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

Percentage Accurate: 99.2% → 99.3%

Time: 12.6s

Alternatives: 20

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: 99.3% 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 99.7%

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

   1. lift--.f64 N/A

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

   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 99.8

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

   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 99.8

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

4. Applied egg-rr 99.8%

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

Alternative 2: 56.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\frac{x - y}{z \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+256)
     (* -60.0 (/ y (- z t)))
     (if (<= t_1 -5e+19)
       (/ (* x 60.0) (- z t))
       (if (<= t_1 -1e-51)
         (/ (* y -60.0) (- z t))
         (if (<= t_1 2e+53)
           (* a 120.0)
           (if (<= t_1 5e+126)
             (/ (- x y) (* z 0.016666666666666666))
             (* -60.0 (/ (- x 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 <= -2e+256) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= -5e+19) {
		tmp = (x * 60.0) / (z - t);
	} else if (t_1 <= -1e-51) {
		tmp = (y * -60.0) / (z - t);
	} else if (t_1 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+126) {
		tmp = (x - y) / (z * 0.016666666666666666);
	} else {
		tmp = -60.0 * ((x - 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 <= (-2d+256)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_1 <= (-5d+19)) then
        tmp = (x * 60.0d0) / (z - t)
    else if (t_1 <= (-1d-51)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (t_1 <= 2d+53) then
        tmp = a * 120.0d0
    else if (t_1 <= 5d+126) then
        tmp = (x - y) / (z * 0.016666666666666666d0)
    else
        tmp = (-60.0d0) * ((x - 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 <= -2e+256) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= -5e+19) {
		tmp = (x * 60.0) / (z - t);
	} else if (t_1 <= -1e-51) {
		tmp = (y * -60.0) / (z - t);
	} else if (t_1 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+126) {
		tmp = (x - y) / (z * 0.016666666666666666);
	} else {
		tmp = -60.0 * ((x - 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 <= -2e+256:
		tmp = -60.0 * (y / (z - t))
	elif t_1 <= -5e+19:
		tmp = (x * 60.0) / (z - t)
	elif t_1 <= -1e-51:
		tmp = (y * -60.0) / (z - t)
	elif t_1 <= 2e+53:
		tmp = a * 120.0
	elif t_1 <= 5e+126:
		tmp = (x - y) / (z * 0.016666666666666666)
	else:
		tmp = -60.0 * ((x - 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 <= -2e+256)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_1 <= -5e+19)
		tmp = Float64(Float64(x * 60.0) / Float64(z - t));
	elseif (t_1 <= -1e-51)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (t_1 <= 2e+53)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 5e+126)
		tmp = Float64(Float64(x - y) / Float64(z * 0.016666666666666666));
	else
		tmp = Float64(-60.0 * Float64(Float64(x - 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 <= -2e+256)
		tmp = -60.0 * (y / (z - t));
	elseif (t_1 <= -5e+19)
		tmp = (x * 60.0) / (z - t);
	elseif (t_1 <= -1e-51)
		tmp = (y * -60.0) / (z - t);
	elseif (t_1 <= 2e+53)
		tmp = a * 120.0;
	elseif (t_1 <= 5e+126)
		tmp = (x - y) / (z * 0.016666666666666666);
	else
		tmp = -60.0 * ((x - 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, -2e+256], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+19], N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-51], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+126], N[(N[(x - y), $MachinePrecision] / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e256

   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. Simplified 74.2%

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

   if -2.0000000000000001e256 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e19

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 55.1

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

   5. Simplified 55.1%

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

   if -5e19 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e-51

   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 85.3

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

   5. Simplified 85.3%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 67.4

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

   8. Simplified 67.4%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e53

   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 76.1

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

   5. Simplified 76.1%

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

   if 2e53 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999977e126

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 77.9

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

   5. Simplified 77.9%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   7. Applied egg-rr 77.9%

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

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 61.1

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

   10. Simplified 61.1%

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

       1. lift--.f64 N/A

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

       2. clear-num N/A

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

       3. un-div-inv N/A

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

       4. lower-/.f64 N/A

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

       5. div-inv N/A

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

       6. lower-*.f64 N/A

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

       7. metadata-eval 61.3

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

   12. Applied egg-rr 61.3%

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

   if 4.99999999999999977e126 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 91.4

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

   5. Simplified 91.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 59.4

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

   8. Simplified 59.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\frac{x - y}{z \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot 60\\ t_2 := \frac{t\_1}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\frac{t\_1}{z}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

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+256)
     (* -60.0 (/ y (- z t)))
     (if (<= t_2 -5e+19)
       (/ (* x 60.0) (- z t))
       (if (<= t_2 -1e-51)
         (/ (* y -60.0) (- z t))
         (if (<= t_2 2e+53)
           (* a 120.0)
           (if (<= t_2 5e+126) (/ t_1 z) (* -60.0 (/ (- x y) t)))))))))

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+256) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_2 <= -5e+19) {
		tmp = (x * 60.0) / (z - t);
	} else if (t_2 <= -1e-51) {
		tmp = (y * -60.0) / (z - t);
	} else if (t_2 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_2 <= 5e+126) {
		tmp = t_1 / z;
	} else {
		tmp = -60.0 * ((x - 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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * 60.0d0
    t_2 = t_1 / (z - t)
    if (t_2 <= (-2d+256)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_2 <= (-5d+19)) then
        tmp = (x * 60.0d0) / (z - t)
    else if (t_2 <= (-1d-51)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (t_2 <= 2d+53) then
        tmp = a * 120.0d0
    else if (t_2 <= 5d+126) then
        tmp = t_1 / z
    else
        tmp = (-60.0d0) * ((x - 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;
	double t_2 = t_1 / (z - t);
	double tmp;
	if (t_2 <= -2e+256) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_2 <= -5e+19) {
		tmp = (x * 60.0) / (z - t);
	} else if (t_2 <= -1e-51) {
		tmp = (y * -60.0) / (z - t);
	} else if (t_2 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_2 <= 5e+126) {
		tmp = t_1 / z;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	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+256:
		tmp = -60.0 * (y / (z - t))
	elif t_2 <= -5e+19:
		tmp = (x * 60.0) / (z - t)
	elif t_2 <= -1e-51:
		tmp = (y * -60.0) / (z - t)
	elif t_2 <= 2e+53:
		tmp = a * 120.0
	elif t_2 <= 5e+126:
		tmp = t_1 / z
	else:
		tmp = -60.0 * ((x - y) / t)
	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+256)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_2 <= -5e+19)
		tmp = Float64(Float64(x * 60.0) / Float64(z - t));
	elseif (t_2 <= -1e-51)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (t_2 <= 2e+53)
		tmp = Float64(a * 120.0);
	elseif (t_2 <= 5e+126)
		tmp = Float64(t_1 / z);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	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+256)
		tmp = -60.0 * (y / (z - t));
	elseif (t_2 <= -5e+19)
		tmp = (x * 60.0) / (z - t);
	elseif (t_2 <= -1e-51)
		tmp = (y * -60.0) / (z - t);
	elseif (t_2 <= 2e+53)
		tmp = a * 120.0;
	elseif (t_2 <= 5e+126)
		tmp = t_1 / z;
	else
		tmp = -60.0 * ((x - y) / t);
	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+256], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e+19], N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-51], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+126], N[(t$95$1 / z), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e256

   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. Simplified 74.2%

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

   if -2.0000000000000001e256 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e19

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 55.1

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

   5. Simplified 55.1%

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

   if -5e19 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e-51

   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 85.3

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

   5. Simplified 85.3%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 67.4

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

   8. Simplified 67.4%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e53

   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 76.1

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

   5. Simplified 76.1%

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

   if 2e53 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999977e126

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 77.9

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

   5. Simplified 77.9%

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

   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 61.2

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

   8. Simplified 61.2%

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

   if 4.99999999999999977e126 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 91.4

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

   5. Simplified 91.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 59.4

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

   8. Simplified 59.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+256)
     (* -60.0 (/ y (- z t)))
     (if (<= t_1 -5e+19)
       (/ (* x 60.0) (- z t))
       (if (<= t_1 -1e-51)
         (/ (* y -60.0) (- z t))
         (if (<= t_1 2e+53)
           (* a 120.0)
           (if (<= t_1 5e+126)
             (* (- x y) (/ 60.0 z))
             (* -60.0 (/ (- x 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 <= -2e+256) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= -5e+19) {
		tmp = (x * 60.0) / (z - t);
	} else if (t_1 <= -1e-51) {
		tmp = (y * -60.0) / (z - t);
	} else if (t_1 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+126) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = -60.0 * ((x - 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 <= (-2d+256)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_1 <= (-5d+19)) then
        tmp = (x * 60.0d0) / (z - t)
    else if (t_1 <= (-1d-51)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (t_1 <= 2d+53) then
        tmp = a * 120.0d0
    else if (t_1 <= 5d+126) then
        tmp = (x - y) * (60.0d0 / z)
    else
        tmp = (-60.0d0) * ((x - 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 <= -2e+256) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= -5e+19) {
		tmp = (x * 60.0) / (z - t);
	} else if (t_1 <= -1e-51) {
		tmp = (y * -60.0) / (z - t);
	} else if (t_1 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+126) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = -60.0 * ((x - 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 <= -2e+256:
		tmp = -60.0 * (y / (z - t))
	elif t_1 <= -5e+19:
		tmp = (x * 60.0) / (z - t)
	elif t_1 <= -1e-51:
		tmp = (y * -60.0) / (z - t)
	elif t_1 <= 2e+53:
		tmp = a * 120.0
	elif t_1 <= 5e+126:
		tmp = (x - y) * (60.0 / z)
	else:
		tmp = -60.0 * ((x - 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 <= -2e+256)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_1 <= -5e+19)
		tmp = Float64(Float64(x * 60.0) / Float64(z - t));
	elseif (t_1 <= -1e-51)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (t_1 <= 2e+53)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 5e+126)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	else
		tmp = Float64(-60.0 * Float64(Float64(x - 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 <= -2e+256)
		tmp = -60.0 * (y / (z - t));
	elseif (t_1 <= -5e+19)
		tmp = (x * 60.0) / (z - t);
	elseif (t_1 <= -1e-51)
		tmp = (y * -60.0) / (z - t);
	elseif (t_1 <= 2e+53)
		tmp = a * 120.0;
	elseif (t_1 <= 5e+126)
		tmp = (x - y) * (60.0 / z);
	else
		tmp = -60.0 * ((x - 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, -2e+256], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+19], N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-51], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+126], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e256

   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. Simplified 74.2%

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

   if -2.0000000000000001e256 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e19

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 55.1

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

   5. Simplified 55.1%

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

   if -5e19 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e-51

   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 85.3

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

   5. Simplified 85.3%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 67.4

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

   8. Simplified 67.4%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e53

   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 76.1

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

   5. Simplified 76.1%

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

   if 2e53 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999977e126

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 77.9

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

   5. Simplified 77.9%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   7. Applied egg-rr 77.9%

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

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 61.1

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

   10. Simplified 61.1%

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

   if 4.99999999999999977e126 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 91.4

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

   5. Simplified 91.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 59.4

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

   8. Simplified 59.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+256)
     (* -60.0 (/ y (- z t)))
     (if (<= t_1 -5e+19)
       (* -60.0 (/ x (- t z)))
       (if (<= t_1 -1e-51)
         (/ (* y -60.0) (- z t))
         (if (<= t_1 2e+53)
           (* a 120.0)
           (if (<= t_1 5e+126)
             (* (- x y) (/ 60.0 z))
             (* -60.0 (/ (- x 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 <= -2e+256) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= -5e+19) {
		tmp = -60.0 * (x / (t - z));
	} else if (t_1 <= -1e-51) {
		tmp = (y * -60.0) / (z - t);
	} else if (t_1 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+126) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = -60.0 * ((x - 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 <= (-2d+256)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_1 <= (-5d+19)) then
        tmp = (-60.0d0) * (x / (t - z))
    else if (t_1 <= (-1d-51)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (t_1 <= 2d+53) then
        tmp = a * 120.0d0
    else if (t_1 <= 5d+126) then
        tmp = (x - y) * (60.0d0 / z)
    else
        tmp = (-60.0d0) * ((x - 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 <= -2e+256) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= -5e+19) {
		tmp = -60.0 * (x / (t - z));
	} else if (t_1 <= -1e-51) {
		tmp = (y * -60.0) / (z - t);
	} else if (t_1 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+126) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = -60.0 * ((x - 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 <= -2e+256:
		tmp = -60.0 * (y / (z - t))
	elif t_1 <= -5e+19:
		tmp = -60.0 * (x / (t - z))
	elif t_1 <= -1e-51:
		tmp = (y * -60.0) / (z - t)
	elif t_1 <= 2e+53:
		tmp = a * 120.0
	elif t_1 <= 5e+126:
		tmp = (x - y) * (60.0 / z)
	else:
		tmp = -60.0 * ((x - 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 <= -2e+256)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_1 <= -5e+19)
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	elseif (t_1 <= -1e-51)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (t_1 <= 2e+53)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 5e+126)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	else
		tmp = Float64(-60.0 * Float64(Float64(x - 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 <= -2e+256)
		tmp = -60.0 * (y / (z - t));
	elseif (t_1 <= -5e+19)
		tmp = -60.0 * (x / (t - z));
	elseif (t_1 <= -1e-51)
		tmp = (y * -60.0) / (z - t);
	elseif (t_1 <= 2e+53)
		tmp = a * 120.0;
	elseif (t_1 <= 5e+126)
		tmp = (x - y) * (60.0 / z);
	else
		tmp = -60.0 * ((x - 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, -2e+256], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+19], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-51], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+126], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e256

   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. Simplified 74.2%

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

   if -2.0000000000000001e256 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e19

   1. Initial program 99.5%

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

      1. lift--.f64 N/A

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

      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 egg-rr 99.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 55.1

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

   7. Simplified 55.1%

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

   if -5e19 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e-51

   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 85.3

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

   5. Simplified 85.3%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 67.4

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

   8. Simplified 67.4%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e53

   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 76.1

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

   5. Simplified 76.1%

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

   if 2e53 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999977e126

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 77.9

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

   5. Simplified 77.9%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   7. Applied egg-rr 77.9%

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

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 61.1

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

   10. Simplified 61.1%

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

   if 4.99999999999999977e126 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 91.4

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

   5. Simplified 91.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 59.4

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

   8. Simplified 59.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

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+256)
     t_1
     (if (<= t_2 -5e+19)
       (* -60.0 (/ x (- t z)))
       (if (<= t_2 -1e-51)
         t_1
         (if (<= t_2 2e+53)
           (* a 120.0)
           (if (<= t_2 5e+126)
             (* (- x y) (/ 60.0 z))
             (* -60.0 (/ (- x y) 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+256) {
		tmp = t_1;
	} else if (t_2 <= -5e+19) {
		tmp = -60.0 * (x / (t - z));
	} else if (t_2 <= -1e-51) {
		tmp = t_1;
	} else if (t_2 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_2 <= 5e+126) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = -60.0 * ((x - 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) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+256)) then
        tmp = t_1
    else if (t_2 <= (-5d+19)) then
        tmp = (-60.0d0) * (x / (t - z))
    else if (t_2 <= (-1d-51)) then
        tmp = t_1
    else if (t_2 <= 2d+53) then
        tmp = a * 120.0d0
    else if (t_2 <= 5d+126) then
        tmp = (x - y) * (60.0d0 / z)
    else
        tmp = (-60.0d0) * ((x - 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 = -60.0 * (y / (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+256) {
		tmp = t_1;
	} else if (t_2 <= -5e+19) {
		tmp = -60.0 * (x / (t - z));
	} else if (t_2 <= -1e-51) {
		tmp = t_1;
	} else if (t_2 <= 2e+53) {
		tmp = a * 120.0;
	} else if (t_2 <= 5e+126) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = -60.0 * ((x - y) / 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+256:
		tmp = t_1
	elif t_2 <= -5e+19:
		tmp = -60.0 * (x / (t - z))
	elif t_2 <= -1e-51:
		tmp = t_1
	elif t_2 <= 2e+53:
		tmp = a * 120.0
	elif t_2 <= 5e+126:
		tmp = (x - y) * (60.0 / z)
	else:
		tmp = -60.0 * ((x - y) / 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+256)
		tmp = t_1;
	elseif (t_2 <= -5e+19)
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	elseif (t_2 <= -1e-51)
		tmp = t_1;
	elseif (t_2 <= 2e+53)
		tmp = Float64(a * 120.0);
	elseif (t_2 <= 5e+126)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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+256)
		tmp = t_1;
	elseif (t_2 <= -5e+19)
		tmp = -60.0 * (x / (t - z));
	elseif (t_2 <= -1e-51)
		tmp = t_1;
	elseif (t_2 <= 2e+53)
		tmp = a * 120.0;
	elseif (t_2 <= 5e+126)
		tmp = (x - y) * (60.0 / z);
	else
		tmp = -60.0 * ((x - y) / 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+256], t$95$1, If[LessEqual[t$95$2, -5e+19], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-51], t$95$1, If[LessEqual[t$95$2, 2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+126], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e256 or -5e19 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e-51

   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 70.7

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

   5. Simplified 70.7%

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

   if -2.0000000000000001e256 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e19

   1. Initial program 99.5%

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

      1. lift--.f64 N/A

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

      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 egg-rr 99.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 55.1

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

   7. Simplified 55.1%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e53

   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 76.1

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

   5. Simplified 76.1%

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

   if 2e53 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999977e126

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 77.9

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

   5. Simplified 77.9%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   7. Applied egg-rr 77.9%

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

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 61.1

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

   10. Simplified 61.1%

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

   if 4.99999999999999977e126 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 91.4

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

   5. Simplified 91.4%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 59.4

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

   8. Simplified 59.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+126}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ t_3 := -60 \cdot \frac{x}{t - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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)))
        (t_3 (* -60.0 (/ x (- t z)))))
   (if (<= t_2 -2e+256)
     t_1
     (if (<= t_2 -5e+19)
       t_3
       (if (<= t_2 -1e-51) t_1 (if (<= t_2 2e+53) (* a 120.0) t_3))))))

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 t_3 = -60.0 * (x / (t - z));
	double tmp;
	if (t_2 <= -2e+256) {
		tmp = t_1;
	} else if (t_2 <= -5e+19) {
		tmp = t_3;
	} else if (t_2 <= -1e-51) {
		tmp = t_1;
	} else if (t_2 <= 2e+53) {
		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 = (-60.0d0) * (y / (z - t))
    t_2 = ((x - y) * 60.0d0) / (z - t)
    t_3 = (-60.0d0) * (x / (t - z))
    if (t_2 <= (-2d+256)) then
        tmp = t_1
    else if (t_2 <= (-5d+19)) then
        tmp = t_3
    else if (t_2 <= (-1d-51)) then
        tmp = t_1
    else if (t_2 <= 2d+53) 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 = -60.0 * (y / (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double t_3 = -60.0 * (x / (t - z));
	double tmp;
	if (t_2 <= -2e+256) {
		tmp = t_1;
	} else if (t_2 <= -5e+19) {
		tmp = t_3;
	} else if (t_2 <= -1e-51) {
		tmp = t_1;
	} else if (t_2 <= 2e+53) {
		tmp = a * 120.0;
	} else {
		tmp = t_3;
	}
	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)
	t_3 = -60.0 * (x / (t - z))
	tmp = 0
	if t_2 <= -2e+256:
		tmp = t_1
	elif t_2 <= -5e+19:
		tmp = t_3
	elif t_2 <= -1e-51:
		tmp = t_1
	elif t_2 <= 2e+53:
		tmp = a * 120.0
	else:
		tmp = t_3
	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))
	t_3 = Float64(-60.0 * Float64(x / Float64(t - z)))
	tmp = 0.0
	if (t_2 <= -2e+256)
		tmp = t_1;
	elseif (t_2 <= -5e+19)
		tmp = t_3;
	elseif (t_2 <= -1e-51)
		tmp = t_1;
	elseif (t_2 <= 2e+53)
		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 = -60.0 * (y / (z - t));
	t_2 = ((x - y) * 60.0) / (z - t);
	t_3 = -60.0 * (x / (t - z));
	tmp = 0.0;
	if (t_2 <= -2e+256)
		tmp = t_1;
	elseif (t_2 <= -5e+19)
		tmp = t_3;
	elseif (t_2 <= -1e-51)
		tmp = t_1;
	elseif (t_2 <= 2e+53)
		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[(-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]}, Block[{t$95$3 = N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+256], t$95$1, If[LessEqual[t$95$2, -5e+19], t$95$3, If[LessEqual[t$95$2, -1e-51], t$95$1, If[LessEqual[t$95$2, 2e+53], N[(a * 120.0), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e256 or -5e19 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e-51

   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 70.7

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

   5. Simplified 70.7%

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

   if -2.0000000000000001e256 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e19 or 2e53 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 egg-rr 99.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 50.9

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

   7. Simplified 50.9%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e53

   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 76.1

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

   5. Simplified 76.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+256}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - y}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{elif}\;t\_1 \leq 10^{-49}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -1e-51)
     (/ (- x y) (* (- t z) -0.016666666666666666))
     (if (<= t_1 1e-49)
       (* a 120.0)
       (if (<= t_1 1e+53)
         (fma -60.0 (/ (- x y) t) (* 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 <= -1e-51) {
		tmp = (x - y) / ((t - z) * -0.016666666666666666);
	} else if (t_1 <= 1e-49) {
		tmp = a * 120.0;
	} else if (t_1 <= 1e+53) {
		tmp = fma(-60.0, ((x - y) / t), (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 <= -1e-51)
		tmp = Float64(Float64(x - y) / Float64(Float64(t - z) * -0.016666666666666666));
	elseif (t_1 <= 1e-49)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 1e+53)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	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-51], N[(N[(x - y), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] * -0.016666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-49], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+53], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e-51

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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. Simplified 83.7%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 83.7

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

   7. Applied egg-rr 83.7%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. metadata-eval N/A

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

      8. div-inv N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. lift--.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval 83.8

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

   9. Applied egg-rr 83.8%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999936e-50

   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 83.4

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

   5. Simplified 83.4%

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

   if 9.99999999999999936e-50 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999999e52

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. 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 82.6

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

   5. Simplified 82.6%

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

   if 9.9999999999999999e52 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 84.6

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

   5. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.7

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

   7. Applied egg-rr 84.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - y}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{-49}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+116}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+122}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+256)
     (* y (/ -60.0 z))
     (if (<= t_1 -1e+116)
       (* -60.0 (/ x t))
       (if (<= t_1 4e+122) (* a 120.0) (/ (* y 60.0) 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+256) {
		tmp = y * (-60.0 / z);
	} else if (t_1 <= -1e+116) {
		tmp = -60.0 * (x / t);
	} else if (t_1 <= 4e+122) {
		tmp = a * 120.0;
	} else {
		tmp = (y * 60.0) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-2d+256)) then
        tmp = y * ((-60.0d0) / z)
    else if (t_1 <= (-1d+116)) then
        tmp = (-60.0d0) * (x / t)
    else if (t_1 <= 4d+122) then
        tmp = a * 120.0d0
    else
        tmp = (y * 60.0d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+256) {
		tmp = y * (-60.0 / z);
	} else if (t_1 <= -1e+116) {
		tmp = -60.0 * (x / t);
	} else if (t_1 <= 4e+122) {
		tmp = a * 120.0;
	} else {
		tmp = (y * 60.0) / 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+256:
		tmp = y * (-60.0 / z)
	elif t_1 <= -1e+116:
		tmp = -60.0 * (x / t)
	elif t_1 <= 4e+122:
		tmp = a * 120.0
	else:
		tmp = (y * 60.0) / 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+256)
		tmp = Float64(y * Float64(-60.0 / z));
	elseif (t_1 <= -1e+116)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (t_1 <= 4e+122)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(y * 60.0) / 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+256)
		tmp = y * (-60.0 / z);
	elseif (t_1 <= -1e+116)
		tmp = -60.0 * (x / t);
	elseif (t_1 <= 4e+122)
		tmp = a * 120.0;
	else
		tmp = (y * 60.0) / 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+256], N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+116], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+122], N[(a * 120.0), $MachinePrecision], N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e256

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. 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 73.8

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

   5. Simplified 73.8%

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

   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 61.4

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

   8. Simplified 61.4%

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

   if -2.0000000000000001e256 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000002e116

   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. 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 egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 69.5

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

   7. Simplified 69.5%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 48.8

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

   10. Simplified 48.8%

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

   if -1.00000000000000002e116 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.00000000000000006e122

   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 59.8

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

   5. Simplified 59.8%

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

   if 4.00000000000000006e122 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 91.8

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

   5. Simplified 91.8%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 43.2

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

   8. Simplified 43.2%

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

   9. Taylor expanded in z around 0

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 38.1

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

   11. Simplified 38.1%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+256}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+116}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 4 \cdot 10^{+122}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-60}{z}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+116}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+264}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ -60.0 z))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+256)
     t_1
     (if (<= t_2 -1e+116)
       (* -60.0 (/ x t))
       (if (<= t_2 5e+264) (* a 120.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-60.0 / z);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+256) {
		tmp = t_1;
	} else if (t_2 <= -1e+116) {
		tmp = -60.0 * (x / t);
	} else if (t_2 <= 5e+264) {
		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 = y * ((-60.0d0) / z)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+256)) then
        tmp = t_1
    else if (t_2 <= (-1d+116)) then
        tmp = (-60.0d0) * (x / t)
    else if (t_2 <= 5d+264) 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 = y * (-60.0 / z);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+256) {
		tmp = t_1;
	} else if (t_2 <= -1e+116) {
		tmp = -60.0 * (x / t);
	} else if (t_2 <= 5e+264) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-60.0 / z)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+256:
		tmp = t_1
	elif t_2 <= -1e+116:
		tmp = -60.0 * (x / t)
	elif t_2 <= 5e+264:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(-60.0 / z))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+256)
		tmp = t_1;
	elseif (t_2 <= -1e+116)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (t_2 <= 5e+264)
		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 = y * (-60.0 / z);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+256)
		tmp = t_1;
	elseif (t_2 <= -1e+116)
		tmp = -60.0 * (x / t);
	elseif (t_2 <= 5e+264)
		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[(y * N[(-60.0 / z), $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+256], t$95$1, If[LessEqual[t$95$2, -1e+116], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+264], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e256 or 5.00000000000000033e264 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 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 68.0

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

   5. Simplified 68.0%

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

   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 51.5

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

   8. Simplified 51.5%

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

   if -2.0000000000000001e256 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000002e116

   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. 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 egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 69.5

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

   7. Simplified 69.5%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 48.8

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

   10. Simplified 48.8%

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

   if -1.00000000000000002e116 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000033e264

   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

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

      1. lower-*.f64 54.9

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

   5. Simplified 54.9%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+256}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+116}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - y}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -1e-51)
     (/ (- x y) (* (- t z) -0.016666666666666666))
     (if (<= t_1 10000000000000.0) (* 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 <= -1e-51) {
		tmp = (x - y) / ((t - z) * -0.016666666666666666);
	} else if (t_1 <= 10000000000000.0) {
		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 <= (-1d-51)) then
        tmp = (x - y) / ((t - z) * (-0.016666666666666666d0))
    else if (t_1 <= 10000000000000.0d0) 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 <= -1e-51) {
		tmp = (x - y) / ((t - z) * -0.016666666666666666);
	} else if (t_1 <= 10000000000000.0) {
		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 <= -1e-51:
		tmp = (x - y) / ((t - z) * -0.016666666666666666)
	elif t_1 <= 10000000000000.0:
		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 <= -1e-51)
		tmp = Float64(Float64(x - y) / Float64(Float64(t - z) * -0.016666666666666666));
	elseif (t_1 <= 10000000000000.0)
		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 <= -1e-51)
		tmp = (x - y) / ((t - z) * -0.016666666666666666);
	elseif (t_1 <= 10000000000000.0)
		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, -1e-51], N[(N[(x - y), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] * -0.016666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], 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)) < -1e-51

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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. Simplified 83.7%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 83.7

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

   7. Applied egg-rr 83.7%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. metadata-eval N/A

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

      8. div-inv N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. lift--.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval 83.8

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

   9. Applied egg-rr 83.8%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e13

   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 79.0

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

   5. Simplified 79.0%

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

   if 1e13 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 82.3

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

   5. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 82.4

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

   7. Applied egg-rr 82.4%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - y}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -1e-51)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= t_1 10000000000000.0) (* 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 <= -1e-51) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= 10000000000000.0) {
		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 <= (-1d-51)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t_1 <= 10000000000000.0d0) 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 <= -1e-51) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= 10000000000000.0) {
		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 <= -1e-51:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t_1 <= 10000000000000.0:
		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 <= -1e-51)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t_1 <= 10000000000000.0)
		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 <= -1e-51)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t_1 <= 10000000000000.0)
		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, -1e-51], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], 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)) < -1e-51

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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. Simplified 83.7%

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

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 83.7

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

   7. Applied egg-rr 83.7%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e13

   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 79.0

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

   5. Simplified 79.0%

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

   if 1e13 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 82.3

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

   5. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 82.4

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

   7. Applied egg-rr 82.4%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z - t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -1e-51) t_1 (if (<= t_2 10000000000000.0) (* 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 <= -1e-51) {
		tmp = t_1;
	} else if (t_2 <= 10000000000000.0) {
		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 <= (-1d-51)) then
        tmp = t_1
    else if (t_2 <= 10000000000000.0d0) 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 <= -1e-51) {
		tmp = t_1;
	} else if (t_2 <= 10000000000000.0) {
		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 <= -1e-51:
		tmp = t_1
	elif t_2 <= 10000000000000.0:
		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 <= -1e-51)
		tmp = t_1;
	elseif (t_2 <= 10000000000000.0)
		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 <= -1e-51)
		tmp = t_1;
	elseif (t_2 <= 10000000000000.0)
		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, -1e-51], t$95$1, If[LessEqual[t$95$2, 10000000000000.0], 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)) < -1e-51 or 1e13 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 83.0

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

   5. Simplified 83.0%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 83.1

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

   7. Applied egg-rr 83.1%

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

   if -1e-51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e13

   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 79.0

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

   5. Simplified 79.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t - z}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x (- t z)))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e-7) t_1 (if (<= t_2 2e+53) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / (t - z));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e-7) {
		tmp = t_1;
	} else if (t_2 <= 2e+53) {
		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) * (x / (t - z))
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d-7)) then
        tmp = t_1
    else if (t_2 <= 2d+53) 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 * (x / (t - z));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e-7) {
		tmp = t_1;
	} else if (t_2 <= 2e+53) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / (t - z))
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e-7:
		tmp = t_1
	elif t_2 <= 2e+53:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / Float64(t - z)))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e-7)
		tmp = t_1;
	elseif (t_2 <= 2e+53)
		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 * (x / (t - z));
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e-7)
		tmp = t_1;
	elseif (t_2 <= 2e+53)
		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[(x / N[(t - z), $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-7], t$95$1, If[LessEqual[t$95$2, 2e+53], 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)) < -1.9999999999999999e-7 or 2e53 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 egg-rr 99.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 47.8

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

   7. Simplified 47.8%

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

   if -1.9999999999999999e-7 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e53

   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 72.7

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

   5. Simplified 72.7%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{-7}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -1e+116) t_1 (if (<= t_2 2e+139) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+116) {
		tmp = t_1;
	} else if (t_2 <= 2e+139) {
		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) * (x / t)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-1d+116)) then
        tmp = t_1
    else if (t_2 <= 2d+139) 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 * (x / t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+116) {
		tmp = t_1;
	} else if (t_2 <= 2e+139) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -1e+116:
		tmp = t_1
	elif t_2 <= 2e+139:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+116)
		tmp = t_1;
	elseif (t_2 <= 2e+139)
		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 * (x / t);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+116)
		tmp = t_1;
	elseif (t_2 <= 2e+139)
		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[(x / 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, -1e+116], t$95$1, If[LessEqual[t$95$2, 2e+139], 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)) < -1.00000000000000002e116 or 2.00000000000000007e139 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 53.1

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

   7. Simplified 53.1%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 30.7

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

   10. Simplified 30.7%

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

   if -1.00000000000000002e116 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000007e139

   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 58.8

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

   5. Simplified 58.8%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+116}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x \cdot -60}{t - z}\right)\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-61}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (/ (* x -60.0) (- t z)))))
   (if (<= (* a 120.0) -5e-63)
     t_1
     (if (<= (* a 120.0) 4e-61) (* (- x y) (/ 60.0 (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((x * -60.0) / (t - z)));
	double tmp;
	if ((a * 120.0) <= -5e-63) {
		tmp = t_1;
	} else if ((a * 120.0) <= 4e-61) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(x * -60.0) / Float64(t - z)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-63)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 4e-61)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(x * -60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-63], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-61], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000002e-63 or 4.0000000000000002e-61 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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 99.9

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

      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 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

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

      3. associate-*r* N/A

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

      4. lower-/.f64 N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 88.7

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

   7. Simplified 88.7%

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

   if -5.0000000000000002e-63 < (*.f64 a #s(literal 120 binary64)) < 4.0000000000000002e-61

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 87.1

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

   5. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 87.2

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

   7. Applied egg-rr 87.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x \cdot -60}{t - z}\right)\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-61}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x \cdot -60}{t - z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-61}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ x (- z t)) (* a 120.0))))
   (if (<= (* a 120.0) -5e-63)
     t_1
     (if (<= (* a 120.0) 4e-61) (* (- x y) (/ 60.0 (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(60.0, (x / (z - t)), (a * 120.0));
	double tmp;
	if ((a * 120.0) <= -5e-63) {
		tmp = t_1;
	} else if ((a * 120.0) <= 4e-61) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(x / Float64(z - t)), Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-63)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 4e-61)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-63], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-61], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000002e-63 or 4.0000000000000002e-61 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 88.7

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

   5. Simplified 88.7%

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

   if -5.0000000000000002e-63 < (*.f64 a #s(literal 120 binary64)) < 4.0000000000000002e-61

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 87.1

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

   5. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 87.2

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

   7. Applied egg-rr 87.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-61}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-136}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-61}:\\ \;\;\;\;\frac{x \cdot 60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-136)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-61) (/ (* x 60.0) z) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e-136) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-61) {
		tmp = (x * 60.0) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-4d-136)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-61) then
        tmp = (x * 60.0d0) / z
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e-136) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-61) {
		tmp = (x * 60.0) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e-136:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-61:
		tmp = (x * 60.0) / z
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-136)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-61)
		tmp = Float64(Float64(x * 60.0) / z);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e-136)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-61)
		tmp = (x * 60.0) / z;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-136], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-61], N[(N[(x * 60.0), $MachinePrecision] / z), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.00000000000000001e-136 or 1e-61 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 66.2

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

   5. Simplified 66.2%

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

   if -4.00000000000000001e-136 < (*.f64 a #s(literal 120 binary64)) < 1e-61

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.2

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

   5. Simplified 58.2%

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

   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 34.8

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

   8. Simplified 34.8%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-136}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-61}:\\ \;\;\;\;\frac{x \cdot 60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{y \cdot 60}{t - z}\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x \cdot -60}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (/ (* y 60.0) (- t z)))))
   (if (<= y -8.2e+155)
     t_1
     (if (<= y 1.08e+71) (fma a 120.0 (/ (* x -60.0) (- t z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((y * 60.0) / (t - z)));
	double tmp;
	if (y <= -8.2e+155) {
		tmp = t_1;
	} else if (y <= 1.08e+71) {
		tmp = fma(a, 120.0, ((x * -60.0) / (t - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(y * 60.0) / Float64(t - z)))
	tmp = 0.0
	if (y <= -8.2e+155)
		tmp = t_1;
	elseif (y <= 1.08e+71)
		tmp = fma(a, 120.0, Float64(Float64(x * -60.0) / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(y * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+155], t$95$1, If[LessEqual[y, 1.08e+71], N[(a * 120.0 + N[(N[(x * -60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999996e155 or 1.08e71 < y

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.7

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

      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 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 89.2

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

   7. Simplified 89.2%

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

   if -8.1999999999999996e155 < y < 1.08e71

   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. 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 99.8

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

      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 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

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

      3. associate-*r* N/A

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

      4. lower-/.f64 N/A

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

      5. associate-*r* N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 90.9

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

   7. Simplified 90.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot 60}{t - z}\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x \cdot -60}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot 60}{t - z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.9% 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 99.7%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 46.2

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

5. Simplified 46.2%

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

6. Final simplification 46.2%

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

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024207 
(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)))