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

Percentage Accurate: 99.3% → 99.3%

Time: 10.2s

Alternatives: 15

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% 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: 99.3% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. distribute-rgt-in N/A

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

   5. lower-fma.f64 N/A

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

   6. *-commutative N/A

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

   7. neg-mul-1 N/A

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

   8. associate-*r* N/A

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

   9. metadata-eval N/A

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

   10. metadata-eval N/A

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

   11. lower-*.f64 N/A

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

   12. metadata-eval 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot z}\\ \mathbf{elif}\;t\_1 \leq 10^{+51}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+197}:\\ \;\;\;\;\frac{-60}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -5e+102)
     (/ (- x y) (* 0.016666666666666666 z))
     (if (<= t_1 1e+51)
       (* 120.0 a)
       (if (<= t_1 5e+197) (* (/ -60.0 t) (- x y)) (* (/ (- x y) z) 60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -5e+102) {
		tmp = (x - y) / (0.016666666666666666 * z);
	} else if (t_1 <= 1e+51) {
		tmp = 120.0 * a;
	} else if (t_1 <= 5e+197) {
		tmp = (-60.0 / t) * (x - y);
	} else {
		tmp = ((x - 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 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-5d+102)) then
        tmp = (x - y) / (0.016666666666666666d0 * z)
    else if (t_1 <= 1d+51) then
        tmp = 120.0d0 * a
    else if (t_1 <= 5d+197) then
        tmp = ((-60.0d0) / t) * (x - y)
    else
        tmp = ((x - 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 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -5e+102) {
		tmp = (x - y) / (0.016666666666666666 * z);
	} else if (t_1 <= 1e+51) {
		tmp = 120.0 * a;
	} else if (t_1 <= 5e+197) {
		tmp = (-60.0 / t) * (x - y);
	} else {
		tmp = ((x - y) / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -5e+102:
		tmp = (x - y) / (0.016666666666666666 * z)
	elif t_1 <= 1e+51:
		tmp = 120.0 * a
	elif t_1 <= 5e+197:
		tmp = (-60.0 / t) * (x - y)
	else:
		tmp = ((x - y) / z) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+102)
		tmp = Float64(Float64(x - y) / Float64(0.016666666666666666 * z));
	elseif (t_1 <= 1e+51)
		tmp = Float64(120.0 * a);
	elseif (t_1 <= 5e+197)
		tmp = Float64(Float64(-60.0 / t) * Float64(x - y));
	else
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+102)
		tmp = (x - y) / (0.016666666666666666 * z);
	elseif (t_1 <= 1e+51)
		tmp = 120.0 * a;
	elseif (t_1 <= 5e+197)
		tmp = (-60.0 / t) * (x - y);
	else
		tmp = ((x - y) / z) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+102], N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+51], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$1, 5e+197], N[(N[(-60.0 / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e102

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 83.1

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

   5. Applied rewrites 83.1%

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

   7. Applied rewrites 83.3%

      \[\leadsto \frac{x - y}{\color{blue}{\left(z - t\right) \cdot 0.016666666666666666}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \frac{x - y}{\frac{1}{60} \cdot \color{blue}{z}} \]
   9. Step-by-step derivation

   10. Applied rewrites 51.2%

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

   if -5e102 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e51

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.8

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

   5. Applied rewrites 76.8%

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

   if 1e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000009e197

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-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 73.8

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 51.4%

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

   if 5.00000000000000009e197 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 89.4

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

   5. Applied rewrites 89.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 74.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+51}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+197}:\\ \;\;\;\;\frac{-60}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot 60\\ t_2 := \frac{t\_1}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{t\_1}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+51}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+197}:\\ \;\;\;\;\frac{-60}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) 60.0)) (t_2 (/ t_1 (- z t))))
   (if (<= t_2 -5e+102)
     (/ t_1 z)
     (if (<= t_2 1e+51)
       (* 120.0 a)
       (if (<= t_2 5e+197) (* (/ -60.0 t) (- x y)) (* (/ (- x y) z) 60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * 60.0;
	double t_2 = t_1 / (z - t);
	double tmp;
	if (t_2 <= -5e+102) {
		tmp = t_1 / z;
	} else if (t_2 <= 1e+51) {
		tmp = 120.0 * a;
	} else if (t_2 <= 5e+197) {
		tmp = (-60.0 / t) * (x - y);
	} else {
		tmp = ((x - 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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * 60.0d0
    t_2 = t_1 / (z - t)
    if (t_2 <= (-5d+102)) then
        tmp = t_1 / z
    else if (t_2 <= 1d+51) then
        tmp = 120.0d0 * a
    else if (t_2 <= 5d+197) then
        tmp = ((-60.0d0) / t) * (x - y)
    else
        tmp = ((x - 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 = (x - y) * 60.0;
	double t_2 = t_1 / (z - t);
	double tmp;
	if (t_2 <= -5e+102) {
		tmp = t_1 / z;
	} else if (t_2 <= 1e+51) {
		tmp = 120.0 * a;
	} else if (t_2 <= 5e+197) {
		tmp = (-60.0 / t) * (x - y);
	} else {
		tmp = ((x - y) / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * 60.0
	t_2 = t_1 / (z - t)
	tmp = 0
	if t_2 <= -5e+102:
		tmp = t_1 / z
	elif t_2 <= 1e+51:
		tmp = 120.0 * a
	elif t_2 <= 5e+197:
		tmp = (-60.0 / t) * (x - y)
	else:
		tmp = ((x - y) / z) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * 60.0)
	t_2 = Float64(t_1 / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+102)
		tmp = Float64(t_1 / z);
	elseif (t_2 <= 1e+51)
		tmp = Float64(120.0 * a);
	elseif (t_2 <= 5e+197)
		tmp = Float64(Float64(-60.0 / t) * Float64(x - y));
	else
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * 60.0;
	t_2 = t_1 / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+102)
		tmp = t_1 / z;
	elseif (t_2 <= 1e+51)
		tmp = 120.0 * a;
	elseif (t_2 <= 5e+197)
		tmp = (-60.0 / t) * (x - y);
	else
		tmp = ((x - y) / z) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+102], N[(t$95$1 / z), $MachinePrecision], If[LessEqual[t$95$2, 1e+51], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$2, 5e+197], N[(N[(-60.0 / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e102

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 83.1

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

   5. Applied rewrites 83.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 51.0%

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

   10. Applied rewrites 51.2%

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

   if -5e102 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e51

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.8

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

   5. Applied rewrites 76.8%

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

   if 1e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000009e197

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-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 73.8

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 51.4%

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

   if 5.00000000000000009e197 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 89.4

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

   5. Applied rewrites 89.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 74.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+51}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+197}:\\ \;\;\;\;\frac{-60}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) (* 0.016666666666666666 (- z t))))
        (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -5e+162)
     t_1
     (if (<= t_2 1e+51) (fma (/ y (- z t)) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / (0.016666666666666666 * (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -5e+162) {
		tmp = t_1;
	} else if (t_2 <= 1e+51) {
		tmp = fma((y / (z - t)), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / Float64(0.016666666666666666 * Float64(z - t)))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+162)
		tmp = t_1;
	elseif (t_2 <= 1e+51)
		tmp = fma(Float64(y / Float64(z - t)), -60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+162], t$95$1, If[LessEqual[t$95$2, 1e+51], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999997e162 or 1e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-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 83.5

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

   5. Applied rewrites 83.5%

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

   7. Applied rewrites 83.6%

      \[\leadsto \frac{x - y}{\color{blue}{\left(z - t\right) \cdot 0.016666666666666666}} \]

   if -4.9999999999999997e162 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e51

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 89.6

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

   5. Applied rewrites 89.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+162}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+51}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) (* 0.016666666666666666 (- z t))))
        (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -1e+41) t_1 (if (<= t_2 1e+51) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / (0.016666666666666666 * (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+41) {
		tmp = t_1;
	} else if (t_2 <= 1e+51) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (0.016666666666666666d0 * (z - t))
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-1d+41)) then
        tmp = t_1
    else if (t_2 <= 1d+51) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / (0.016666666666666666 * (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+41) {
		tmp = t_1;
	} else if (t_2 <= 1e+51) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) / (0.016666666666666666 * (z - t))
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -1e+41:
		tmp = t_1
	elif t_2 <= 1e+51:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / Float64(0.016666666666666666 * Float64(z - t)))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+41)
		tmp = t_1;
	elseif (t_2 <= 1e+51)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) / (0.016666666666666666 * (z - t));
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+41)
		tmp = t_1;
	elseif (t_2 <= 1e+51)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+41], t$95$1, If[LessEqual[t$95$2, 1e+51], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000001e41 or 1e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 77.9

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

   5. Applied rewrites 77.9%

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

   7. Applied rewrites 78.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(z - t\right) \cdot 0.016666666666666666}} \]

   if -1.00000000000000001e41 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e51

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 80.8

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

   5. Applied rewrites 80.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+41}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+51}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+51}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -1e+41) t_1 (if (<= t_2 1e+51) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+41) {
		tmp = t_1;
	} else if (t_2 <= 1e+51) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / (z - t)) * (x - y)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-1d+41)) then
        tmp = t_1
    else if (t_2 <= 1d+51) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+41) {
		tmp = t_1;
	} else if (t_2 <= 1e+51) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / (z - t)) * (x - y)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -1e+41:
		tmp = t_1
	elif t_2 <= 1e+51:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+41)
		tmp = t_1;
	elseif (t_2 <= 1e+51)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 / (z - t)) * (x - y);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+41)
		tmp = t_1;
	elseif (t_2 <= 1e+51)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+41], t$95$1, If[LessEqual[t$95$2, 1e+51], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000001e41 or 1e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 77.9

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

   5. Applied rewrites 77.9%

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

   if -1.00000000000000001e41 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e51

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 80.8

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

   5. Applied rewrites 80.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+41}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+51}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot 60\\ t_2 := \frac{t\_1}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{t\_1}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) 60.0)) (t_2 (/ t_1 (- z t))))
   (if (<= t_2 -5e+102)
     (/ t_1 z)
     (if (<= t_2 2e+176) (* 120.0 a) (* (/ (- x y) z) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * 60.0;
	double t_2 = t_1 / (z - t);
	double tmp;
	if (t_2 <= -5e+102) {
		tmp = t_1 / z;
	} else if (t_2 <= 2e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - 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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * 60.0d0
    t_2 = t_1 / (z - t)
    if (t_2 <= (-5d+102)) then
        tmp = t_1 / z
    else if (t_2 <= 2d+176) then
        tmp = 120.0d0 * a
    else
        tmp = ((x - 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 = (x - y) * 60.0;
	double t_2 = t_1 / (z - t);
	double tmp;
	if (t_2 <= -5e+102) {
		tmp = t_1 / z;
	} else if (t_2 <= 2e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * 60.0
	t_2 = t_1 / (z - t)
	tmp = 0
	if t_2 <= -5e+102:
		tmp = t_1 / z
	elif t_2 <= 2e+176:
		tmp = 120.0 * a
	else:
		tmp = ((x - y) / z) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * 60.0)
	t_2 = Float64(t_1 / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+102)
		tmp = Float64(t_1 / z);
	elseif (t_2 <= 2e+176)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * 60.0;
	t_2 = t_1 / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+102)
		tmp = t_1 / z;
	elseif (t_2 <= 2e+176)
		tmp = 120.0 * a;
	else
		tmp = ((x - y) / z) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+102], N[(t$95$1 / z), $MachinePrecision], If[LessEqual[t$95$2, 2e+176], N[(120.0 * a), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / 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)) < -5e102

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 83.1

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

   5. Applied rewrites 83.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 51.0%

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

   10. Applied rewrites 51.2%

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

   if -5e102 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e176

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.0

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

   5. Applied rewrites 70.0%

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

   if 2e176 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-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 89.1

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

   5. Applied rewrites 89.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 66.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z} \cdot 60\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) z) 60.0)) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -5e+102) t_1 (if (<= t_2 2e+176) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / z) * 60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -5e+102) {
		tmp = t_1;
	} else if (t_2 <= 2e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x - y) / z) * 60.0d0
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-5d+102)) then
        tmp = t_1
    else if (t_2 <= 2d+176) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / z) * 60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -5e+102) {
		tmp = t_1;
	} else if (t_2 <= 2e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) / z) * 60.0
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -5e+102:
		tmp = t_1
	elif t_2 <= 2e+176:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) / z) * 60.0)
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+102)
		tmp = t_1;
	elseif (t_2 <= 2e+176)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) / z) * 60.0;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+102)
		tmp = t_1;
	elseif (t_2 <= 2e+176)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+102], t$95$1, If[LessEqual[t$95$2, 2e+176], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e102 or 2e176 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-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 85.7

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.7%

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

   if -5e102 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e176

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.0

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

   5. Applied rewrites 70.0%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+192)
     (* (/ x z) 60.0)
     (if (<= t_1 2e+176) (* 120.0 a) (* (/ y z) -60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+192) {
		tmp = (x / z) * 60.0;
	} else if (t_1 <= 2e+176) {
		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 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-2d+192)) then
        tmp = (x / z) * 60.0d0
    else if (t_1 <= 2d+176) 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 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+192) {
		tmp = (x / z) * 60.0;
	} else if (t_1 <= 2e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / z) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -2e+192:
		tmp = (x / z) * 60.0
	elif t_1 <= 2e+176:
		tmp = 120.0 * a
	else:
		tmp = (y / z) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+192)
		tmp = Float64(Float64(x / z) * 60.0);
	elseif (t_1 <= 2e+176)
		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 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+192)
		tmp = (x / z) * 60.0;
	elseif (t_1 <= 2e+176)
		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[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+192], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+176], 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)) < -2.00000000000000008e192

   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 94.9

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

   5. Applied rewrites 94.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 40.9%

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

   if -2.00000000000000008e192 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e176

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.0

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

   5. Applied rewrites 66.0%

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

   if 2e176 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. neg-mul-1 N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 52.3

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

   7. Applied rewrites 52.3%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 44.4%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot 60\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x z) 60.0)) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+192) t_1 (if (<= t_2 2e+176) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * 60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+192) {
		tmp = t_1;
	} else if (t_2 <= 2e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) * 60.0d0
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+192)) then
        tmp = t_1
    else if (t_2 <= 2d+176) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * 60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+192) {
		tmp = t_1;
	} else if (t_2 <= 2e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / z) * 60.0
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+192:
		tmp = t_1
	elif t_2 <= 2e+176:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / z) * 60.0)
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+192)
		tmp = t_1;
	elseif (t_2 <= 2e+176)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / z) * 60.0;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+192)
		tmp = t_1;
	elseif (t_2 <= 2e+176)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+192], t$95$1, If[LessEqual[t$95$2, 2e+176], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000008e192 or 2e176 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 91.4

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

   5. Applied rewrites 91.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 39.4%

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

   if -2.00000000000000008e192 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e176

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.0

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

   5. Applied rewrites 66.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x}{z - t} \cdot 60\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* (/ x (- z t)) 60.0))))
   (if (<= x -6e+61)
     t_1
     (if (<= x 9e+101) (fma a 120.0 (/ (* y -60.0) (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((x / (z - t)) * 60.0));
	double tmp;
	if (x <= -6e+61) {
		tmp = t_1;
	} else if (x <= 9e+101) {
		tmp = fma(a, 120.0, ((y * -60.0) / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(x / Float64(z - t)) * 60.0))
	tmp = 0.0
	if (x <= -6e+61)
		tmp = t_1;
	elseif (x <= 9e+101)
		tmp = fma(a, 120.0, Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+61], t$95$1, If[LessEqual[x, 9e+101], N[(a * 120.0 + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6e61 or 9.0000000000000004e101 < x

   1. Initial program 99.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. neg-mul-1 N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 90.4

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

   7. Applied rewrites 90.4%

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

   if -6e61 < x < 9.0000000000000004e101

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 93.6

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

   5. Applied rewrites 93.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 93.6

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

   7. Applied rewrites 93.6%

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

Alternative 12: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x}{z - t} \cdot 60\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* (/ x (- z t)) 60.0))))
   (if (<= x -6e+61)
     t_1
     (if (<= x 9e+101) (fma (/ y (- z t)) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((x / (z - t)) * 60.0));
	double tmp;
	if (x <= -6e+61) {
		tmp = t_1;
	} else if (x <= 9e+101) {
		tmp = fma((y / (z - t)), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(x / Float64(z - t)) * 60.0))
	tmp = 0.0
	if (x <= -6e+61)
		tmp = t_1;
	elseif (x <= 9e+101)
		tmp = fma(Float64(y / Float64(z - t)), -60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+61], t$95$1, If[LessEqual[x, 9e+101], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6e61 or 9.0000000000000004e101 < x

   1. Initial program 99.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. neg-mul-1 N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 90.4

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

   7. Applied rewrites 90.4%

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

   if -6e61 < x < 9.0000000000000004e101

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.6

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

   5. Applied rewrites 93.6%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z - t} \cdot 60\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z - t} \cdot 60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+34}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.8e+34)
   (* 120.0 a)
   (if (<= z 1.25e+129) (fma (/ y t) 60.0 (* 120.0 a)) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.8e+34) {
		tmp = 120.0 * a;
	} else if (z <= 1.25e+129) {
		tmp = fma((y / t), 60.0, (120.0 * a));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.8e+34)
		tmp = Float64(120.0 * a);
	elseif (z <= 1.25e+129)
		tmp = fma(Float64(y / t), 60.0, Float64(120.0 * a));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.8e+34], N[(120.0 * a), $MachinePrecision], If[LessEqual[z, 1.25e+129], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.80000000000000038e34 or 1.2500000000000001e129 < 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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 73.9

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

   5. Applied rewrites 73.9%

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

   if -7.80000000000000038e34 < z < 1.2500000000000001e129

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 73.5

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

   5. Applied rewrites 73.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 65.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+34}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.8

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

   5. lift-/.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-/l* N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. frac-2neg N/A

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

   12. lower-/.f64 N/A

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

   13. metadata-eval N/A

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

   14. neg-sub0 N/A

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

   15. lift--.f64 N/A

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

   16. sub-neg N/A

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

   17. +-commutative N/A

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

   18. associate--r+ N/A

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

   19. neg-sub0 N/A

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

   20. remove-double-neg N/A

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

   21. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 15: 50.5% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in a around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 55.2

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

5. Applied rewrites 55.2%

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

6. Final simplification 55.2%

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

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024277 
(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)))