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

Percentage Accurate: 99.4% → 99.8%

Time: 10.7s

Alternatives: 17

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.1

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

   5. lift-/.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-/l* N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. frac-2neg N/A

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

   12. lower-/.f64 N/A

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

   13. metadata-eval N/A

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

   14. neg-sub0 N/A

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

   15. lift--.f64 N/A

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

   16. sub-neg N/A

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

   17. +-commutative N/A

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

   18. associate--r+ N/A

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

   19. neg-sub0 N/A

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

   20. remove-double-neg N/A

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

   21. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 59.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+240}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\frac{-60}{z - t} \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.016666666666666666 \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+240)
     (/ (- x y) (* 0.016666666666666666 z))
     (if (<= t_1 -1e+78)
       (* (/ -60.0 (- z t)) y)
       (if (<= t_1 1e+120)
         (* 120.0 a)
         (/ x (* -0.016666666666666666 (- t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+240) {
		tmp = (x - y) / (0.016666666666666666 * z);
	} else if (t_1 <= -1e+78) {
		tmp = (-60.0 / (z - t)) * y;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = x / (-0.016666666666666666 * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+240)) then
        tmp = (x - y) / (0.016666666666666666d0 * z)
    else if (t_1 <= (-1d+78)) then
        tmp = ((-60.0d0) / (z - t)) * y
    else if (t_1 <= 1d+120) then
        tmp = 120.0d0 * a
    else
        tmp = x / ((-0.016666666666666666d0) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+240) {
		tmp = (x - y) / (0.016666666666666666 * z);
	} else if (t_1 <= -1e+78) {
		tmp = (-60.0 / (z - t)) * y;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = x / (-0.016666666666666666 * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+240:
		tmp = (x - y) / (0.016666666666666666 * z)
	elif t_1 <= -1e+78:
		tmp = (-60.0 / (z - t)) * y
	elif t_1 <= 1e+120:
		tmp = 120.0 * a
	else:
		tmp = x / (-0.016666666666666666 * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+240)
		tmp = Float64(Float64(x - y) / Float64(0.016666666666666666 * z));
	elseif (t_1 <= -1e+78)
		tmp = Float64(Float64(-60.0 / Float64(z - t)) * y);
	elseif (t_1 <= 1e+120)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(x / Float64(-0.016666666666666666 * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+240)
		tmp = (x - y) / (0.016666666666666666 * z);
	elseif (t_1 <= -1e+78)
		tmp = (-60.0 / (z - t)) * y;
	elseif (t_1 <= 1e+120)
		tmp = 120.0 * a;
	else
		tmp = x / (-0.016666666666666666 * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+240], N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+78], N[(N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+120], N[(120.0 * a), $MachinePrecision], N[(x / N[(-0.016666666666666666 * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000001e240

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 92.2

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

   5. Applied rewrites 92.2%

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

   7. Applied rewrites 92.4%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 82.9%

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

   if -1.00000000000000001e240 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000001e78

   1. Initial program 99.6%

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

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

      2. *-lft-identity N/A

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

      3. associate-*l/ N/A

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

      4. distribute-lft-neg-in N/A

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

      5. associate-*l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 63.2

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

   5. Applied rewrites 63.2%

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

   if -1.00000000000000001e78 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999998e119

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   if 9.9999999999999998e119 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 97.2

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 58.9

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

   7. Applied rewrites 58.9%

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

   9. Applied rewrites 61.4%

      \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot -0.016666666666666666}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+240}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\frac{-60}{z - t} \cdot y\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.016666666666666666 \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+240}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\frac{-60}{z - t} \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.016666666666666666 \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+240)
     (* (/ (- x y) z) 60.0)
     (if (<= t_1 -1e+78)
       (* (/ -60.0 (- z t)) y)
       (if (<= t_1 1e+120)
         (* 120.0 a)
         (/ x (* -0.016666666666666666 (- t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+240) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= -1e+78) {
		tmp = (-60.0 / (z - t)) * y;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = x / (-0.016666666666666666 * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+240)) then
        tmp = ((x - y) / z) * 60.0d0
    else if (t_1 <= (-1d+78)) then
        tmp = ((-60.0d0) / (z - t)) * y
    else if (t_1 <= 1d+120) then
        tmp = 120.0d0 * a
    else
        tmp = x / ((-0.016666666666666666d0) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+240) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= -1e+78) {
		tmp = (-60.0 / (z - t)) * y;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = x / (-0.016666666666666666 * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+240:
		tmp = ((x - y) / z) * 60.0
	elif t_1 <= -1e+78:
		tmp = (-60.0 / (z - t)) * y
	elif t_1 <= 1e+120:
		tmp = 120.0 * a
	else:
		tmp = x / (-0.016666666666666666 * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+240)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (t_1 <= -1e+78)
		tmp = Float64(Float64(-60.0 / Float64(z - t)) * y);
	elseif (t_1 <= 1e+120)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(x / Float64(-0.016666666666666666 * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+240)
		tmp = ((x - y) / z) * 60.0;
	elseif (t_1 <= -1e+78)
		tmp = (-60.0 / (z - t)) * y;
	elseif (t_1 <= 1e+120)
		tmp = 120.0 * a;
	else
		tmp = x / (-0.016666666666666666 * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+240], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, -1e+78], N[(N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+120], N[(120.0 * a), $MachinePrecision], N[(x / N[(-0.016666666666666666 * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000001e240

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 92.2

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 82.9%

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

   if -1.00000000000000001e240 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000001e78

   1. Initial program 99.6%

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

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

      2. *-lft-identity N/A

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

      3. associate-*l/ N/A

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

      4. distribute-lft-neg-in N/A

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

      5. associate-*l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 63.2

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

   5. Applied rewrites 63.2%

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

   if -1.00000000000000001e78 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999998e119

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   if 9.9999999999999998e119 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 97.2

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 58.9

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

   7. Applied rewrites 58.9%

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

   9. Applied rewrites 61.4%

      \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot -0.016666666666666666}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+240}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\frac{-60}{z - t} \cdot y\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.016666666666666666 \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, 60 \cdot \frac{x}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+78)
     (* (/ 60.0 (- z t)) (- x y))
     (if (<= t_1 1e+37)
       (fma a 120.0 (* 60.0 (/ x (- z t))))
       (/ (- x y) (* 0.016666666666666666 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+78) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (t_1 <= 1e+37) {
		tmp = fma(a, 120.0, (60.0 * (x / (z - t))));
	} else {
		tmp = (x - y) / (0.016666666666666666 * (z - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+78)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (t_1 <= 1e+37)
		tmp = fma(a, 120.0, Float64(60.0 * Float64(x / Float64(z - t))));
	else
		tmp = Float64(Float64(x - y) / Float64(0.016666666666666666 * Float64(z - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+78], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+37], N[(a * 120.0 + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * 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)) < -1.00000000000000001e78

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 90.8

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

   5. Applied rewrites 90.8%

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

   if -1.00000000000000001e78 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999954e36

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 79.8

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

   5. Applied rewrites 79.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 79.9

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

   7. Applied rewrites 79.9%

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

   8. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 89.5

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

   10. Applied rewrites 89.5%

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

   if 9.99999999999999954e36 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.9%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 83.9

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

   5. Applied rewrites 83.9%

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

   7. Applied rewrites 83.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, 60 \cdot \frac{x}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-39} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (or (<= t_1 -5e-39) (not (<= t_1 2e-15)))
     (* (/ 60.0 (- z t)) (- x y))
     (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e-39) || !(t_1 <= 2e-15)) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if ((t_1 <= (-5d-39)) .or. (.not. (t_1 <= 2d-15))) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e-39) || !(t_1 <= 2e-15)) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if (t_1 <= -5e-39) or not (t_1 <= 2e-15):
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -5e-39) || !(t_1 <= 2e-15))
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if ((t_1 <= -5e-39) || ~((t_1 <= 2e-15)))
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-39], N[Not[LessEqual[t$95$1, 2e-15]], $MachinePrecision]], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999998e-39 or 2.0000000000000002e-15 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.5%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 76.9

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

   5. Applied rewrites 76.9%

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

   if -4.9999999999999998e-39 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000002e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 81.8

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

   5. Applied rewrites 81.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{-39} \lor \neg \left(\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+98}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.016666666666666666 \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+98)
     (* (/ (- x y) z) 60.0)
     (if (<= t_1 1e+120)
       (* 120.0 a)
       (/ x (* -0.016666666666666666 (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+98) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = x / (-0.016666666666666666 * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+98)) then
        tmp = ((x - y) / z) * 60.0d0
    else if (t_1 <= 1d+120) then
        tmp = 120.0d0 * a
    else
        tmp = x / ((-0.016666666666666666d0) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+98) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = x / (-0.016666666666666666 * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+98:
		tmp = ((x - y) / z) * 60.0
	elif t_1 <= 1e+120:
		tmp = 120.0 * a
	else:
		tmp = x / (-0.016666666666666666 * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+98)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (t_1 <= 1e+120)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(x / Float64(-0.016666666666666666 * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+98)
		tmp = ((x - y) / z) * 60.0;
	elseif (t_1 <= 1e+120)
		tmp = 120.0 * a;
	else
		tmp = x / (-0.016666666666666666 * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+98], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+120], N[(120.0 * a), $MachinePrecision], N[(x / N[(-0.016666666666666666 * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999998e97

   1. Initial program 97.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 90.4

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

   5. Applied rewrites 90.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 65.2%

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

   if -9.99999999999999998e97 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999998e119

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.0

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

   5. Applied rewrites 66.0%

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

   if 9.9999999999999998e119 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 97.2

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 58.9

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

   7. Applied rewrites 58.9%

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

   9. Applied rewrites 61.4%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+98}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.016666666666666666 \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{-z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+98)
     (* (/ y z) -60.0)
     (if (<= t_1 1e+120) (* 120.0 a) (* (/ -60.0 (- z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+98) {
		tmp = (y / z) * -60.0;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / -z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+98)) then
        tmp = (y / z) * (-60.0d0)
    else if (t_1 <= 1d+120) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) / -z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+98) {
		tmp = (y / z) * -60.0;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / -z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+98:
		tmp = (y / z) * -60.0
	elif t_1 <= 1e+120:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 / -z) * x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+98)
		tmp = Float64(Float64(y / z) * -60.0);
	elseif (t_1 <= 1e+120)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 / Float64(-z)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+98)
		tmp = (y / z) * -60.0;
	elseif (t_1 <= 1e+120)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 / -z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+98], N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+120], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 / (-z)), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999998e97

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 11.7

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

   5. Applied rewrites 11.7%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. distribute-neg-frac2 N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. associate-*r/ N/A

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

      14. *-commutative N/A

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. remove-double-neg N/A

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

      18. unsub-neg N/A

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

      19. distribute-neg-in N/A

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

      20. +-commutative N/A

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

      21. sub-neg N/A

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

      22. distribute-neg-frac2 N/A

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

      23. metadata-eval N/A

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

      24. associate-*r/ N/A

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

   8. Applied rewrites 55.3%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 42.4%

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

   if -9.99999999999999998e97 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999998e119

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.0

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

   5. Applied rewrites 66.0%

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

   if 9.9999999999999998e119 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 97.2

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 58.9

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

   7. Applied rewrites 58.9%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 36.1%

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

   12. Applied rewrites 38.6%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{-z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+98)
     (* (/ y z) -60.0)
     (if (<= t_1 1e+120) (* 120.0 a) (* (/ x z) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+98) {
		tmp = (y / z) * -60.0;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / z) * 60.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+98)) then
        tmp = (y / z) * (-60.0d0)
    else if (t_1 <= 1d+120) then
        tmp = 120.0d0 * a
    else
        tmp = (x / z) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+98) {
		tmp = (y / z) * -60.0;
	} else if (t_1 <= 1e+120) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+98:
		tmp = (y / z) * -60.0
	elif t_1 <= 1e+120:
		tmp = 120.0 * a
	else:
		tmp = (x / z) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+98)
		tmp = Float64(Float64(y / z) * -60.0);
	elseif (t_1 <= 1e+120)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / z) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+98)
		tmp = (y / z) * -60.0;
	elseif (t_1 <= 1e+120)
		tmp = 120.0 * a;
	else
		tmp = (x / z) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+98], N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+120], N[(120.0 * a), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999998e97

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 11.7

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

   5. Applied rewrites 11.7%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. distribute-neg-frac2 N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. associate-*r/ N/A

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

      14. *-commutative N/A

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. remove-double-neg N/A

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

      18. unsub-neg N/A

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

      19. distribute-neg-in N/A

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

      20. +-commutative N/A

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

      21. sub-neg N/A

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

      22. distribute-neg-frac2 N/A

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

      23. metadata-eval N/A

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

      24. associate-*r/ N/A

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

   8. Applied rewrites 55.3%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 42.4%

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

   if -9.99999999999999998e97 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999998e119

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.0

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

   5. Applied rewrites 66.0%

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

   if 9.9999999999999998e119 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 91.0

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

   5. Applied rewrites 91.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 38.6%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+120}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+38} \lor \neg \left(x \leq 5 \cdot 10^{+56}\right):\\ \;\;\;\;\mathsf{fma}\left(a, 120, 60 \cdot \frac{x}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3e+38) (not (<= x 5e+56)))
   (fma a 120.0 (* 60.0 (/ x (- z t))))
   (fma a 120.0 (/ (* y -60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3e+38) || !(x <= 5e+56)) {
		tmp = fma(a, 120.0, (60.0 * (x / (z - t))));
	} else {
		tmp = fma(a, 120.0, ((y * -60.0) / (z - t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3e+38) || !(x <= 5e+56))
		tmp = fma(a, 120.0, Float64(60.0 * Float64(x / Float64(z - t))));
	else
		tmp = fma(a, 120.0, Float64(Float64(y * -60.0) / Float64(z - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3e+38], N[Not[LessEqual[x, 5e+56]], $MachinePrecision]], N[(a * 120.0 + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0000000000000001e38 or 5.00000000000000024e56 < x

   1. Initial program 98.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 42.5

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

   5. Applied rewrites 42.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 42.5

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

   7. Applied rewrites 42.5%

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

   8. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 90.5

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

   10. Applied rewrites 90.5%

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

   if -3.0000000000000001e38 < x < 5.00000000000000024e56

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 93.5

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

   5. Applied rewrites 93.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 93.5

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

   7. Applied rewrites 93.5%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+38} \lor \neg \left(x \leq 5 \cdot 10^{+56}\right):\\ \;\;\;\;\mathsf{fma}\left(a, 120, 60 \cdot \frac{x}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-57} \lor \neg \left(t \leq 3 \cdot 10^{-66}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{z} \cdot 60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e-57) (not (<= t 3e-66)))
   (fma (/ (- x y) t) -60.0 (* 120.0 a))
   (fma a 120.0 (* (/ (- x y) z) 60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e-57) || !(t <= 3e-66)) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else {
		tmp = fma(a, 120.0, (((x - y) / z) * 60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e-57) || !(t <= 3e-66))
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	else
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) / z) * 60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e-57], N[Not[LessEqual[t, 3e-66]], $MachinePrecision]], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999993e-57 or 3.0000000000000002e-66 < t

   1. Initial program 99.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 87.8

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

   5. Applied rewrites 87.8%

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

   if -1.29999999999999993e-57 < t < 3.0000000000000002e-66

   1. Initial program 98.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.0

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 85.4

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

   7. Applied rewrites 85.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-57} \lor \neg \left(t \leq 3 \cdot 10^{-66}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{z} \cdot 60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-57} \lor \neg \left(t \leq 3 \cdot 10^{-66}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e-57) (not (<= t 3e-66)))
   (fma (/ (- x y) t) -60.0 (* 120.0 a))
   (fma (/ (- x y) z) 60.0 (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e-57) || !(t <= 3e-66)) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e-57) || !(t <= 3e-66))
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e-57], N[Not[LessEqual[t, 3e-66]], $MachinePrecision]], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999993e-57 or 3.0000000000000002e-66 < t

   1. Initial program 99.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 87.8

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

   5. Applied rewrites 87.8%

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

   if -1.29999999999999993e-57 < t < 3.0000000000000002e-66

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.4

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

   5. Applied rewrites 85.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-57} \lor \neg \left(t \leq 3 \cdot 10^{-66}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.22e+39)
   (fma a 120.0 (* (/ x t) -60.0))
   (if (<= t 4.2e-66)
     (* (/ 60.0 (- z t)) (- x y))
     (fma (/ (- x y) t) -60.0 (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+39) {
		tmp = fma(a, 120.0, ((x / t) * -60.0));
	} else if (t <= 4.2e-66) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.22e+39)
		tmp = fma(a, 120.0, Float64(Float64(x / t) * -60.0));
	elseif (t <= 4.2e-66)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.22e+39], N[(a * 120.0 + N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-66], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22e39

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 77.3

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

   7. Applied rewrites 77.3%

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

   8. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 98.1

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

   10. Applied rewrites 98.1%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 91.4%

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

   if -1.22e39 < t < 4.2000000000000001e-66

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 70.9

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

   5. Applied rewrites 70.9%

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

   if 4.2000000000000001e-66 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.8

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

   5. Applied rewrites 93.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+93} \lor \neg \left(x \leq 3.6 \cdot 10^{+167}\right):\\ \;\;\;\;\frac{x}{-0.016666666666666666 \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -9e+93) (not (<= x 3.6e+167)))
   (/ x (* -0.016666666666666666 (- t z)))
   (* 120.0 a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -9e+93) || !(x <= 3.6e+167)) {
		tmp = x / (-0.016666666666666666 * (t - z));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-9d+93)) .or. (.not. (x <= 3.6d+167))) then
        tmp = x / ((-0.016666666666666666d0) * (t - z))
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -9e+93) || !(x <= 3.6e+167)) {
		tmp = x / (-0.016666666666666666 * (t - z));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -9e+93) or not (x <= 3.6e+167):
		tmp = x / (-0.016666666666666666 * (t - z))
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -9e+93) || !(x <= 3.6e+167))
		tmp = Float64(x / Float64(-0.016666666666666666 * Float64(t - z)));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -9e+93) || ~((x <= 3.6e+167)))
		tmp = x / (-0.016666666666666666 * (t - z));
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -9e+93], N[Not[LessEqual[x, 3.6e+167]], $MachinePrecision]], N[(x / N[(-0.016666666666666666 * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999981e93 or 3.60000000000000024e167 < x

   1. Initial program 98.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 98.6

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 72.1

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

   7. Applied rewrites 72.1%

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

   9. Applied rewrites 73.4%

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

   if -8.99999999999999981e93 < x < 3.60000000000000024e167

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 60.3

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

   5. Applied rewrites 60.3%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+93} \lor \neg \left(x \leq 3.6 \cdot 10^{+167}\right):\\ \;\;\;\;\frac{x}{-0.016666666666666666 \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+133} \lor \neg \left(x \leq 2.2 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.8e+133) (not (<= x 2.2e+168)))
   (* (/ -60.0 t) x)
   (* 120.0 a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.8e+133) || !(x <= 2.2e+168)) {
		tmp = (-60.0 / t) * x;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.8d+133)) .or. (.not. (x <= 2.2d+168))) then
        tmp = ((-60.0d0) / t) * x
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.8e+133) || !(x <= 2.2e+168)) {
		tmp = (-60.0 / t) * x;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.8e+133) or not (x <= 2.2e+168):
		tmp = (-60.0 / t) * x
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.8e+133) || !(x <= 2.2e+168))
		tmp = Float64(Float64(-60.0 / t) * x);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.8e+133) || ~((x <= 2.2e+168)))
		tmp = (-60.0 / t) * x;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.8e+133], N[Not[LessEqual[x, 2.2e+168]], $MachinePrecision]], N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.79999999999999989e133 or 2.2000000000000002e168 < x

   1. Initial program 98.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 98.5

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 72.5

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 41.9%

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

   12. Applied rewrites 41.9%

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

   if -1.79999999999999989e133 < x < 2.2000000000000002e168

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.5

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

   5. Applied rewrites 59.5%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+133} \lor \neg \left(x \leq 2.2 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+133}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+168}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.8e+133)
   (* (/ -60.0 t) x)
   (if (<= x 3.5e+168) (* 120.0 a) (* (/ x z) 60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.8e+133) {
		tmp = (-60.0 / t) * x;
	} else if (x <= 3.5e+168) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / z) * 60.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.8d+133)) then
        tmp = ((-60.0d0) / t) * x
    else if (x <= 3.5d+168) then
        tmp = 120.0d0 * a
    else
        tmp = (x / z) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.8e+133) {
		tmp = (-60.0 / t) * x;
	} else if (x <= 3.5e+168) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.8e+133:
		tmp = (-60.0 / t) * x
	elif x <= 3.5e+168:
		tmp = 120.0 * a
	else:
		tmp = (x / z) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.8e+133)
		tmp = Float64(Float64(-60.0 / t) * x);
	elseif (x <= 3.5e+168)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / z) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.8e+133)
		tmp = (-60.0 / t) * x;
	elseif (x <= 3.5e+168)
		tmp = 120.0 * a;
	else
		tmp = (x / z) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.8e+133], N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 3.5e+168], N[(120.0 * a), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999989e133

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 70.4

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

   7. Applied rewrites 70.4%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 47.6%

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

   12. Applied rewrites 47.7%

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

   if -1.79999999999999989e133 < x < 3.5000000000000002e168

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.5

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

   5. Applied rewrites 59.5%

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

   if 3.5000000000000002e168 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 84.2

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

   5. Applied rewrites 84.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 64.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 58.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+133}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+168}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+133}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.8e+133)
   (* (/ -60.0 t) x)
   (if (<= x 2.2e+168) (* 120.0 a) (* (/ x t) -60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.8e+133) {
		tmp = (-60.0 / t) * x;
	} else if (x <= 2.2e+168) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -60.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.8d+133)) then
        tmp = ((-60.0d0) / t) * x
    else if (x <= 2.2d+168) then
        tmp = 120.0d0 * a
    else
        tmp = (x / t) * (-60.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.8e+133) {
		tmp = (-60.0 / t) * x;
	} else if (x <= 2.2e+168) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.8e+133:
		tmp = (-60.0 / t) * x
	elif x <= 2.2e+168:
		tmp = 120.0 * a
	else:
		tmp = (x / t) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.8e+133)
		tmp = Float64(Float64(-60.0 / t) * x);
	elseif (x <= 2.2e+168)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / t) * -60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.8e+133)
		tmp = (-60.0 / t) * x;
	elseif (x <= 2.2e+168)
		tmp = 120.0 * a;
	else
		tmp = (x / t) * -60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.8e+133], N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2.2e+168], N[(120.0 * a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999989e133

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 70.4

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

   7. Applied rewrites 70.4%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 47.6%

       \[\leadsto \frac{x}{t} \cdot \color{blue}{-60} \]
   11. Step-by-step derivation

   12. Applied rewrites 47.7%

       \[\leadsto x \cdot \frac{-60}{\color{blue}{t}} \]

   if -1.79999999999999989e133 < x < 2.2000000000000002e168

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120} \]

      2. lower-*.f64 59.5

         \[\leadsto \color{blue}{a \cdot 120} \]

   5. Applied rewrites 59.5%

      \[\leadsto \color{blue}{a \cdot 120} \]

   if 2.2000000000000002e168 < x

   1. Initial program 96.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

      4. lower-fma.f64 96.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

      5. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)}\right) \]

      11. frac-2neg N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{\mathsf{neg}\left(60\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} \cdot \left(x - y\right)\right) \]

      12. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{\mathsf{neg}\left(60\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} \cdot \left(x - y\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{-60}}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(x - y\right)\right) \]

      14. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{0 - \left(z - t\right)}} \cdot \left(x - y\right)\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{0 - \color{blue}{\left(z - t\right)}} \cdot \left(x - y\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)}} \cdot \left(x - y\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)}} \cdot \left(x - y\right)\right) \]

      18. associate--r+ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(t\right)\right)\right) - z}} \cdot \left(x - y\right)\right) \]

      19. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right)} - z} \cdot \left(x - y\right)\right) \]

      20. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{t} - z} \cdot \left(x - y\right)\right) \]

      21. lower--.f64 99.7

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{t - z}} \cdot \left(x - y\right)\right) \]

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{t - z} \cdot \left(x - y\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-60 \cdot x}{t - z}} \]

      2. remove-double-neg N/A

         \[\leadsto \frac{-60 \cdot x}{\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right)} - z} \]

      3. unsub-neg N/A

         \[\leadsto \frac{-60 \cdot x}{\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}} \]

      4. distribute-neg-in N/A

         \[\leadsto \frac{-60 \cdot x}{\color{blue}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}} \]

      5. +-commutative N/A

         \[\leadsto \frac{-60 \cdot x}{\mathsf{neg}\left(\color{blue}{\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)}\right)} \]

      6. sub-neg N/A

         \[\leadsto \frac{-60 \cdot x}{\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \frac{-60 \cdot x}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-60 \cdot x}{-1 \cdot \left(z - t\right)}} \]

      9. *-commutative N/A

         \[\leadsto \frac{\color{blue}{x \cdot -60}}{-1 \cdot \left(z - t\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\color{blue}{x \cdot -60}}{-1 \cdot \left(z - t\right)} \]

      11. mul-1-neg N/A

          \[\leadsto \frac{x \cdot -60}{\color{blue}{\mathsf{neg}\left(\left(z - t\right)\right)}} \]

      12. sub-neg N/A

          \[\leadsto \frac{x \cdot -60}{\mathsf{neg}\left(\color{blue}{\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)}\right)} \]

      13. +-commutative N/A

          \[\leadsto \frac{x \cdot -60}{\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)}\right)} \]

      14. distribute-neg-in N/A

          \[\leadsto \frac{x \cdot -60}{\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}} \]

      15. unsub-neg N/A

          \[\leadsto \frac{x \cdot -60}{\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}} \]

      16. remove-double-neg N/A

          \[\leadsto \frac{x \cdot -60}{\color{blue}{t} - z} \]

      17. lower--.f64 75.1

          \[\leadsto \frac{x \cdot -60}{\color{blue}{t - z}} \]

   7. Applied rewrites 75.1%

      \[\leadsto \color{blue}{\frac{x \cdot -60}{t - z}} \]

   8. Taylor expanded in t around inf

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]
   9. Step-by-step derivation

   10. Applied rewrites 34.3%

       \[\leadsto \frac{x}{t} \cdot \color{blue}{-60} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+133}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.5% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ 120 \cdot a \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* 120.0 a))

C

double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 120.0d0 * a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

Python

def code(x, y, z, t, a):
	return 120.0 * a

Julia

function code(x, y, z, t, a)
	return Float64(120.0 * a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 120.0 * a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(120.0 * a), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{a \cdot 120} \]

   2. lower-*.f64 48.3

      \[\leadsto \color{blue}{a \cdot 120} \]

5. Applied rewrites 48.3%

   \[\leadsto \color{blue}{a \cdot 120} \]

6. Final simplification 48.3%

   \[\leadsto 120 \cdot a \]
7. Add Preprocessing

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (60.0d0 / ((z - t) / (x - y))) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(60.0 / Float64(Float64(z - t) / Float64(x - y))) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (60.0 / ((z - t) / (x - y))) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024271 
(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)))