3

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

   5. Applied rewrites 50.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 26.8%

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

Alternative 8: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-145}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-60}{t}, x - y, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(\frac{60}{z}, x - y, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+80}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e-145)
   (fma (/ -60.0 t) (- x y) (* 120.0 a))
   (if (<= t 3.6e-79)
     (fma (/ 60.0 z) (- x y) (* 120.0 a))
     (if (<= t 5e+80)
       (+ (/ (* -60.0 y) (- z t)) (* a 120.0))
       (fma (/ (- x y) t) -60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-145) {
		tmp = fma((-60.0 / t), (x - y), (120.0 * a));
	} else if (t <= 3.6e-79) {
		tmp = fma((60.0 / z), (x - y), (120.0 * a));
	} else if (t <= 5e+80) {
		tmp = ((-60.0 * y) / (z - t)) + (a * 120.0);
	} else {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e-145)
		tmp = fma(Float64(-60.0 / t), Float64(x - y), Float64(120.0 * a));
	elseif (t <= 3.6e-79)
		tmp = fma(Float64(60.0 / z), Float64(x - y), Float64(120.0 * a));
	elseif (t <= 5e+80)
		tmp = Float64(Float64(Float64(-60.0 * y) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e-145], N[(N[(-60.0 / t), $MachinePrecision] * N[(x - y), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-79], N[(N[(60.0 / z), $MachinePrecision] * N[(x - y), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+80], N[(N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.60000000000000004e-145

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.9

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 82.5

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

   7. Applied rewrites 82.5%

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

   if -1.60000000000000004e-145 < t < 3.6000000000000002e-79

   1. Initial program 98.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.8

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 90.0

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

   7. Applied rewrites 90.0%

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

   if 3.6000000000000002e-79 < t < 4.99999999999999961e80

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 86.1

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

   5. Applied rewrites 86.1%

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

   if 4.99999999999999961e80 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. *-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. lower-*.f64 96.0

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

   5. Applied rewrites 96.0%

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

Alternative 9: 71.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-39}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-60}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-60}{t}, -y, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-104)
   (fma (/ x z) 60.0 (* 120.0 a))
   (if (<= a 5.4e-39)
     (* (- x y) (/ 60.0 (- z t)))
     (if (<= a 1.85e-12)
       (fma y (/ -60.0 z) (* a 120.0))
       (fma (/ -60.0 t) (- y) (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-104) {
		tmp = fma((x / z), 60.0, (120.0 * a));
	} else if (a <= 5.4e-39) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (a <= 1.85e-12) {
		tmp = fma(y, (-60.0 / z), (a * 120.0));
	} else {
		tmp = fma((-60.0 / t), -y, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-104)
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	elseif (a <= 5.4e-39)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (a <= 1.85e-12)
		tmp = fma(y, Float64(-60.0 / z), Float64(a * 120.0));
	else
		tmp = fma(Float64(-60.0 / t), Float64(-y), Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-104], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e-39], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-12], N[(y * N[(-60.0 / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 / t), $MachinePrecision] * (-y) + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.5000000000000002e-104

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 75.0%

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

   if -9.5000000000000002e-104 < a < 5.4000000000000001e-39

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 82.6

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

   5. Applied rewrites 82.6%

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

   if 5.4000000000000001e-39 < a < 1.84999999999999999e-12

   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

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 67.7

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

   5. Applied rewrites 67.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 89.5%

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

   10. Applied rewrites 89.8%

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

   if 1.84999999999999999e-12 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.9

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 76.4

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

   7. Applied rewrites 76.4%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 83.0

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

   10. Applied rewrites 83.0%

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

Alternative 10: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-21} \lor \neg \left(y \leq 125000000000\right):\\ \;\;\;\;\frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.8e-21) (not (<= y 125000000000.0)))
   (+ (/ (* -60.0 y) (- z t)) (* a 120.0))
   (+ (/ (* 60.0 x) (- z t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.8e-21) || !(y <= 125000000000.0)) {
		tmp = ((-60.0 * y) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.8d-21)) .or. (.not. (y <= 125000000000.0d0))) then
        tmp = (((-60.0d0) * y) / (z - t)) + (a * 120.0d0)
    else
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.8e-21) || !(y <= 125000000000.0)) {
		tmp = ((-60.0 * y) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.8e-21) or not (y <= 125000000000.0):
		tmp = ((-60.0 * y) / (z - t)) + (a * 120.0)
	else:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.8e-21) || !(y <= 125000000000.0))
		tmp = Float64(Float64(Float64(-60.0 * y) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.8e-21) || ~((y <= 125000000000.0)))
		tmp = ((-60.0 * y) / (z - t)) + (a * 120.0);
	else
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.8e-21], N[Not[LessEqual[y, 125000000000.0]], $MachinePrecision]], N[(N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $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 2 regimes

2. if y < -2.80000000000000004e-21 or 1.25e11 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 84.0

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

   5. Applied rewrites 84.0%

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

   if -2.80000000000000004e-21 < y < 1.25e11

   1. Initial program 99.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 97.1

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

   5. Applied rewrites 97.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-21} \lor \neg \left(y \leq 125000000000\right):\\ \;\;\;\;\frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-145} \lor \neg \left(t \leq 7 \cdot 10^{-17}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.6e-145) (not (<= t 7e-17)))
   (fma (/ (- x y) t) -60.0 (* 120.0 a))
   (fma (/ (- x y) z) 60.0 (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.6e-145) || !(t <= 7e-17)) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.6e-145) || !(t <= 7e-17))
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.6e-145], N[Not[LessEqual[t, 7e-17]], $MachinePrecision]], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.60000000000000004e-145 or 7.0000000000000003e-17 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. *-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. lower-*.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if -1.60000000000000004e-145 < t < 7.0000000000000003e-17

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 88.1

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

   5. Applied rewrites 88.1%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-145} \lor \neg \left(t \leq 7 \cdot 10^{-17}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-145}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-60}{t}, x - y, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{60}{z}, x - y, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e-145)
   (fma (/ -60.0 t) (- x y) (* 120.0 a))
   (if (<= t 7e-17)
     (fma (/ 60.0 z) (- x y) (* 120.0 a))
     (fma (/ (- x y) t) -60.0 (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-145) {
		tmp = fma((-60.0 / t), (x - y), (120.0 * a));
	} else if (t <= 7e-17) {
		tmp = fma((60.0 / z), (x - y), (120.0 * a));
	} else {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e-145)
		tmp = fma(Float64(-60.0 / t), Float64(x - y), Float64(120.0 * a));
	elseif (t <= 7e-17)
		tmp = fma(Float64(60.0 / z), Float64(x - y), Float64(120.0 * a));
	else
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e-145], N[(N[(-60.0 / t), $MachinePrecision] * N[(x - y), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-17], N[(N[(60.0 / z), $MachinePrecision] * N[(x - y), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.60000000000000004e-145

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.9

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 82.5

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

   7. Applied rewrites 82.5%

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

   if -1.60000000000000004e-145 < t < 7.0000000000000003e-17

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.8

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 88.2

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

   7. Applied rewrites 88.2%

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

   if 7.0000000000000003e-17 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. *-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. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

Alternative 13: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-145}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-60}{t}, x - y, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e-145)
   (fma (/ -60.0 t) (- x y) (* 120.0 a))
   (if (<= t 7e-17)
     (fma (/ (- x y) z) 60.0 (* 120.0 a))
     (fma (/ (- x y) t) -60.0 (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-145) {
		tmp = fma((-60.0 / t), (x - y), (120.0 * a));
	} else if (t <= 7e-17) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e-145)
		tmp = fma(Float64(-60.0 / t), Float64(x - y), Float64(120.0 * a));
	elseif (t <= 7e-17)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e-145], N[(N[(-60.0 / t), $MachinePrecision] * N[(x - y), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-17], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.60000000000000004e-145

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.9

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 82.5

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

   7. Applied rewrites 82.5%

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

   if -1.60000000000000004e-145 < t < 7.0000000000000003e-17

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if 7.0000000000000003e-17 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. *-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. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

Alternative 14: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-60}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-137}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.65e-45)
   (fma y (/ -60.0 z) (* a 120.0))
   (if (<= z 1.05e-137)
     (fma (/ (- x y) t) -60.0 (* 120.0 a))
     (fma (/ x z) 60.0 (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.65e-45) {
		tmp = fma(y, (-60.0 / z), (a * 120.0));
	} else if (z <= 1.05e-137) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else {
		tmp = fma((x / z), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.65e-45)
		tmp = fma(y, Float64(-60.0 / z), Float64(a * 120.0));
	elseif (z <= 1.05e-137)
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.65e-45], N[(y * N[(-60.0 / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-137], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6499999999999999e-45

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 82.6

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

   5. Applied rewrites 82.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.3%

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

   10. Applied rewrites 74.4%

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

   if -2.6499999999999999e-45 < z < 1.04999999999999996e-137

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. *-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. lower-*.f64 89.7

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

   5. Applied rewrites 89.7%

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

   if 1.04999999999999996e-137 < z

   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

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 80.7

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 73.2%

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

Alternative 15: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-47} \lor \neg \left(a \leq 5.2 \cdot 10^{-39}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.4e-47) (not (<= a 5.2e-39)))
   (* 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 <= -2.4e-47) || !(a <= 5.2e-39)) {
		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 <= (-2.4d-47)) .or. (.not. (a <= 5.2d-39))) 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 <= -2.4e-47) || !(a <= 5.2e-39)) {
		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 <= -2.4e-47) or not (a <= 5.2e-39):
		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 ((a <= -2.4e-47) || !(a <= 5.2e-39))
		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 <= -2.4e-47) || ~((a <= 5.2e-39)))
		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[a, -2.4e-47], N[Not[LessEqual[a, 5.2e-39]], $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 a < -2.3999999999999999e-47 or 5.2e-39 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

   if -2.3999999999999999e-47 < a < 5.2e-39

   1. Initial program 98.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 80.1

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

   5. Applied rewrites 80.1%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-47} \lor \neg \left(a \leq 5.2 \cdot 10^{-39}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-39}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-104)
   (fma (/ x z) 60.0 (* 120.0 a))
   (if (<= a 5.2e-39) (* (- x y) (/ 60.0 (- z t))) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-104) {
		tmp = fma((x / z), 60.0, (120.0 * a));
	} else if (a <= 5.2e-39) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-104)
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	elseif (a <= 5.2e-39)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-104], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-39], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000002e-104

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 75.0%

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

   if -9.5000000000000002e-104 < a < 5.2e-39

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 82.6

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

   5. Applied rewrites 82.6%

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

   if 5.2e-39 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 75.6

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

   5. Applied rewrites 75.6%

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

Alternative 17: 57.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+155} \lor \neg \left(y \leq 2 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9e+155) (not (<= y 2e+128)))
   (* (/ y (- z t)) -60.0)
   (* 120.0 a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9e+155) || !(y <= 2e+128)) {
		tmp = (y / (z - 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 ((y <= (-9d+155)) .or. (.not. (y <= 2d+128))) then
        tmp = (y / (z - 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 ((y <= -9e+155) || !(y <= 2e+128)) {
		tmp = (y / (z - t)) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9e+155) or not (y <= 2e+128):
		tmp = (y / (z - t)) * -60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9e+155) || !(y <= 2e+128))
		tmp = Float64(Float64(y / Float64(z - 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 ((y <= -9e+155) || ~((y <= 2e+128)))
		tmp = (y / (z - t)) * -60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9e+155], N[Not[LessEqual[y, 2e+128]], $MachinePrecision]], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999947e155 or 2.0000000000000002e128 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-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 81.3

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 66.4%

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

   if -8.99999999999999947e155 < y < 2.0000000000000002e128

   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 61.7

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

   5. Applied rewrites 61.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+155} \lor \neg \left(y \leq 2 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.9% 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 99.5%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 50.3

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

5. Applied rewrites 50.3%

   \[\leadsto \color{blue}{120 \cdot a} \]
6. Add Preprocessing

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024339 
(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)))