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

Percentage Accurate: 99.5% → 99.5%

Time: 11.9s

Alternatives: 17

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% 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: 99.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

Alternative 2: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -5e+135)
     t_1
     (if (<= t_1 1e+30) (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 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -5e+135) {
		tmp = t_1;
	} else if (t_1 <= 1e+30) {
		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 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+135)
		tmp = t_1;
	elseif (t_1 <= 1e+30)
		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[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+135], t$95$1, If[LessEqual[t$95$1, 1e+30], 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 (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000029e135 or 1e30 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 85.5

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

   5. Applied rewrites 85.5%

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

   if -5.00000000000000029e135 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e30

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 87.0

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

   5. Applied rewrites 87.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+135}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot 60\\ t_2 := \frac{t\_1}{z}\\ t_3 := \frac{t\_1}{z - t}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) 60.0)) (t_2 (/ t_1 z)) (t_3 (/ t_1 (- z t))))
   (if (<= t_3 -5e+135) t_2 (if (<= t_3 5e+14) (* a 120.0) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * 60.0;
	double t_2 = t_1 / z;
	double t_3 = t_1 / (z - t);
	double tmp;
	if (t_3 <= -5e+135) {
		tmp = t_2;
	} else if (t_3 <= 5e+14) {
		tmp = a * 120.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x - y) * 60.0d0
    t_2 = t_1 / z
    t_3 = t_1 / (z - t)
    if (t_3 <= (-5d+135)) then
        tmp = t_2
    else if (t_3 <= 5d+14) then
        tmp = a * 120.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * 60.0;
	double t_2 = t_1 / z;
	double t_3 = t_1 / (z - t);
	double tmp;
	if (t_3 <= -5e+135) {
		tmp = t_2;
	} else if (t_3 <= 5e+14) {
		tmp = a * 120.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * 60.0
	t_2 = t_1 / z
	t_3 = t_1 / (z - t)
	tmp = 0
	if t_3 <= -5e+135:
		tmp = t_2
	elif t_3 <= 5e+14:
		tmp = a * 120.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * 60.0)
	t_2 = Float64(t_1 / z)
	t_3 = Float64(t_1 / Float64(z - t))
	tmp = 0.0
	if (t_3 <= -5e+135)
		tmp = t_2;
	elseif (t_3 <= 5e+14)
		tmp = Float64(a * 120.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * 60.0;
	t_2 = t_1 / z;
	t_3 = t_1 / (z - t);
	tmp = 0.0;
	if (t_3 <= -5e+135)
		tmp = t_2;
	elseif (t_3 <= 5e+14)
		tmp = a * 120.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / z), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+135], t$95$2, If[LessEqual[t$95$3, 5e+14], N[(a * 120.0), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000029e135 or 5e14 < (/.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

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 61.7

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

   5. Applied rewrites 61.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 53.0%

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

   if -5.00000000000000029e135 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5e14

   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 72.0

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

   5. Applied rewrites 72.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+135}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \mathbf{if}\;a \cdot 120 \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-38}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ x z) (* a 120.0))))
   (if (<= (* a 120.0) -1.5e-25)
     t_1
     (if (<= (* a 120.0) 4e-38)
       (/ (* (- x y) 60.0) (- z t))
       (if (<= (* a 120.0) 1e+43) (fma y (/ 60.0 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, (x / z), (a * 120.0));
	double tmp;
	if ((a * 120.0) <= -1.5e-25) {
		tmp = t_1;
	} else if ((a * 120.0) <= 4e-38) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else if ((a * 120.0) <= 1e+43) {
		tmp = fma(y, (60.0 / t), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(x / z), Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -1.5e-25)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 4e-38)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t));
	elseif (Float64(a * 120.0) <= 1e+43)
		tmp = fma(y, Float64(60.0 / 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[(x / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -1.5e-25], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-38], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+43], N[(y * N[(60.0 / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.4999999999999999e-25 or 1.00000000000000001e43 < (*.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

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 81.1

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

   5. Applied rewrites 81.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 85.2%

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

   if -1.4999999999999999e-25 < (*.f64 a #s(literal 120 binary64)) < 3.9999999999999998e-38

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if 3.9999999999999998e-38 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000001e43

   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 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 92.9

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

   5. Applied rewrites 92.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 86.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-38}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ t_2 := \mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-158}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ x (- z t)) (* a 120.0)))
        (t_2 (fma -60.0 (/ (- x y) t) (* a 120.0))))
   (if (<= t -2.3e+126)
     t_2
     (if (<= t -1e-84)
       t_1
       (if (<= t 1.25e-158)
         (fma 60.0 (/ (- x y) z) (* a 120.0))
         (if (<= t 8e+26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(60.0, (x / (z - t)), (a * 120.0));
	double t_2 = fma(-60.0, ((x - y) / t), (a * 120.0));
	double tmp;
	if (t <= -2.3e+126) {
		tmp = t_2;
	} else if (t <= -1e-84) {
		tmp = t_1;
	} else if (t <= 1.25e-158) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else if (t <= 8e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(x / Float64(z - t)), Float64(a * 120.0))
	t_2 = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0))
	tmp = 0.0
	if (t <= -2.3e+126)
		tmp = t_2;
	elseif (t <= -1e-84)
		tmp = t_1;
	elseif (t <= 1.25e-158)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	elseif (t <= 8e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+126], t$95$2, If[LessEqual[t, -1e-84], t$95$1, If[LessEqual[t, 1.25e-158], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+26], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3000000000000001e126 or 8.00000000000000038e26 < 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 z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 90.1

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

   5. Applied rewrites 90.1%

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

   if -2.3000000000000001e126 < t < -1e-84 or 1.24999999999999993e-158 < t < 8.00000000000000038e26

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 87.9

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

   5. Applied rewrites 87.9%

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

   if -1e-84 < t < 1.24999999999999993e-158

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 93.4

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

   5. Applied rewrites 93.4%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+126}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-84}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-158}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-41}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1.5e-25)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-41) (/ (* (- x y) 60.0) (- z t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1.5e-25) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-41) {
		tmp = ((x - y) * 60.0) / (z - 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) <= (-1.5d-25)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-41) then
        tmp = ((x - y) * 60.0d0) / (z - 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) <= -1.5e-25) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-41) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1.5e-25:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-41:
		tmp = ((x - y) * 60.0) / (z - t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1.5e-25)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-41)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - 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) <= -1.5e-25)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-41)
		tmp = ((x - y) * 60.0) / (z - 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], -1.5e-25], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-41], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.4999999999999999e-25 or 1.00000000000000001e-41 < (*.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 78.8

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

   5. Applied rewrites 78.8%

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

   if -1.4999999999999999e-25 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000001e-41

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 77.5

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

   5. Applied rewrites 77.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-41}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+167}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot 60}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ x (- z t)) (* a 120.0))))
   (if (<= x -2.1e+167)
     (/ (* (- x y) 60.0) (- z t))
     (if (<= x -3e+19)
       t_1
       (if (<= x 6.8e+97) (fma a 120.0 (/ (* y 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, (x / (z - t)), (a * 120.0));
	double tmp;
	if (x <= -2.1e+167) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else if (x <= -3e+19) {
		tmp = t_1;
	} else if (x <= 6.8e+97) {
		tmp = fma(a, 120.0, ((y * 60.0) / (t - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(x / Float64(z - t)), Float64(a * 120.0))
	tmp = 0.0
	if (x <= -2.1e+167)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t));
	elseif (x <= -3e+19)
		tmp = t_1;
	elseif (x <= 6.8e+97)
		tmp = fma(a, 120.0, Float64(Float64(y * 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[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+167], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e+19], t$95$1, If[LessEqual[x, 6.8e+97], N[(a * 120.0 + N[(N[(y * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0999999999999999e167

   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 95.7

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

   5. Applied rewrites 95.7%

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

   if -2.0999999999999999e167 < x < -3e19 or 6.8000000000000002e97 < 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 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 92.6

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

   5. Applied rewrites 92.6%

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

   if -3e19 < x < 6.8000000000000002e97

   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

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

      1. *-commutative N/A

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

      2. lower-*.f64 94.3

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

   7. Applied rewrites 94.3%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+167}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot 60}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-41}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1.5e-25)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-41) (* -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) <= -1.5e-25) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-41) {
		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) <= (-1.5d-25)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-41) 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) <= -1.5e-25) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-41) {
		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) <= -1.5e-25:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-41:
		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) <= -1.5e-25)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-41)
		tmp = Float64(-60.0 * Float64(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) <= -1.5e-25)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-41)
		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], -1.5e-25], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-41], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.4999999999999999e-25 or 1.00000000000000001e-41 < (*.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 78.8

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

   5. Applied rewrites 78.8%

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

   if -1.4999999999999999e-25 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000001e-41

   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 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 56.2

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 44.5%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-41}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z - t}\\ \mathbf{if}\;x \leq -8 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-137}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 (- z t)))))
   (if (<= x -8e+162)
     t_1
     (if (<= x -5.8e-137)
       (fma -60.0 (/ y z) (* a 120.0))
       (if (<= x 3.5e+143) (fma y (/ 60.0 t) (* 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 - t));
	double tmp;
	if (x <= -8e+162) {
		tmp = t_1;
	} else if (x <= -5.8e-137) {
		tmp = fma(-60.0, (y / z), (a * 120.0));
	} else if (x <= 3.5e+143) {
		tmp = fma(y, (60.0 / t), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(60.0 / Float64(z - t)))
	tmp = 0.0
	if (x <= -8e+162)
		tmp = t_1;
	elseif (x <= -5.8e-137)
		tmp = fma(-60.0, Float64(y / z), Float64(a * 120.0));
	elseif (x <= 3.5e+143)
		tmp = fma(y, Float64(60.0 / 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[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+162], t$95$1, If[LessEqual[x, -5.8e-137], N[(-60.0 * N[(y / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+143], N[(y * N[(60.0 / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.9999999999999995e162 or 3.50000000000000008e143 < 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 70.0

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

   5. Applied rewrites 70.0%

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

   7. Applied rewrites 70.2%

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

   if -7.9999999999999995e162 < x < -5.7999999999999997e-137

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 78.0

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

   5. Applied rewrites 78.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 72.0%

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

   if -5.7999999999999997e-137 < x < 3.50000000000000008e143

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 72.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-137}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z - t}\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 (- z t)))))
   (if (<= x -9.2e+162)
     t_1
     (if (<= x -6.8e-137)
       (* a 120.0)
       (if (<= x 3.5e+143) (fma y (/ 60.0 t) (* 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 - t));
	double tmp;
	if (x <= -9.2e+162) {
		tmp = t_1;
	} else if (x <= -6.8e-137) {
		tmp = a * 120.0;
	} else if (x <= 3.5e+143) {
		tmp = fma(y, (60.0 / t), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(60.0 / Float64(z - t)))
	tmp = 0.0
	if (x <= -9.2e+162)
		tmp = t_1;
	elseif (x <= -6.8e-137)
		tmp = Float64(a * 120.0);
	elseif (x <= 3.5e+143)
		tmp = fma(y, Float64(60.0 / 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[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e+162], t$95$1, If[LessEqual[x, -6.8e-137], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 3.5e+143], N[(y * N[(60.0 / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.19999999999999975e162 or 3.50000000000000008e143 < 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 70.0

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

   5. Applied rewrites 70.0%

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

   7. Applied rewrites 70.2%

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

   if -9.19999999999999975e162 < x < -6.80000000000000028e-137

   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 64.6

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

   5. Applied rewrites 64.6%

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

   if -6.80000000000000028e-137 < x < 3.50000000000000008e143

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 72.6%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{60}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, 60 \cdot \frac{x}{z}\right)\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* 60.0 (/ x z)))))
   (if (<= z -1.26e+162)
     t_1
     (if (<= z 7.4e-25) (fma -60.0 (/ (- x y) t) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, (60.0 * (x / z)));
	double tmp;
	if (z <= -1.26e+162) {
		tmp = t_1;
	} else if (z <= 7.4e-25) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(60.0 * Float64(x / z)))
	tmp = 0.0
	if (z <= -1.26e+162)
		tmp = t_1;
	elseif (z <= 7.4e-25)
		tmp = fma(-60.0, Float64(Float64(x - y) / 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[(a * 120.0 + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.26e+162], t$95$1, If[LessEqual[z, 7.4e-25], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.26e162 or 7.40000000000000017e-25 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 90.3

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

   5. Applied rewrites 90.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 82.4%

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

   10. Applied rewrites 82.5%

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

   if -1.26e162 < z < 7.40000000000000017e-25

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 78.8

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

   5. Applied rewrites 78.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, 60 \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, 60 \cdot \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z - t}\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+240}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 (- z t)))))
   (if (<= x -9.2e+162) t_1 (if (<= x 1.42e+240) (* 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 - t));
	double tmp;
	if (x <= -9.2e+162) {
		tmp = t_1;
	} else if (x <= 1.42e+240) {
		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) :: tmp
    t_1 = x * (60.0d0 / (z - t))
    if (x <= (-9.2d+162)) then
        tmp = t_1
    else if (x <= 1.42d+240) 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 - t));
	double tmp;
	if (x <= -9.2e+162) {
		tmp = t_1;
	} else if (x <= 1.42e+240) {
		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))
	tmp = 0
	if x <= -9.2e+162:
		tmp = t_1
	elif x <= 1.42e+240:
		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 / Float64(z - t)))
	tmp = 0.0
	if (x <= -9.2e+162)
		tmp = t_1;
	elseif (x <= 1.42e+240)
		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));
	tmp = 0.0;
	if (x <= -9.2e+162)
		tmp = t_1;
	elseif (x <= 1.42e+240)
		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 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e+162], t$95$1, If[LessEqual[x, 1.42e+240], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.19999999999999975e162 or 1.41999999999999999e240 < 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 78.8

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

   5. Applied rewrites 78.8%

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

   7. Applied rewrites 79.0%

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

   if -9.19999999999999975e162 < x < 1.41999999999999999e240

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 63.4

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

   5. Applied rewrites 63.4%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+240}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z}\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+241}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 z))))
   (if (<= x -2.15e+164) t_1 (if (<= x 1.55e+241) (* 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 tmp;
	if (x <= -2.15e+164) {
		tmp = t_1;
	} else if (x <= 1.55e+241) {
		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) :: tmp
    t_1 = x * (60.0d0 / z)
    if (x <= (-2.15d+164)) then
        tmp = t_1
    else if (x <= 1.55d+241) 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 tmp;
	if (x <= -2.15e+164) {
		tmp = t_1;
	} else if (x <= 1.55e+241) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (60.0 / z)
	tmp = 0
	if x <= -2.15e+164:
		tmp = t_1
	elif x <= 1.55e+241:
		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))
	tmp = 0.0
	if (x <= -2.15e+164)
		tmp = t_1;
	elseif (x <= 1.55e+241)
		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);
	tmp = 0.0;
	if (x <= -2.15e+164)
		tmp = t_1;
	elseif (x <= 1.55e+241)
		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]}, If[LessEqual[x, -2.15e+164], t$95$1, If[LessEqual[x, 1.55e+241], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15e164 or 1.55e241 < 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 78.8

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

   5. Applied rewrites 78.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.4%

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

   if -2.15e164 < x < 1.55e241

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 63.4

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

   5. Applied rewrites 63.4%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+241}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 60}{z}\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+241}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x 60.0) z)))
   (if (<= x -2.15e+164) t_1 (if (<= x 2.05e+241) (* 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 tmp;
	if (x <= -2.15e+164) {
		tmp = t_1;
	} else if (x <= 2.05e+241) {
		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) :: tmp
    t_1 = (x * 60.0d0) / z
    if (x <= (-2.15d+164)) then
        tmp = t_1
    else if (x <= 2.05d+241) 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 tmp;
	if (x <= -2.15e+164) {
		tmp = t_1;
	} else if (x <= 2.05e+241) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * 60.0) / z
	tmp = 0
	if x <= -2.15e+164:
		tmp = t_1
	elif x <= 2.05e+241:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * 60.0) / z)
	tmp = 0.0
	if (x <= -2.15e+164)
		tmp = t_1;
	elseif (x <= 2.05e+241)
		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;
	tmp = 0.0;
	if (x <= -2.15e+164)
		tmp = t_1;
	elseif (x <= 2.05e+241)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * 60.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -2.15e+164], t$95$1, If[LessEqual[x, 2.05e+241], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15e164 or 2.05000000000000007e241 < 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 z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 55.8%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 47.4%

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

   if -2.15e164 < x < 2.05000000000000007e241

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 63.4

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

   5. Applied rewrites 63.4%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+164}:\\ \;\;\;\;\frac{x \cdot 60}{z}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+241}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+241}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x z))))
   (if (<= x -2.15e+164) t_1 (if (<= x 2.05e+241) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / z);
	double tmp;
	if (x <= -2.15e+164) {
		tmp = t_1;
	} else if (x <= 2.05e+241) {
		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) :: tmp
    t_1 = 60.0d0 * (x / z)
    if (x <= (-2.15d+164)) then
        tmp = t_1
    else if (x <= 2.05d+241) 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 / z);
	double tmp;
	if (x <= -2.15e+164) {
		tmp = t_1;
	} else if (x <= 2.05e+241) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / z)
	tmp = 0
	if x <= -2.15e+164:
		tmp = t_1
	elif x <= 2.05e+241:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / z))
	tmp = 0.0
	if (x <= -2.15e+164)
		tmp = t_1;
	elseif (x <= 2.05e+241)
		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 / z);
	tmp = 0.0;
	if (x <= -2.15e+164)
		tmp = t_1;
	elseif (x <= 2.05e+241)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e+164], t$95$1, If[LessEqual[x, 2.05e+241], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15e164 or 2.05000000000000007e241 < 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 z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 55.8%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 47.4%

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

   13. Applied rewrites 47.3%

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

   if -2.15e164 < x < 2.05000000000000007e241

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 63.4

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

   5. Applied rewrites 63.4%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+164}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+241}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+180}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.52e+180) (* -60.0 (/ x t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.52e+180) {
		tmp = -60.0 * (x / 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 (x <= (-1.52d+180)) then
        tmp = (-60.0d0) * (x / 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 (x <= -1.52e+180) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.52e+180:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.52e+180)
		tmp = Float64(-60.0 * Float64(x / 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 (x <= -1.52e+180)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.52e+180], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.52e180

   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 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 61.7

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

   5. Applied rewrites 61.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 61.7%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 48.7%

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

   if -1.52e180 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 58.8

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

   5. Applied rewrites 58.8%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+180}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.5% 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 53.2

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

5. Applied rewrites 53.2%

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

6. Final simplification 53.2%

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

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024223 
(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)))