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

Percentage Accurate: 99.2% → 99.3%

Time: 12.4s

Alternatives: 19

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.8

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

   5. lift-/.f64 N/A

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

   6. frac-2neg N/A

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

   7. lower-/.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

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

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

   11. lower-*.f64 N/A

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

   12. metadata-eval N/A

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

   13. neg-sub0 N/A

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

   14. lift--.f64 N/A

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

   15. sub-neg N/A

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

   16. +-commutative N/A

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

   17. associate--r+ N/A

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

   18. neg-sub0 N/A

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

   19. remove-double-neg N/A

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

   20. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Taylor expanded in x around 0

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

   1. lower-fma.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 99.9

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

7. Applied rewrites 99.9%

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

Alternative 2: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-92}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+61)
     t_1
     (if (<= t_1 -1e-92)
       (fma y (/ 60.0 t) (* a 120.0))
       (if (<= t_1 4e-8) (* a 120.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+61) {
		tmp = t_1;
	} else if (t_1 <= -1e-92) {
		tmp = fma(y, (60.0 / t), (a * 120.0));
	} else if (t_1 <= 4e-8) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+61)
		tmp = t_1;
	elseif (t_1 <= -1e-92)
		tmp = fma(y, Float64(60.0 / t), Float64(a * 120.0));
	elseif (t_1 <= 4e-8)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+61], t$95$1, If[LessEqual[t$95$1, -1e-92], N[(y * N[(60.0 / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-8], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999949e60 or 4.0000000000000001e-8 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

   if -9.99999999999999949e60 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999988e-93

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 82.2

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 78.8%

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

   if -9.99999999999999988e-93 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.0000000000000001e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+61}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{-92}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+61)
     t_1
     (if (<= t_1 4e-8) (fma -60.0 (/ y (- z t)) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+61) {
		tmp = t_1;
	} else if (t_1 <= 4e-8) {
		tmp = fma(-60.0, (y / (z - t)), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+61)
		tmp = t_1;
	elseif (t_1 <= 4e-8)
		tmp = fma(-60.0, Float64(y / Float64(z - t)), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+61], t$95$1, If[LessEqual[t$95$1, 4e-8], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $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)) < -9.99999999999999949e60 or 4.0000000000000001e-8 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

   if -9.99999999999999949e60 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.0000000000000001e-8

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 91.6

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

   5. Applied rewrites 91.6%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+61}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+65)
     (/ (* x 60.0) (- z t))
     (if (<= t_1 4e-8) (* a 120.0) (/ (* -60.0 (- x y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+65) {
		tmp = (x * 60.0) / (z - t);
	} else if (t_1 <= 4e-8) {
		tmp = a * 120.0;
	} else {
		tmp = (-60.0 * (x - y)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+65)) then
        tmp = (x * 60.0d0) / (z - t)
    else if (t_1 <= 4d-8) then
        tmp = a * 120.0d0
    else
        tmp = ((-60.0d0) * (x - y)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+65) {
		tmp = (x * 60.0) / (z - t);
	} else if (t_1 <= 4e-8) {
		tmp = a * 120.0;
	} else {
		tmp = (-60.0 * (x - y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+65:
		tmp = (x * 60.0) / (z - t)
	elif t_1 <= 4e-8:
		tmp = a * 120.0
	else:
		tmp = (-60.0 * (x - y)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+65)
		tmp = Float64(Float64(x * 60.0) / Float64(z - t));
	elseif (t_1 <= 4e-8)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(-60.0 * Float64(x - y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+65)
		tmp = (x * 60.0) / (z - t);
	elseif (t_1 <= 4e-8)
		tmp = a * 120.0;
	else
		tmp = (-60.0 * (x - y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+65], N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-8], N[(a * 120.0), $MachinePrecision], N[(N[(-60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999999e64

   1. Initial program 99.9%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 50.5

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

   5. Applied rewrites 50.5%

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

   if -9.9999999999999999e64 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.0000000000000001e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if 4.0000000000000001e-8 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 19.3

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

   5. Applied rewrites 19.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 81.6

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

   8. Applied rewrites 81.6%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 51.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+65)
     (* x (/ 60.0 (- z t)))
     (if (<= t_1 4e-8) (* a 120.0) (/ (* -60.0 (- x y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+65) {
		tmp = x * (60.0 / (z - t));
	} else if (t_1 <= 4e-8) {
		tmp = a * 120.0;
	} else {
		tmp = (-60.0 * (x - y)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+65)) then
        tmp = x * (60.0d0 / (z - t))
    else if (t_1 <= 4d-8) then
        tmp = a * 120.0d0
    else
        tmp = ((-60.0d0) * (x - y)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+65) {
		tmp = x * (60.0 / (z - t));
	} else if (t_1 <= 4e-8) {
		tmp = a * 120.0;
	} else {
		tmp = (-60.0 * (x - y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+65:
		tmp = x * (60.0 / (z - t))
	elif t_1 <= 4e-8:
		tmp = a * 120.0
	else:
		tmp = (-60.0 * (x - y)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+65)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (t_1 <= 4e-8)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(-60.0 * Float64(x - y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+65)
		tmp = x * (60.0 / (z - t));
	elseif (t_1 <= 4e-8)
		tmp = a * 120.0;
	else
		tmp = (-60.0 * (x - y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+65], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-8], N[(a * 120.0), $MachinePrecision], N[(N[(-60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999999e64

   1. Initial program 99.9%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 50.5

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

   5. Applied rewrites 50.5%

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

   7. Applied rewrites 50.5%

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

   if -9.9999999999999999e64 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.0000000000000001e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if 4.0000000000000001e-8 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 19.3

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

   5. Applied rewrites 19.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 81.6

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

   8. Applied rewrites 81.6%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 51.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+163) t_1 (if (<= t_2 1e+206) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+163) {
		tmp = t_1;
	} else if (t_2 <= 1e+206) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+163)) then
        tmp = t_1
    else if (t_2 <= 1d+206) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+163) {
		tmp = t_1;
	} else if (t_2 <= 1e+206) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+163:
		tmp = t_1
	elif t_2 <= 1e+206:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+163)
		tmp = t_1;
	elseif (t_2 <= 1e+206)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+163)
		tmp = t_1;
	elseif (t_2 <= 1e+206)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $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, -5e+163], t$95$1, If[LessEqual[t$95$2, 1e+206], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e163 or 1e206 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 7.0

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

   5. Applied rewrites 7.0%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 94.1

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

   8. Applied rewrites 94.1%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 58.9%

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

   if -5e163 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e206

   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 65.9

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

   5. Applied rewrites 65.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+163}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \frac{60}{-t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+163)
     (* x (/ 60.0 (- t)))
     (if (<= t_1 2e+153) (* a 120.0) (/ (* y 60.0) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+163) {
		tmp = x * (60.0 / -t);
	} else if (t_1 <= 2e+153) {
		tmp = a * 120.0;
	} else {
		tmp = (y * 60.0) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+163)) then
        tmp = x * (60.0d0 / -t)
    else if (t_1 <= 2d+153) then
        tmp = a * 120.0d0
    else
        tmp = (y * 60.0d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+163) {
		tmp = x * (60.0 / -t);
	} else if (t_1 <= 2e+153) {
		tmp = a * 120.0;
	} else {
		tmp = (y * 60.0) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+163:
		tmp = x * (60.0 / -t)
	elif t_1 <= 2e+153:
		tmp = a * 120.0
	else:
		tmp = (y * 60.0) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+163)
		tmp = Float64(x * Float64(60.0 / Float64(-t)));
	elseif (t_1 <= 2e+153)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(y * 60.0) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+163)
		tmp = x * (60.0 / -t);
	elseif (t_1 <= 2e+153)
		tmp = a * 120.0;
	else
		tmp = (y * 60.0) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+163], N[(x * N[(60.0 / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+153], N[(a * 120.0), $MachinePrecision], N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e163

   1. Initial program 99.9%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 51.0

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

   5. Applied rewrites 51.0%

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

   7. Applied rewrites 51.0%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 37.7%

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

   12. Applied rewrites 37.7%

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

   if -5e163 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e153

   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 67.0

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

   5. Applied rewrites 67.0%

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

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

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 40.4

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

   5. Applied rewrites 40.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 30.1%

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

   9. Taylor expanded in y around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. lower--.f64 63.2

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

   11. Applied rewrites 63.2%

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

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 43.1%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \frac{60}{-t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+163)
     (/ (* x -60.0) t)
     (if (<= t_1 2e+153) (* a 120.0) (/ (* y 60.0) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+163) {
		tmp = (x * -60.0) / t;
	} else if (t_1 <= 2e+153) {
		tmp = a * 120.0;
	} else {
		tmp = (y * 60.0) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+163)) then
        tmp = (x * (-60.0d0)) / t
    else if (t_1 <= 2d+153) then
        tmp = a * 120.0d0
    else
        tmp = (y * 60.0d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+163) {
		tmp = (x * -60.0) / t;
	} else if (t_1 <= 2e+153) {
		tmp = a * 120.0;
	} else {
		tmp = (y * 60.0) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+163:
		tmp = (x * -60.0) / t
	elif t_1 <= 2e+153:
		tmp = a * 120.0
	else:
		tmp = (y * 60.0) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+163)
		tmp = Float64(Float64(x * -60.0) / t);
	elseif (t_1 <= 2e+153)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(y * 60.0) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+163)
		tmp = (x * -60.0) / t;
	elseif (t_1 <= 2e+153)
		tmp = a * 120.0;
	else
		tmp = (y * 60.0) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+163], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+153], N[(a * 120.0), $MachinePrecision], N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e163

   1. Initial program 99.9%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 51.0

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

   5. Applied rewrites 51.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 37.7%

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

   if -5e163 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e153

   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 67.0

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

   5. Applied rewrites 67.0%

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

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

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 40.4

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

   5. Applied rewrites 40.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 30.1%

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

   9. Taylor expanded in y around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. lower--.f64 63.2

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

   11. Applied rewrites 63.2%

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

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 43.1%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+163}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+163)
     (/ (* x -60.0) t)
     (if (<= t_1 1e+206) (* a 120.0) (/ x (* z 0.016666666666666666))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+163) {
		tmp = (x * -60.0) / t;
	} else if (t_1 <= 1e+206) {
		tmp = a * 120.0;
	} else {
		tmp = x / (z * 0.016666666666666666);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+163)) then
        tmp = (x * (-60.0d0)) / t
    else if (t_1 <= 1d+206) then
        tmp = a * 120.0d0
    else
        tmp = x / (z * 0.016666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+163) {
		tmp = (x * -60.0) / t;
	} else if (t_1 <= 1e+206) {
		tmp = a * 120.0;
	} else {
		tmp = x / (z * 0.016666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+163:
		tmp = (x * -60.0) / t
	elif t_1 <= 1e+206:
		tmp = a * 120.0
	else:
		tmp = x / (z * 0.016666666666666666)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+163)
		tmp = Float64(Float64(x * -60.0) / t);
	elseif (t_1 <= 1e+206)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x / Float64(z * 0.016666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+163)
		tmp = (x * -60.0) / t;
	elseif (t_1 <= 1e+206)
		tmp = a * 120.0;
	else
		tmp = x / (z * 0.016666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+163], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 1e+206], N[(a * 120.0), $MachinePrecision], N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e163

   1. Initial program 99.9%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 51.0

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

   5. Applied rewrites 51.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 37.7%

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

   if -5e163 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e206

   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 65.9

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

   5. Applied rewrites 65.9%

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

   if 1e206 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 44.0

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

   5. Applied rewrites 44.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 36.1%

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

   10. Applied rewrites 36.2%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+163}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+188)
     (* x (/ 60.0 z))
     (if (<= t_1 1e+206) (* a 120.0) (/ x (* z 0.016666666666666666))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+188) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= 1e+206) {
		tmp = a * 120.0;
	} else {
		tmp = x / (z * 0.016666666666666666);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+188)) then
        tmp = x * (60.0d0 / z)
    else if (t_1 <= 1d+206) then
        tmp = a * 120.0d0
    else
        tmp = x / (z * 0.016666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+188) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= 1e+206) {
		tmp = a * 120.0;
	} else {
		tmp = x / (z * 0.016666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+188:
		tmp = x * (60.0 / z)
	elif t_1 <= 1e+206:
		tmp = a * 120.0
	else:
		tmp = x / (z * 0.016666666666666666)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+188)
		tmp = Float64(x * Float64(60.0 / z));
	elseif (t_1 <= 1e+206)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x / Float64(z * 0.016666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+188)
		tmp = x * (60.0 / z);
	elseif (t_1 <= 1e+206)
		tmp = a * 120.0;
	else
		tmp = x / (z * 0.016666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+188], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+206], N[(a * 120.0), $MachinePrecision], N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e188

   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 inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 53.1

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

   5. Applied rewrites 53.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 30.4%

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

   if -1e188 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e206

   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 64.9

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

   5. Applied rewrites 64.9%

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

   if 1e206 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 44.0

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

   5. Applied rewrites 44.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 36.1%

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

   10. Applied rewrites 36.2%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 z))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+188) t_1 (if (<= t_2 1e+206) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (60.0 / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+188) {
		tmp = t_1;
	} else if (t_2 <= 1e+206) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (60.0d0 / z)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+188)) then
        tmp = t_1
    else if (t_2 <= 1d+206) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (60.0 / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+188) {
		tmp = t_1;
	} else if (t_2 <= 1e+206) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (60.0 / z)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+188:
		tmp = t_1
	elif t_2 <= 1e+206:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(60.0 / z))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+188)
		tmp = t_1;
	elseif (t_2 <= 1e+206)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (60.0 / z);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+188)
		tmp = t_1;
	elseif (t_2 <= 1e+206)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(60.0 / z), $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, -1e+188], t$95$1, If[LessEqual[t$95$2, 1e+206], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e188 or 1e206 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 47.9

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

   5. Applied rewrites 47.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 33.7%

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

   if -1e188 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e206

   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 64.9

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

   5. Applied rewrites 64.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-45}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-184}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-33}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-45)
   (* a 120.0)
   (if (<= (* a 120.0) -5e-184)
     (* 60.0 (/ (- x y) z))
     (if (<= (* a 120.0) 2e-33) (/ (* -60.0 (- x y)) t) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-45) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e-184) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((a * 120.0) <= 2e-33) {
		tmp = (-60.0 * (x - y)) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-45)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-5d-184)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if ((a * 120.0d0) <= 2d-33) then
        tmp = ((-60.0d0) * (x - y)) / t
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-45) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e-184) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((a * 120.0) <= 2e-33) {
		tmp = (-60.0 * (x - y)) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-45:
		tmp = a * 120.0
	elif (a * 120.0) <= -5e-184:
		tmp = 60.0 * ((x - y) / z)
	elif (a * 120.0) <= 2e-33:
		tmp = (-60.0 * (x - y)) / t
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-45)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -5e-184)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (Float64(a * 120.0) <= 2e-33)
		tmp = Float64(Float64(-60.0 * Float64(x - y)) / t);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-45)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -5e-184)
		tmp = 60.0 * ((x - y) / z);
	elseif ((a * 120.0) <= 2e-33)
		tmp = (-60.0 * (x - y)) / t;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-45], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-184], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-33], N[(N[(-60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999997e-45 or 2.0000000000000001e-33 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 78.0

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

   5. Applied rewrites 78.0%

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

   if -1.99999999999999997e-45 < (*.f64 a #s(literal 120 binary64)) < -5.00000000000000003e-184

   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 19.2

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

   5. Applied rewrites 19.2%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 80.0

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

   8. Applied rewrites 80.0%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 55.2%

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

   if -5.00000000000000003e-184 < (*.f64 a #s(literal 120 binary64)) < 2.0000000000000001e-33

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 16.9

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

   5. Applied rewrites 16.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 85.6

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

   8. Applied rewrites 85.6%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 54.4%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-45}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-184}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-33}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 90.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x \cdot -60}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ y (- z t)) (* a 120.0))))
   (if (<= y -9.5e+98)
     t_1
     (if (<= y 4.9e+55) (fma a 120.0 (/ (* x -60.0) (- t z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, (y / (z - t)), (a * 120.0));
	double tmp;
	if (y <= -9.5e+98) {
		tmp = t_1;
	} else if (y <= 4.9e+55) {
		tmp = fma(a, 120.0, ((x * -60.0) / (t - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(y / Float64(z - t)), Float64(a * 120.0))
	tmp = 0.0
	if (y <= -9.5e+98)
		tmp = t_1;
	elseif (y <= 4.9e+55)
		tmp = fma(a, 120.0, Float64(Float64(x * -60.0) / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+98], t$95$1, If[LessEqual[y, 4.9e+55], N[(a * 120.0 + N[(N[(x * -60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000001e98 or 4.90000000000000015e55 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -9.5000000000000001e98 < y < 4.90000000000000015e55

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. neg-sub0 N/A

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. associate--r+ N/A

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

      18. neg-sub0 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 94.9

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

   7. Applied rewrites 94.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x \cdot -60}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 90.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, x \cdot \frac{-60}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ y (- z t)) (* a 120.0))))
   (if (<= y -9.5e+98)
     t_1
     (if (<= y 4.9e+55) (fma a 120.0 (* x (/ -60.0 (- t z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, (y / (z - t)), (a * 120.0));
	double tmp;
	if (y <= -9.5e+98) {
		tmp = t_1;
	} else if (y <= 4.9e+55) {
		tmp = fma(a, 120.0, (x * (-60.0 / (t - z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(y / Float64(z - t)), Float64(a * 120.0))
	tmp = 0.0
	if (y <= -9.5e+98)
		tmp = t_1;
	elseif (y <= 4.9e+55)
		tmp = fma(a, 120.0, Float64(x * Float64(-60.0 / Float64(t - z))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+98], t$95$1, If[LessEqual[y, 4.9e+55], N[(a * 120.0 + N[(x * N[(-60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000001e98 or 4.90000000000000015e55 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -9.5000000000000001e98 < y < 4.90000000000000015e55

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. neg-sub0 N/A

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. associate--r+ N/A

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

      18. neg-sub0 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.9

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

   7. Applied rewrites 99.9%

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

   8. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 94.8

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

   10. Applied rewrites 94.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, x \cdot \frac{-60}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 90.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{60}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ y (- z t)) (* a 120.0))))
   (if (<= y -9.5e+98)
     t_1
     (if (<= y 4.9e+55) (fma x (/ 60.0 (- z t)) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, (y / (z - t)), (a * 120.0));
	double tmp;
	if (y <= -9.5e+98) {
		tmp = t_1;
	} else if (y <= 4.9e+55) {
		tmp = fma(x, (60.0 / (z - t)), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(y / Float64(z - t)), Float64(a * 120.0))
	tmp = 0.0
	if (y <= -9.5e+98)
		tmp = t_1;
	elseif (y <= 4.9e+55)
		tmp = fma(x, Float64(60.0 / Float64(z - t)), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+98], t$95$1, If[LessEqual[y, 4.9e+55], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000001e98 or 4.90000000000000015e55 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -9.5000000000000001e98 < y < 4.90000000000000015e55

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 63.4

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

         \[\leadsto x \cdot \frac{\color{blue}{60 \cdot 1}}{z - t} + 120 \cdot a \]

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 94.8

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

   8. Applied rewrites 94.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{60}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 90.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ y (- z t)) (* a 120.0))))
   (if (<= y -9.5e+98)
     t_1
     (if (<= y 4.9e+55) (fma 60.0 (/ x (- z t)) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, (y / (z - t)), (a * 120.0));
	double tmp;
	if (y <= -9.5e+98) {
		tmp = t_1;
	} else if (y <= 4.9e+55) {
		tmp = fma(60.0, (x / (z - t)), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(y / Float64(z - t)), Float64(a * 120.0))
	tmp = 0.0
	if (y <= -9.5e+98)
		tmp = t_1;
	elseif (y <= 4.9e+55)
		tmp = fma(60.0, Float64(x / Float64(z - t)), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+98], t$95$1, If[LessEqual[y, 4.9e+55], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000001e98 or 4.90000000000000015e55 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -9.5000000000000001e98 < y < 4.90000000000000015e55

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 94.8

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

   5. Applied rewrites 94.8%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z - t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.1e+107)
   (/ (* x 60.0) (- z t))
   (if (<= x 7.4e+112) (fma y (/ 60.0 t) (* a 120.0)) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.1e+107) {
		tmp = (x * 60.0) / (z - t);
	} else if (x <= 7.4e+112) {
		tmp = fma(y, (60.0 / t), (a * 120.0));
	} else {
		tmp = x * (60.0 / (z - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.1e+107)
		tmp = Float64(Float64(x * 60.0) / Float64(z - t));
	elseif (x <= 7.4e+112)
		tmp = fma(y, Float64(60.0 / t), Float64(a * 120.0));
	else
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.1e+107], N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e+112], N[(y * N[(60.0 / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e107

   1. Initial program 99.9%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 61.4

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

   5. Applied rewrites 61.4%

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

   if -2.1e107 < x < 7.40000000000000008e112

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 71.4%

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

   if 7.40000000000000008e112 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 62.7

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

   5. Applied rewrites 62.7%

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

   7. Applied rewrites 62.8%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 99.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.8

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

   5. lift-/.f64 N/A

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

   6. frac-2neg N/A

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

   7. lower-/.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

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

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

   11. lower-*.f64 N/A

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

   12. metadata-eval N/A

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

   13. neg-sub0 N/A

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

   14. lift--.f64 N/A

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

   15. sub-neg N/A

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

   16. +-commutative N/A

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

   17. associate--r+ N/A

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

   18. neg-sub0 N/A

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

   19. remove-double-neg N/A

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

   20. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 19: 51.1% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 55.1

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

5. Applied rewrites 55.1%

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

6. Final simplification 55.1%

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

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024227 
(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)))