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

Percentage Accurate: 99.4% → 99.8%

Time: 10.4s

Alternatives: 20

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. lift-+.f64 N/A

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

   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. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. div-inv N/A

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

   8. lower-*.f64 N/A

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

   9. metadata-eval 99.8

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

6. Applied rewrites 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+170)
     t_1
     (if (<= t_2 5e+153) (fma (/ x (- z t)) 60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+170) {
		tmp = t_1;
	} else if (t_2 <= 5e+153) {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+170)
		tmp = t_1;
	elseif (t_2 <= 5e+153)
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+170], t$95$1, If[LessEqual[t$95$2, 5e+153], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000007e170 or 5.00000000000000018e153 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 35.6

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

   5. Applied rewrites 35.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 27.7%

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

   9. Taylor expanded in a around 0

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

       4. metadata-eval N/A

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

       5. associate-*r/ N/A

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

       6. lower-*.f64 N/A

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

       7. lower--.f64 N/A

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

       8. associate-*r/ N/A

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

       9. metadata-eval N/A

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

       10. lower-/.f64 N/A

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

       11. lower--.f64 89.9

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

   11. Applied rewrites 89.9%

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

   if -2.00000000000000007e170 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000018e153

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 82.8

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

   5. Applied rewrites 82.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+170}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{t} \cdot y\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-y}{0.016666666666666666 \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e+35)
   (fma a 120.0 (* (/ 60.0 t) y))
   (if (<= (* 120.0 a) 5e-55)
     (* (/ 60.0 (- z t)) (- x y))
     (fma a 120.0 (/ (- y) (* 0.016666666666666666 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e+35) {
		tmp = fma(a, 120.0, ((60.0 / t) * y));
	} else if ((120.0 * a) <= 5e-55) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = fma(a, 120.0, (-y / (0.016666666666666666 * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e+35)
		tmp = fma(a, 120.0, Float64(Float64(60.0 / t) * y));
	elseif (Float64(120.0 * a) <= 5e-55)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = fma(a, 120.0, Float64(Float64(-y) / Float64(0.016666666666666666 * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e+35], N[(a * 120.0 + N[(N[(60.0 / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 5e-55], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[((-y) / N[(0.016666666666666666 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000021e35

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 80.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 82.4

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

   10. Applied rewrites 82.4%

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

   if -5.00000000000000021e35 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-55

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 43.1

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

   5. Applied rewrites 43.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.9%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   10. 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 79.3

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

   11. Applied rewrites 79.3%

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

   if 5.0000000000000002e-55 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      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 99.9

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

      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 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. div-inv N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 83.4

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

   9. Applied rewrites 83.4%

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

   10. Taylor expanded in x around 0

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 78.5

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

   12. Applied rewrites 78.5%

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{-y}}{0.016666666666666666 \cdot z}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{t} \cdot y\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-y}{0.016666666666666666 \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{t} \cdot y\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{z} \cdot y + 120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e+35)
   (fma a 120.0 (* (/ 60.0 t) y))
   (if (<= (* 120.0 a) 5e-55)
     (* (/ 60.0 (- z t)) (- x y))
     (+ (* (/ -60.0 z) y) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e+35) {
		tmp = fma(a, 120.0, ((60.0 / t) * y));
	} else if ((120.0 * a) <= 5e-55) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = ((-60.0 / z) * y) + (120.0 * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e+35)
		tmp = fma(a, 120.0, Float64(Float64(60.0 / t) * y));
	elseif (Float64(120.0 * a) <= 5e-55)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(Float64(Float64(-60.0 / z) * y) + Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e+35], N[(a * 120.0 + N[(N[(60.0 / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 5e-55], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-60.0 / z), $MachinePrecision] * y), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000021e35

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 80.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 82.4

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

   10. Applied rewrites 82.4%

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

   if -5.00000000000000021e35 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-55

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 43.1

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

   5. Applied rewrites 43.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.9%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   10. 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 79.3

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

   11. Applied rewrites 79.3%

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

   if 5.0000000000000002e-55 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 88.2

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

   5. Applied rewrites 88.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 78.5%

      \[\leadsto \frac{-60}{z} \cdot y + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{t} \cdot y\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{z} \cdot y + 120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{t} \cdot y\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z} \cdot -60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e+35)
   (fma a 120.0 (* (/ 60.0 t) y))
   (if (<= (* 120.0 a) 5e-55)
     (* (/ 60.0 (- z t)) (- x y))
     (fma a 120.0 (* (/ y z) -60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e+35) {
		tmp = fma(a, 120.0, ((60.0 / t) * y));
	} else if ((120.0 * a) <= 5e-55) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = fma(a, 120.0, ((y / z) * -60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e+35)
		tmp = fma(a, 120.0, Float64(Float64(60.0 / t) * y));
	elseif (Float64(120.0 * a) <= 5e-55)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = fma(a, 120.0, Float64(Float64(y / z) * -60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e+35], N[(a * 120.0 + N[(N[(60.0 / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 5e-55], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000021e35

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 80.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 82.4

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

   10. Applied rewrites 82.4%

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

   if -5.00000000000000021e35 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-55

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 43.1

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

   5. Applied rewrites 43.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.9%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   10. 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 79.3

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

   11. Applied rewrites 79.3%

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

   if 5.0000000000000002e-55 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 88.2

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

   5. Applied rewrites 88.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 59.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 59.1

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

   10. Applied rewrites 59.1%

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

   11. Taylor expanded in z around inf

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

   13. Applied rewrites 78.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{t} \cdot y\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z} \cdot -60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z} \cdot -60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e+35)
   (fma a 120.0 (* (/ y t) 60.0))
   (if (<= (* 120.0 a) 5e-55)
     (* (/ 60.0 (- z t)) (- x y))
     (fma a 120.0 (* (/ y z) -60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e+35) {
		tmp = fma(a, 120.0, ((y / t) * 60.0));
	} else if ((120.0 * a) <= 5e-55) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = fma(a, 120.0, ((y / z) * -60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e+35)
		tmp = fma(a, 120.0, Float64(Float64(y / t) * 60.0));
	elseif (Float64(120.0 * a) <= 5e-55)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = fma(a, 120.0, Float64(Float64(y / z) * -60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e+35], N[(a * 120.0 + N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 5e-55], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000021e35

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 80.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 82.4

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

   10. Applied rewrites 82.4%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 82.3%

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

   if -5.00000000000000021e35 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-55

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 43.1

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

   5. Applied rewrites 43.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.9%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   10. 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 79.3

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

   11. Applied rewrites 79.3%

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

   if 5.0000000000000002e-55 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 88.2

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

   5. Applied rewrites 88.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 59.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 59.1

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

   10. Applied rewrites 59.1%

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

   11. Taylor expanded in z around inf

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

   13. Applied rewrites 78.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z} \cdot -60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e+35)
   (fma a 120.0 (* (/ y t) 60.0))
   (if (<= (* 120.0 a) 5e-55)
     (* (/ 60.0 (- z t)) (- x y))
     (fma a 120.0 (* (/ x z) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e+35) {
		tmp = fma(a, 120.0, ((y / t) * 60.0));
	} else if ((120.0 * a) <= 5e-55) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e+35)
		tmp = fma(a, 120.0, Float64(Float64(y / t) * 60.0));
	elseif (Float64(120.0 * a) <= 5e-55)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e+35], N[(a * 120.0 + N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 5e-55], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000021e35

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 80.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 82.4

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

   10. Applied rewrites 82.4%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 82.3%

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

   if -5.00000000000000021e35 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-55

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 43.1

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

   5. Applied rewrites 43.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.9%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   10. 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 79.3

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

   11. Applied rewrites 79.3%

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

   if 5.0000000000000002e-55 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.3%

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

   10. Applied rewrites 77.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-60}{t}, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -1e+68)
   (fma x (/ -60.0 t) (* 120.0 a))
   (if (<= (* 120.0 a) 5e-55)
     (* (/ 60.0 (- z t)) (- x y))
     (fma a 120.0 (* (/ x z) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -1e+68) {
		tmp = fma(x, (-60.0 / t), (120.0 * a));
	} else if ((120.0 * a) <= 5e-55) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -1e+68)
		tmp = fma(x, Float64(-60.0 / t), Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= 5e-55)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -1e+68], N[(x * N[(-60.0 / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 5e-55], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.99999999999999953e67

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 85.5

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

   5. Applied rewrites 85.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 79.6%

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

   10. Applied rewrites 79.6%

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

   if -9.99999999999999953e67 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-55

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 41.6

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

   5. Applied rewrites 41.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.1%

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

   9. Taylor expanded in a around 0

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

       4. metadata-eval N/A

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

       5. associate-*r/ N/A

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

       6. lower-*.f64 N/A

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

       7. lower--.f64 N/A

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

       8. associate-*r/ N/A

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

       9. metadata-eval N/A

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

       10. lower-/.f64 N/A

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

       11. lower--.f64 77.6

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

   11. Applied rewrites 77.6%

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

   if 5.0000000000000002e-55 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.3%

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

   10. Applied rewrites 77.3%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-60}{t}, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-60}{t}, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -1e+68)
   (fma x (/ -60.0 t) (* 120.0 a))
   (if (<= (* 120.0 a) 5e-55) (* (/ 60.0 (- z t)) (- x y)) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -1e+68) {
		tmp = fma(x, (-60.0 / t), (120.0 * a));
	} else if ((120.0 * a) <= 5e-55) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -1e+68)
		tmp = fma(x, Float64(-60.0 / t), Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= 5e-55)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -1e+68], N[(x * N[(-60.0 / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 5e-55], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.99999999999999953e67

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 85.5

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

   5. Applied rewrites 85.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 79.6%

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

   10. Applied rewrites 79.6%

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

   if -9.99999999999999953e67 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-55

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 41.6

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

   5. Applied rewrites 41.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.1%

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

   9. Taylor expanded in a around 0

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

       4. metadata-eval N/A

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

       5. associate-*r/ N/A

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

       6. lower-*.f64 N/A

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

       7. lower--.f64 N/A

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

       8. associate-*r/ N/A

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

       9. metadata-eval N/A

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

       10. lower-/.f64 N/A

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

       11. lower--.f64 77.6

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

   11. Applied rewrites 77.6%

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

   if 5.0000000000000002e-55 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 74.4

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

   5. Applied rewrites 74.4%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-60}{t}, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -1e-104)
   (fma (/ x t) -60.0 (* 120.0 a))
   (if (<= (* 120.0 a) 2e-74) (* (/ 60.0 (- z t)) x) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -1e-104) {
		tmp = fma((x / t), -60.0, (120.0 * a));
	} else if ((120.0 * a) <= 2e-74) {
		tmp = (60.0 / (z - t)) * x;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -1e-104)
		tmp = fma(Float64(x / t), -60.0, Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= 2e-74)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -1e-104], N[(N[(x / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 2e-74], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.99999999999999927e-105

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 66.9%

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

   if -9.99999999999999927e-105 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999992e-74

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 46.9

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

   5. Applied rewrites 46.9%

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

   7. Applied rewrites 46.9%

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

   if 1.99999999999999992e-74 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-60}{t}, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -1e-104)
   (fma x (/ -60.0 t) (* 120.0 a))
   (if (<= (* 120.0 a) 2e-74) (* (/ 60.0 (- z t)) x) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -1e-104) {
		tmp = fma(x, (-60.0 / t), (120.0 * a));
	} else if ((120.0 * a) <= 2e-74) {
		tmp = (60.0 / (z - t)) * x;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -1e-104)
		tmp = fma(x, Float64(-60.0 / t), Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= 2e-74)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -1e-104], N[(x * N[(-60.0 / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 2e-74], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.99999999999999927e-105

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 66.9%

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

   10. Applied rewrites 66.9%

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

   if -9.99999999999999927e-105 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999992e-74

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 46.9

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

   5. Applied rewrites 46.9%

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

   7. Applied rewrites 46.9%

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

   if 1.99999999999999992e-74 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-60}{t}, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -2 \cdot 10^{-80}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -2e-80)
   (* 120.0 a)
   (if (<= (* 120.0 a) 2e-74) (* (/ x (- z t)) 60.0) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -2e-80) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 2e-74) {
		tmp = (x / (z - t)) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((120.0d0 * a) <= (-2d-80)) then
        tmp = 120.0d0 * a
    else if ((120.0d0 * a) <= 2d-74) then
        tmp = (x / (z - t)) * 60.0d0
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -2e-80) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 2e-74) {
		tmp = (x / (z - t)) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (120.0 * a) <= -2e-80:
		tmp = 120.0 * a
	elif (120.0 * a) <= 2e-74:
		tmp = (x / (z - t)) * 60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -2e-80)
		tmp = Float64(120.0 * a);
	elseif (Float64(120.0 * a) <= 2e-74)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((120.0 * a) <= -2e-80)
		tmp = 120.0 * a;
	elseif ((120.0 * a) <= 2e-74)
		tmp = (x / (z - t)) * 60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -2e-80], N[(120.0 * a), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 2e-74], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999992e-80 or 1.99999999999999992e-74 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 67.3

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

   5. Applied rewrites 67.3%

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

   if -1.99999999999999992e-80 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999992e-74

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 47.7

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

   5. Applied rewrites 47.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -2 \cdot 10^{-80}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -2 \cdot 10^{-80}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -2e-80)
   (* 120.0 a)
   (if (<= (* 120.0 a) 2e-74) (* (/ 60.0 (- z t)) x) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -2e-80) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 2e-74) {
		tmp = (60.0 / (z - 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 ((120.0d0 * a) <= (-2d-80)) then
        tmp = 120.0d0 * a
    else if ((120.0d0 * a) <= 2d-74) then
        tmp = (60.0d0 / (z - 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 ((120.0 * a) <= -2e-80) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 2e-74) {
		tmp = (60.0 / (z - t)) * x;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (120.0 * a) <= -2e-80:
		tmp = 120.0 * a
	elif (120.0 * a) <= 2e-74:
		tmp = (60.0 / (z - t)) * x
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -2e-80)
		tmp = Float64(120.0 * a);
	elseif (Float64(120.0 * a) <= 2e-74)
		tmp = Float64(Float64(60.0 / Float64(z - 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 ((120.0 * a) <= -2e-80)
		tmp = 120.0 * a;
	elseif ((120.0 * a) <= 2e-74)
		tmp = (60.0 / (z - t)) * x;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -2e-80], N[(120.0 * a), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 2e-74], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999992e-80 or 1.99999999999999992e-74 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 67.3

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

   5. Applied rewrites 67.3%

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

   if -1.99999999999999992e-80 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999992e-74

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 47.7

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

   5. Applied rewrites 47.7%

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

   7. Applied rewrites 47.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -2 \cdot 10^{-80}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-19}:\\ \;\;\;\;120 \cdot a + \frac{-60}{z - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x (- z t)) 60.0 (* 120.0 a))))
   (if (<= x -3.8e-20)
     t_1
     (if (<= x 1.26e-19) (+ (* 120.0 a) (* (/ -60.0 (- z t)) y)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / (z - t)), 60.0, (120.0 * a));
	double tmp;
	if (x <= -3.8e-20) {
		tmp = t_1;
	} else if (x <= 1.26e-19) {
		tmp = (120.0 * a) + ((-60.0 / (z - t)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (x <= -3.8e-20)
		tmp = t_1;
	elseif (x <= 1.26e-19)
		tmp = Float64(Float64(120.0 * a) + Float64(Float64(-60.0 / Float64(z - t)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e-20], t$95$1, If[LessEqual[x, 1.26e-19], N[(N[(120.0 * a), $MachinePrecision] + N[(N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998e-20 or 1.2599999999999999e-19 < x

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if -3.7999999999999998e-20 < x < 1.2599999999999999e-19

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 99.1

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

   5. Applied rewrites 99.1%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-19}:\\ \;\;\;\;120 \cdot a + \frac{-60}{z - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{-193}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e-193)
   (* 120.0 a)
   (if (<= (* 120.0 a) 5e-144) (* (/ x z) 60.0) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e-193) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 5e-144) {
		tmp = (x / z) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((120.0d0 * a) <= (-5d-193)) then
        tmp = 120.0d0 * a
    else if ((120.0d0 * a) <= 5d-144) then
        tmp = (x / z) * 60.0d0
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e-193) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 5e-144) {
		tmp = (x / z) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (120.0 * a) <= -5e-193:
		tmp = 120.0 * a
	elif (120.0 * a) <= 5e-144:
		tmp = (x / z) * 60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e-193)
		tmp = Float64(120.0 * a);
	elseif (Float64(120.0 * a) <= 5e-144)
		tmp = Float64(Float64(x / z) * 60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((120.0 * a) <= -5e-193)
		tmp = 120.0 * a;
	elseif ((120.0 * a) <= 5e-144)
		tmp = (x / z) * 60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e-193], N[(120.0 * a), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 5e-144], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000005e-193 or 4.9999999999999998e-144 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 60.1

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

   5. Applied rewrites 60.1%

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

   if -5.0000000000000005e-193 < (*.f64 a #s(literal 120 binary64)) < 4.9999999999999998e-144

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 51.3

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

   5. Applied rewrites 51.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 37.0%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{-193}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x (- z t)) 60.0 (* 120.0 a))))
   (if (<= x -3.8e-20)
     t_1
     (if (<= x 1.26e-19) (fma (/ y (- z t)) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / (z - t)), 60.0, (120.0 * a));
	double tmp;
	if (x <= -3.8e-20) {
		tmp = t_1;
	} else if (x <= 1.26e-19) {
		tmp = fma((y / (z - t)), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (x <= -3.8e-20)
		tmp = t_1;
	elseif (x <= 1.26e-19)
		tmp = fma(Float64(y / Float64(z - t)), -60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e-20], t$95$1, If[LessEqual[x, 1.26e-19], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998e-20 or 1.2599999999999999e-19 < x

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if -3.7999999999999998e-20 < x < 1.2599999999999999e-19

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 99.0

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

   5. Applied rewrites 99.0%

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

Alternative 17: 52.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+237}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+210}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9.5e+237)
   (* (/ -60.0 t) x)
   (if (<= x 8.8e+210) (* 120.0 a) (* (/ x t) -60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9.5e+237) {
		tmp = (-60.0 / t) * x;
	} else if (x <= 8.8e+210) {
		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 <= (-9.5d+237)) then
        tmp = ((-60.0d0) / t) * x
    else if (x <= 8.8d+210) 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 <= -9.5e+237) {
		tmp = (-60.0 / t) * x;
	} else if (x <= 8.8e+210) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -9.5e+237:
		tmp = (-60.0 / t) * x
	elif x <= 8.8e+210:
		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 <= -9.5e+237)
		tmp = Float64(Float64(-60.0 / t) * x);
	elseif (x <= 8.8e+210)
		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 <= -9.5e+237)
		tmp = (-60.0 / t) * x;
	elseif (x <= 8.8e+210)
		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, -9.5e+237], N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 8.8e+210], N[(120.0 * a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000061e237

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 82.2

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 58.8%

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

   10. Applied rewrites 58.8%

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

   if -9.50000000000000061e237 < x < 8.79999999999999948e210

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 53.8

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

   5. Applied rewrites 53.8%

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

   if 8.79999999999999948e210 < x

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 70.5

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

   5. Applied rewrites 70.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 53.9%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+237}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+210}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{t} \cdot x\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+210}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ -60.0 t) x)))
   (if (<= x -9.5e+237) t_1 (if (<= x 8.8e+210) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / t) * x;
	double tmp;
	if (x <= -9.5e+237) {
		tmp = t_1;
	} else if (x <= 8.8e+210) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-60.0d0) / t) * x
    if (x <= (-9.5d+237)) then
        tmp = t_1
    else if (x <= 8.8d+210) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / t) * x;
	double tmp;
	if (x <= -9.5e+237) {
		tmp = t_1;
	} else if (x <= 8.8e+210) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 / t) * x
	tmp = 0
	if x <= -9.5e+237:
		tmp = t_1
	elif x <= 8.8e+210:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 / t) * x)
	tmp = 0.0
	if (x <= -9.5e+237)
		tmp = t_1;
	elseif (x <= 8.8e+210)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 / t) * x;
	tmp = 0.0;
	if (x <= -9.5e+237)
		tmp = t_1;
	elseif (x <= 8.8e+210)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -9.5e+237], t$95$1, If[LessEqual[x, 8.8e+210], N[(120.0 * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000061e237 or 8.79999999999999948e210 < x

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 76.6

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 56.5%

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

   10. Applied rewrites 56.4%

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

   if -9.50000000000000061e237 < x < 8.79999999999999948e210

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 53.8

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

   5. Applied rewrites 53.8%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+237}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+210}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. lift-+.f64 N/A

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

   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. Add Preprocessing

Alternative 20: 50.9% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 48.5

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

5. Applied rewrites 48.5%

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

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024294 
(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)))