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

Percentage Accurate: 99.2% → 99.8%

Time: 12.3s

Alternatives: 18

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(a, 120, \frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma a 120.0 (/ (- x y) (* (- z t) 0.016666666666666666))))

C

double code(double x, double y, double z, double t, double a) {
	return fma(a, 120.0, ((x - y) / ((z - t) * 0.016666666666666666)));
}

Julia

function code(x, y, z, t, a)
	return fma(a, 120.0, Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666)))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. lift--.f64 N/A

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

   5. remove-double-neg N/A

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

   6. div-inv N/A

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

   7. lift-*.f64 N/A

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

   8. div-inv N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. associate-/l* N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lower-/.f64 99.8

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

4. Applied rewrites 99.8%

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

   1. metadata-eval N/A

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. remove-double-neg N/A

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

   5. distribute-neg-in N/A

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

   6. sub-neg N/A

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

   7. lift--.f64 N/A

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

   8. frac-2neg N/A

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

   9. un-div-inv N/A

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

   10. lift-/.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lift--.f64 N/A

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

   13. *-commutative N/A

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

   14. lift-*.f64 N/A

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

   15. lift-fma.f64 99.7

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

6. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\right)} \]
7. Add Preprocessing

Alternative 2: 58.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot 60\\ t_2 := \frac{t\_1}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+233}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+125}:\\ \;\;\;\;\frac{t\_1}{z}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_2 \leq 6 \cdot 10^{+103}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

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 -2e+233)
     (* -60.0 (/ y (- z t)))
     (if (<= t_2 -2e+125)
       (/ t_1 z)
       (if (<= t_2 -2e+14)
         (* (- x y) (/ -60.0 t))
         (if (<= t_2 6e+103)
           (* a 120.0)
           (/ (- x y) (* z 0.016666666666666666))))))))

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 <= -2e+233) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_2 <= -2e+125) {
		tmp = t_1 / z;
	} else if (t_2 <= -2e+14) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_2 <= 6e+103) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) / (z * 0.016666666666666666);
	}
	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 <= (-2d+233)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_2 <= (-2d+125)) then
        tmp = t_1 / z
    else if (t_2 <= (-2d+14)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (t_2 <= 6d+103) then
        tmp = a * 120.0d0
    else
        tmp = (x - y) / (z * 0.016666666666666666d0)
    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 <= -2e+233) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_2 <= -2e+125) {
		tmp = t_1 / z;
	} else if (t_2 <= -2e+14) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_2 <= 6e+103) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) / (z * 0.016666666666666666);
	}
	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 <= -2e+233:
		tmp = -60.0 * (y / (z - t))
	elif t_2 <= -2e+125:
		tmp = t_1 / z
	elif t_2 <= -2e+14:
		tmp = (x - y) * (-60.0 / t)
	elif t_2 <= 6e+103:
		tmp = a * 120.0
	else:
		tmp = (x - y) / (z * 0.016666666666666666)
	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 <= -2e+233)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_2 <= -2e+125)
		tmp = Float64(t_1 / z);
	elseif (t_2 <= -2e+14)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (t_2 <= 6e+103)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x - y) / Float64(z * 0.016666666666666666));
	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 <= -2e+233)
		tmp = -60.0 * (y / (z - t));
	elseif (t_2 <= -2e+125)
		tmp = t_1 / z;
	elseif (t_2 <= -2e+14)
		tmp = (x - y) * (-60.0 / t);
	elseif (t_2 <= 6e+103)
		tmp = a * 120.0;
	else
		tmp = (x - y) / (z * 0.016666666666666666);
	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, -2e+233], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e+125], N[(t$95$1 / z), $MachinePrecision], If[LessEqual[t$95$2, -2e+14], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 6e+103], N[(a * 120.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.99999999999999995e233

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 74.2

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

   5. Applied rewrites 74.2%

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

   if -1.99999999999999995e233 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999998e125

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 83.7

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

   5. Applied rewrites 83.7%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 62.2

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

   8. Applied rewrites 62.2%

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

   if -1.9999999999999998e125 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e14

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 78.5

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 50.7

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

   8. Applied rewrites 50.7%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 50.7

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

   10. Applied rewrites 50.7%

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

   if -2e14 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 6e103

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 70.6

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

   5. Applied rewrites 70.6%

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

   if 6e103 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.5%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 86.5

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

   5. Applied rewrites 86.5%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. div-inv N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 88.6

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

   7. Applied rewrites 88.6%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{\color{blue}{z \cdot \frac{1}{60}}} \]

      2. lower-*.f64 58.0

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

   10. Applied rewrites 58.0%

       \[\leadsto \frac{x - y}{\color{blue}{z \cdot 0.016666666666666666}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+233}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+125}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 6 \cdot 10^{+103}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z \cdot 0.016666666666666666}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot 60\\ t_2 := \frac{t\_1}{z - t}\\ t_3 := \frac{t\_1}{z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+233}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+125}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+107}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) 60.0)) (t_2 (/ t_1 (- z t))) (t_3 (/ t_1 z)))
   (if (<= t_2 -2e+233)
     (* -60.0 (/ y (- z t)))
     (if (<= t_2 -2e+125)
       t_3
       (if (<= t_2 -2e+14)
         (* (- x y) (/ -60.0 t))
         (if (<= t_2 1e+107) (* a 120.0) t_3))))))

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 t_3 = t_1 / z;
	double tmp;
	if (t_2 <= -2e+233) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_2 <= -2e+125) {
		tmp = t_3;
	} else if (t_2 <= -2e+14) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_2 <= 1e+107) {
		tmp = a * 120.0;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (x - y) * 60.0d0
    t_2 = t_1 / (z - t)
    t_3 = t_1 / z
    if (t_2 <= (-2d+233)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_2 <= (-2d+125)) then
        tmp = t_3
    else if (t_2 <= (-2d+14)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (t_2 <= 1d+107) then
        tmp = a * 120.0d0
    else
        tmp = t_3
    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 t_3 = t_1 / z;
	double tmp;
	if (t_2 <= -2e+233) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_2 <= -2e+125) {
		tmp = t_3;
	} else if (t_2 <= -2e+14) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_2 <= 1e+107) {
		tmp = a * 120.0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * 60.0
	t_2 = t_1 / (z - t)
	t_3 = t_1 / z
	tmp = 0
	if t_2 <= -2e+233:
		tmp = -60.0 * (y / (z - t))
	elif t_2 <= -2e+125:
		tmp = t_3
	elif t_2 <= -2e+14:
		tmp = (x - y) * (-60.0 / t)
	elif t_2 <= 1e+107:
		tmp = a * 120.0
	else:
		tmp = t_3
	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))
	t_3 = Float64(t_1 / z)
	tmp = 0.0
	if (t_2 <= -2e+233)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_2 <= -2e+125)
		tmp = t_3;
	elseif (t_2 <= -2e+14)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (t_2 <= 1e+107)
		tmp = Float64(a * 120.0);
	else
		tmp = t_3;
	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);
	t_3 = t_1 / z;
	tmp = 0.0;
	if (t_2 <= -2e+233)
		tmp = -60.0 * (y / (z - t));
	elseif (t_2 <= -2e+125)
		tmp = t_3;
	elseif (t_2 <= -2e+14)
		tmp = (x - y) * (-60.0 / t);
	elseif (t_2 <= 1e+107)
		tmp = a * 120.0;
	else
		tmp = t_3;
	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]}, Block[{t$95$3 = N[(t$95$1 / z), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+233], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e+125], t$95$3, If[LessEqual[t$95$2, -2e+14], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+107], N[(a * 120.0), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.99999999999999995e233

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 74.2

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

   5. Applied rewrites 74.2%

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

   if -1.99999999999999995e233 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999998e125 or 9.9999999999999997e106 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 60.5

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

   8. Applied rewrites 60.5%

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

   if -1.9999999999999998e125 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e14

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 78.5

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 50.7

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

   8. Applied rewrites 50.7%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 50.7

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

   10. Applied rewrites 50.7%

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

   if -2e14 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999997e106

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 69.8

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

   5. Applied rewrites 69.8%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+233}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+125}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+107}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot -60}{z - t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_2 \leq 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y -60.0) (- z t))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+33)
     t_1
     (if (<= t_2 5e+14)
       (* a 120.0)
       (if (<= t_2 1e+214) t_1 (/ (* x 60.0) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * -60.0) / (z - t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = a * 120.0;
	} else if (t_2 <= 1e+214) {
		tmp = t_1;
	} else {
		tmp = (x * 60.0) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (-60.0d0)) / (z - t)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+33)) then
        tmp = t_1
    else if (t_2 <= 5d+14) then
        tmp = a * 120.0d0
    else if (t_2 <= 1d+214) then
        tmp = t_1
    else
        tmp = (x * 60.0d0) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * -60.0) / (z - t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = a * 120.0;
	} else if (t_2 <= 1e+214) {
		tmp = t_1;
	} else {
		tmp = (x * 60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * -60.0) / (z - t)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+33:
		tmp = t_1
	elif t_2 <= 5e+14:
		tmp = a * 120.0
	elif t_2 <= 1e+214:
		tmp = t_1
	else:
		tmp = (x * 60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * -60.0) / Float64(z - t))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = Float64(a * 120.0);
	elseif (t_2 <= 1e+214)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * 60.0) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * -60.0) / (z - t);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = a * 120.0;
	elseif (t_2 <= 1e+214)
		tmp = t_1;
	else
		tmp = (x * 60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $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, -2e+33], t$95$1, If[LessEqual[t$95$2, 5e+14], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$2, 1e+214], t$95$1, N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999999e33 or 5e14 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999995e213

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 80.0

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 51.3

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

   8. Applied rewrites 51.3%

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

   if -1.9999999999999999e33 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5e14

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

   if 9.9999999999999995e213 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 62.1

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

   5. Applied rewrites 62.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+33}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+214}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot -60}{z - t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y -60.0) (- z t))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+33)
     t_1
     (if (<= t_2 5e+14)
       (* a 120.0)
       (if (<= t_2 2e+214) t_1 (* (- x y) (/ -60.0 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * -60.0) / (z - t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = a * 120.0;
	} else if (t_2 <= 2e+214) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (-60.0d0)) / (z - t)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+33)) then
        tmp = t_1
    else if (t_2 <= 5d+14) then
        tmp = a * 120.0d0
    else if (t_2 <= 2d+214) then
        tmp = t_1
    else
        tmp = (x - y) * ((-60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * -60.0) / (z - t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = a * 120.0;
	} else if (t_2 <= 2e+214) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * -60.0) / (z - t)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+33:
		tmp = t_1
	elif t_2 <= 5e+14:
		tmp = a * 120.0
	elif t_2 <= 2e+214:
		tmp = t_1
	else:
		tmp = (x - y) * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * -60.0) / Float64(z - t))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = Float64(a * 120.0);
	elseif (t_2 <= 2e+214)
		tmp = t_1;
	else
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * -60.0) / (z - t);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = a * 120.0;
	elseif (t_2 <= 2e+214)
		tmp = t_1;
	else
		tmp = (x - y) * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $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, -2e+33], t$95$1, If[LessEqual[t$95$2, 5e+14], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+214], t$95$1, N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999999e33 or 5e14 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.9999999999999999e214

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 80.2

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 50.8

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

   8. Applied rewrites 50.8%

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

   if -1.9999999999999999e33 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5e14

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

   if 1.9999999999999999e214 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 94.1%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 88.8

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

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 55.4

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

   8. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 61.2

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

   10. Applied rewrites 61.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+33}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+33)
     t_1
     (if (<= t_2 5e+14)
       (* a 120.0)
       (if (<= t_2 2e+214) t_1 (* (- x y) (/ -60.0 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = a * 120.0;
	} else if (t_2 <= 2e+214) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+33)) then
        tmp = t_1
    else if (t_2 <= 5d+14) then
        tmp = a * 120.0d0
    else if (t_2 <= 2d+214) then
        tmp = t_1
    else
        tmp = (x - y) * ((-60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = a * 120.0;
	} else if (t_2 <= 2e+214) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+33:
		tmp = t_1
	elif t_2 <= 5e+14:
		tmp = a * 120.0
	elif t_2 <= 2e+214:
		tmp = t_1
	else:
		tmp = (x - y) * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = Float64(a * 120.0);
	elseif (t_2 <= 2e+214)
		tmp = t_1;
	else
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = a * 120.0;
	elseif (t_2 <= 2e+214)
		tmp = t_1;
	else
		tmp = (x - y) * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / 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, -2e+33], t$95$1, If[LessEqual[t$95$2, 5e+14], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+214], t$95$1, N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999999e33 or 5e14 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.9999999999999999e214

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 50.8

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

   5. Applied rewrites 50.8%

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

   if -1.9999999999999999e33 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5e14

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

   if 1.9999999999999999e214 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 94.1%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 88.8

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

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 55.4

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

   8. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 61.2

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

   10. Applied rewrites 61.2%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+33}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+214}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(120, a, 60 \cdot \frac{y}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -1e+33)
     t_1
     (if (<= t_1 2e+124)
       (fma 120.0 a (* 60.0 (/ y (- t z))))
       (* (- x y) (/ 60.0 (- z t)))))))

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 <= -1e+33) {
		tmp = t_1;
	} else if (t_1 <= 2e+124) {
		tmp = fma(120.0, a, (60.0 * (y / (t - z))));
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	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 <= -1e+33)
		tmp = t_1;
	elseif (t_1 <= 2e+124)
		tmp = fma(120.0, a, Float64(60.0 * Float64(y / Float64(t - z))));
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return 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, -1e+33], t$95$1, If[LessEqual[t$95$1, 2e+124], N[(120.0 * a + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999995e32

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

   if -9.9999999999999995e32 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.9999999999999999e124

   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

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. div-inv N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. frac-2neg N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. associate-*l* N/A

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

      13. lower-fma.f64 N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 87.9

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

   7. Applied rewrites 87.9%

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

   if 1.9999999999999999e124 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.1%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 89.5

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

   5. Applied rewrites 89.5%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lift-/.f64 N/A

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

      5. lower-*.f64 92.2

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

   7. Applied rewrites 92.2%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+33}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(120, a, 60 \cdot \frac{y}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-16}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\mathsf{fma}\left(z, 0.016666666666666666, t \cdot -0.016666666666666666\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+14)
     t_1
     (if (<= t_1 1e-16)
       (* a 120.0)
       (/ (- x y) (fma z 0.016666666666666666 (* t -0.016666666666666666)))))))

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+14) {
		tmp = t_1;
	} else if (t_1 <= 1e-16) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) / fma(z, 0.016666666666666666, (t * -0.016666666666666666));
	}
	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+14)
		tmp = t_1;
	elseif (t_1 <= 1e-16)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x - y) / fma(z, 0.016666666666666666, Float64(t * -0.016666666666666666)));
	end
	return 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+14], t$95$1, If[LessEqual[t$95$1, 1e-16], N[(a * 120.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(z * 0.016666666666666666 + N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e14

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 83.1

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

   5. Applied rewrites 83.1%

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

   if -2e14 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999998e-17

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 78.8

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

   5. Applied rewrites 78.8%

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

   if 9.9999999999999998e-17 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. div-inv N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 78.2

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

   7. Applied rewrites 78.2%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{x - y}{\color{blue}{\frac{1}{60} \cdot z + \frac{-1}{60} \cdot t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x - y}{\color{blue}{z \cdot \frac{1}{60}} + \frac{-1}{60} \cdot t} \]

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 78.3

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

   10. Applied rewrites 78.3%

       \[\leadsto \frac{x - y}{\color{blue}{\mathsf{fma}\left(z, 0.016666666666666666, t \cdot -0.016666666666666666\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{-16}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\mathsf{fma}\left(z, 0.016666666666666666, t \cdot -0.016666666666666666\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-16}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+14)
     t_1
     (if (<= t_1 1e-16) (* a 120.0) (* (- x y) (/ 60.0 (- z t)))))))

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+14) {
		tmp = t_1;
	} else if (t_1 <= 1e-16) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-2d+14)) then
        tmp = t_1
    else if (t_1 <= 1d-16) then
        tmp = a * 120.0d0
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+14) {
		tmp = t_1;
	} else if (t_1 <= 1e-16) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -2e+14:
		tmp = t_1
	elif t_1 <= 1e-16:
		tmp = a * 120.0
	else:
		tmp = (x - y) * (60.0 / (z - t))
	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+14)
		tmp = t_1;
	elseif (t_1 <= 1e-16)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+14)
		tmp = t_1;
	elseif (t_1 <= 1e-16)
		tmp = a * 120.0;
	else
		tmp = (x - y) * (60.0 / (z - t));
	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+14], t$95$1, If[LessEqual[t$95$1, 1e-16], N[(a * 120.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e14

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 83.1

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

   5. Applied rewrites 83.1%

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

   if -2e14 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999998e-17

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 78.8

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

   5. Applied rewrites 78.8%

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

   if 9.9999999999999998e-17 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lift-/.f64 N/A

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

      5. lower-*.f64 78.3

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

   7. Applied rewrites 78.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{-16}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z - t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-16}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ 60.0 (- z t)))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+14) t_1 (if (<= t_2 1e-16) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (60.0 / (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+14) {
		tmp = t_1;
	} else if (t_2 <= 1e-16) {
		tmp = a * 120.0;
	} 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) * (60.0d0 / (z - t))
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+14)) then
        tmp = t_1
    else if (t_2 <= 1d-16) then
        tmp = a * 120.0d0
    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) * (60.0 / (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+14) {
		tmp = t_1;
	} else if (t_2 <= 1e-16) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * (60.0 / (z - t))
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+14:
		tmp = t_1
	elif t_2 <= 1e-16:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+14)
		tmp = t_1;
	elseif (t_2 <= 1e-16)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * (60.0 / (z - t));
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+14)
		tmp = t_1;
	elseif (t_2 <= 1e-16)
		tmp = a * 120.0;
	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[(60.0 / 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, -2e+14], t$95$1, If[LessEqual[t$95$2, 1e-16], N[(a * 120.0), $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)) < -2e14 or 9.9999999999999998e-17 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 80.0

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

   5. Applied rewrites 80.0%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lift-/.f64 N/A

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

      5. lower-*.f64 80.6

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

   7. Applied rewrites 80.6%

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

   if -2e14 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999998e-17

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 78.8

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

   5. Applied rewrites 78.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{-16}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+33) t_1 (if (<= t_2 5e+14) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = a * 120.0;
	} 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) * (y / (z - t))
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+33)) then
        tmp = t_1
    else if (t_2 <= 5d+14) then
        tmp = a * 120.0d0
    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 * (y / (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+33:
		tmp = t_1
	elif t_2 <= 5e+14:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / 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, -2e+33], t$95$1, If[LessEqual[t$95$2, 5e+14], N[(a * 120.0), $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)) < -1.9999999999999999e33 or 5e14 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 48.2

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

   5. Applied rewrites 48.2%

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

   if -1.9999999999999999e33 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5e14

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+33}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+124}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -4e+65)
     (/ (* y -60.0) z)
     (if (<= t_1 2e+124) (* a 120.0) (* x (/ 60.0 z))))))

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 <= -4e+65) {
		tmp = (y * -60.0) / z;
	} else if (t_1 <= 2e+124) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-4d+65)) then
        tmp = (y * (-60.0d0)) / z
    else if (t_1 <= 2d+124) then
        tmp = a * 120.0d0
    else
        tmp = x * (60.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -4e+65) {
		tmp = (y * -60.0) / z;
	} else if (t_1 <= 2e+124) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -4e+65:
		tmp = (y * -60.0) / z
	elif t_1 <= 2e+124:
		tmp = a * 120.0
	else:
		tmp = x * (60.0 / z)
	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 <= -4e+65)
		tmp = Float64(Float64(y * -60.0) / z);
	elseif (t_1 <= 2e+124)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(60.0 / z));
	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 <= -4e+65)
		tmp = (y * -60.0) / z;
	elseif (t_1 <= 2e+124)
		tmp = a * 120.0;
	else
		tmp = x * (60.0 / z);
	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, -4e+65], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2e+124], N[(a * 120.0), $MachinePrecision], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 53.4

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

   5. Applied rewrites 53.4%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 31.4

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

   8. Applied rewrites 31.4%

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

   if -4e65 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.9999999999999999e124

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 66.2

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

   5. Applied rewrites 66.2%

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

   if 1.9999999999999999e124 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 64.1

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

   5. Applied rewrites 64.1%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 40.3

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

   8. Applied rewrites 40.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 40.3

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

   10. Applied rewrites 40.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+65}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+124}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+124}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -4e+65)
     (* y (/ -60.0 z))
     (if (<= t_1 2e+124) (* a 120.0) (* x (/ 60.0 z))))))

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 <= -4e+65) {
		tmp = y * (-60.0 / z);
	} else if (t_1 <= 2e+124) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-4d+65)) then
        tmp = y * ((-60.0d0) / z)
    else if (t_1 <= 2d+124) then
        tmp = a * 120.0d0
    else
        tmp = x * (60.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -4e+65) {
		tmp = y * (-60.0 / z);
	} else if (t_1 <= 2e+124) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -4e+65:
		tmp = y * (-60.0 / z)
	elif t_1 <= 2e+124:
		tmp = a * 120.0
	else:
		tmp = x * (60.0 / z)
	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 <= -4e+65)
		tmp = Float64(y * Float64(-60.0 / z));
	elseif (t_1 <= 2e+124)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(60.0 / z));
	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 <= -4e+65)
		tmp = y * (-60.0 / z);
	elseif (t_1 <= 2e+124)
		tmp = a * 120.0;
	else
		tmp = x * (60.0 / z);
	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, -4e+65], N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+124], N[(a * 120.0), $MachinePrecision], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 53.4

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

   5. Applied rewrites 53.4%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 31.4

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

   8. Applied rewrites 31.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 31.3

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

   10. Applied rewrites 31.3%

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

   if -4e65 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.9999999999999999e124

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 66.2

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

   5. Applied rewrites 66.2%

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

   if 1.9999999999999999e124 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 64.1

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

   5. Applied rewrites 64.1%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 40.3

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

   8. Applied rewrites 40.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 40.3

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

   10. Applied rewrites 40.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+124}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+165}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -4e+65)
     (* y (/ -60.0 z))
     (if (<= t_1 4e+165) (* a 120.0) (* 60.0 (/ y t))))))

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 <= -4e+65) {
		tmp = y * (-60.0 / z);
	} else if (t_1 <= 4e+165) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-4d+65)) then
        tmp = y * ((-60.0d0) / z)
    else if (t_1 <= 4d+165) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -4e+65) {
		tmp = y * (-60.0 / z);
	} else if (t_1 <= 4e+165) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -4e+65:
		tmp = y * (-60.0 / z)
	elif t_1 <= 4e+165:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	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 <= -4e+65)
		tmp = Float64(y * Float64(-60.0 / z));
	elseif (t_1 <= 4e+165)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	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 <= -4e+65)
		tmp = y * (-60.0 / z);
	elseif (t_1 <= 4e+165)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	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, -4e+65], N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+165], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 53.4

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

   5. Applied rewrites 53.4%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 31.4

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

   8. Applied rewrites 31.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 31.3

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

   10. Applied rewrites 31.3%

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

   if -4e65 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 3.9999999999999996e165

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 63.7

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

   5. Applied rewrites 63.7%

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

   if 3.9999999999999996e165 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 96.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. metadata-eval N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg N/A

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

      9. un-div-inv N/A

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

      10. lift-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lift-fma.f64 99.7

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

   6. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\right)} \]

   7. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 52.2

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}}\right) \]

   9. Applied rewrites 52.2%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}}\right) \]

   10. Taylor expanded in y around inf

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

       1. lower-*.f64 N/A

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

       2. lower-/.f64 36.2

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

   12. Applied rewrites 36.2%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 4 \cdot 10^{+165}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+165}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ y t))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+205) t_1 (if (<= t_2 4e+165) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (y / t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+205) {
		tmp = t_1;
	} else if (t_2 <= 4e+165) {
		tmp = a * 120.0;
	} 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 * (y / t)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+205)) then
        tmp = t_1
    else if (t_2 <= 4d+165) then
        tmp = a * 120.0d0
    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 * (y / t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+205) {
		tmp = t_1;
	} else if (t_2 <= 4e+165) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (y / t)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+205:
		tmp = t_1
	elif t_2 <= 4e+165:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(y / t))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+205)
		tmp = t_1;
	elseif (t_2 <= 4e+165)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (y / t);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+205)
		tmp = t_1;
	elseif (t_2 <= 4e+165)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(y / t), $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, -2e+205], t$95$1, If[LessEqual[t$95$2, 4e+165], N[(a * 120.0), $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)) < -2.00000000000000003e205 or 3.9999999999999996e165 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. metadata-eval N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg N/A

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

      9. un-div-inv N/A

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

      10. lift-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lift-fma.f64 99.6

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

   6. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\right)} \]

   7. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 56.4

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}}\right) \]

   9. Applied rewrites 56.4%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}}\right) \]

   10. Taylor expanded in y around inf

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

       1. lower-*.f64 N/A

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

       2. lower-/.f64 37.9

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

   12. Applied rewrites 37.9%

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

   if -2.00000000000000003e205 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 3.9999999999999996e165

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 56.4

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

   5. Applied rewrites 56.4%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+205}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 4 \cdot 10^{+165}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* a 120.0))))
   (if (<= t -1.3e-10)
     t_1
     (if (<= t 7.5e-9) (fma 60.0 (/ (- x y) z) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (a * 120.0));
	double tmp;
	if (t <= -1.3e-10) {
		tmp = t_1;
	} else if (t <= 7.5e-9) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0))
	tmp = 0.0
	if (t <= -1.3e-10)
		tmp = t_1;
	elseif (t <= 7.5e-9)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e-10], t$95$1, If[LessEqual[t, 7.5e-9], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999991e-10 or 7.49999999999999933e-9 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 86.1

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

   5. Applied rewrites 86.1%

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

   if -1.29999999999999991e-10 < t < 7.49999999999999933e-9

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 83.7

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

   5. Applied rewrites 83.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 99.3% accurate, 1.1× speedup

Math

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

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(Float64(x - y) * -60.0) / Float64(t - z)))
end

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. lift--.f64 N/A

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

   5. remove-double-neg N/A

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

   6. lift-/.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. +-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. lower-fma.f64 99.4

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

   11. lift-/.f64 N/A

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

   12. frac-2neg N/A

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

   13. lower-/.f64 N/A

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

   14. lift-*.f64 N/A

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

   15. *-commutative N/A

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

   16. distribute-rgt-neg-in N/A

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

   17. lower-*.f64 N/A

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

   18. metadata-eval N/A

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

   19. neg-sub0 N/A

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

   20. lift--.f64 N/A

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

   21. sub-neg N/A

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

   22. +-commutative N/A

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

   23. associate--r+ N/A

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

   24. neg-sub0 N/A

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

   25. remove-double-neg N/A

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

   26. lower--.f64 99.4

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

4. Applied rewrites 99.4%

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

Alternative 18: 51.0% accurate, 5.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return 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 = a * 120.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 46.9

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

5. Applied rewrites 46.9%

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

6. Final simplification 46.9%

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

Developer Target 1: 99.7% 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 2024214 
(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)))