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

Percentage Accurate: 99.4% → 99.8%

Time: 13.1s

Alternatives: 15

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. /-lowering-/.f64 N/A

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

   6. --lowering--.f64 N/A

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

   7. --lowering--.f64 N/A

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

   8. *-lowering-*.f64 99.8

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

4. Applied egg-rr 99.8%

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

Alternative 2: 58.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \left(x - y\right)\\ t_2 := \frac{t\_1}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+253}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+96}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_2 \leq -200000:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+75}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+155}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (- x y))) (t_2 (/ t_1 (- z t))))
   (if (<= t_2 -1e+253)
     (/ x (* (- z t) 0.016666666666666666))
     (if (<= t_2 -2e+96)
       (* -60.0 (/ y (- z t)))
       (if (<= t_2 -200000.0)
         (* (/ 60.0 (- z t)) x)
         (if (<= t_2 5e+75)
           (* a 120.0)
           (if (<= t_2 5e+155) (* -60.0 (/ (- x y) t)) (/ t_1 z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x - y);
	double t_2 = t_1 / (z - t);
	double tmp;
	if (t_2 <= -1e+253) {
		tmp = x / ((z - t) * 0.016666666666666666);
	} else if (t_2 <= -2e+96) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_2 <= -200000.0) {
		tmp = (60.0 / (z - t)) * x;
	} else if (t_2 <= 5e+75) {
		tmp = a * 120.0;
	} else if (t_2 <= 5e+155) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = t_1 / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * (x - y)
    t_2 = t_1 / (z - t)
    if (t_2 <= (-1d+253)) then
        tmp = x / ((z - t) * 0.016666666666666666d0)
    else if (t_2 <= (-2d+96)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_2 <= (-200000.0d0)) then
        tmp = (60.0d0 / (z - t)) * x
    else if (t_2 <= 5d+75) then
        tmp = a * 120.0d0
    else if (t_2 <= 5d+155) then
        tmp = (-60.0d0) * ((x - y) / t)
    else
        tmp = t_1 / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x - y);
	double t_2 = t_1 / (z - t);
	double tmp;
	if (t_2 <= -1e+253) {
		tmp = x / ((z - t) * 0.016666666666666666);
	} else if (t_2 <= -2e+96) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_2 <= -200000.0) {
		tmp = (60.0 / (z - t)) * x;
	} else if (t_2 <= 5e+75) {
		tmp = a * 120.0;
	} else if (t_2 <= 5e+155) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = t_1 / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x - y)
	t_2 = t_1 / (z - t)
	tmp = 0
	if t_2 <= -1e+253:
		tmp = x / ((z - t) * 0.016666666666666666)
	elif t_2 <= -2e+96:
		tmp = -60.0 * (y / (z - t))
	elif t_2 <= -200000.0:
		tmp = (60.0 / (z - t)) * x
	elif t_2 <= 5e+75:
		tmp = a * 120.0
	elif t_2 <= 5e+155:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = t_1 / z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x - y))
	t_2 = Float64(t_1 / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+253)
		tmp = Float64(x / Float64(Float64(z - t) * 0.016666666666666666));
	elseif (t_2 <= -2e+96)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_2 <= -200000.0)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (t_2 <= 5e+75)
		tmp = Float64(a * 120.0);
	elseif (t_2 <= 5e+155)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	else
		tmp = Float64(t_1 / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x - y);
	t_2 = t_1 / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+253)
		tmp = x / ((z - t) * 0.016666666666666666);
	elseif (t_2 <= -2e+96)
		tmp = -60.0 * (y / (z - t));
	elseif (t_2 <= -200000.0)
		tmp = (60.0 / (z - t)) * x;
	elseif (t_2 <= 5e+75)
		tmp = a * 120.0;
	elseif (t_2 <= 5e+155)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = t_1 / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+253], N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e+96], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -200000.0], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+75], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+155], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999994e252

   1. Initial program 93.8%

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

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 69.6

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

   5. Simplified 69.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

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

      6. div-inv N/A

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

      7. *-lowering-*.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. metadata-eval 75.8

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

   7. Applied egg-rr 75.8%

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

   if -9.9999999999999994e252 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e96

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 57.3

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

   5. Simplified 57.3%

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

   if -2.0000000000000001e96 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e5

   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. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 49.5

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

   5. Simplified 49.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 49.6

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

   7. Applied egg-rr 49.6%

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

   if -2e5 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000002e75

   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. *-lowering-*.f64 72.2

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

   5. Simplified 72.2%

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

   if 5.0000000000000002e75 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e155

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.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. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 77.8

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

   7. Simplified 77.8%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 61.4

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

   10. Simplified 61.4%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 N/A

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

       5. --lowering--.f64 61.6

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

   12. Applied egg-rr 61.6%

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

   if 4.9999999999999999e155 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.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. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 84.0

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

   7. Simplified 84.0%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 73.2%

       \[\leadsto \frac{\left(x - y\right) \cdot 60}{\color{blue}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+253}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+96}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -200000:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+75}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+155}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+252}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+259}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+252)
     (* x (/ 60.0 z))
     (if (<= t_1 -5e+129)
       (* y (/ 60.0 t))
       (if (<= t_1 1e+259) (* 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 <= -2e+252) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= -5e+129) {
		tmp = y * (60.0 / t);
	} else if (t_1 <= 1e+259) {
		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 <= (-2d+252)) then
        tmp = x * (60.0d0 / z)
    else if (t_1 <= (-5d+129)) then
        tmp = y * (60.0d0 / t)
    else if (t_1 <= 1d+259) 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 <= -2e+252) {
		tmp = x * (60.0 / z);
	} else if (t_1 <= -5e+129) {
		tmp = y * (60.0 / t);
	} else if (t_1 <= 1e+259) {
		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 <= -2e+252:
		tmp = x * (60.0 / z)
	elif t_1 <= -5e+129:
		tmp = y * (60.0 / t)
	elif t_1 <= 1e+259:
		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 <= -2e+252)
		tmp = Float64(x * Float64(60.0 / z));
	elseif (t_1 <= -5e+129)
		tmp = Float64(y * Float64(60.0 / t));
	elseif (t_1 <= 1e+259)
		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 <= -2e+252)
		tmp = x * (60.0 / z);
	elseif (t_1 <= -5e+129)
		tmp = y * (60.0 / t);
	elseif (t_1 <= 1e+259)
		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, -2e+252], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+129], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+259], N[(a * 120.0), $MachinePrecision], N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000002e252

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 65.6

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

   5. Simplified 65.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 71.3

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

   7. Applied egg-rr 71.3%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. /-lowering-/.f64 48.8

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

   10. Simplified 48.8%

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

   if -2.0000000000000002e252 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000003e129

   1. Initial program 99.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.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. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 84.1

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

   7. Simplified 84.1%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 47.6

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

   10. Simplified 47.6%

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

   11. Taylor expanded in x around 0

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

       1. *-lft-identity N/A

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

       2. associate-*l/ N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 N/A

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

       6. associate-*r/ N/A

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

       7. metadata-eval N/A

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

       8. /-lowering-/.f64 34.5

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

   13. Simplified 34.5%

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

   if -5.0000000000000003e129 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.999999999999999e258

   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. *-lowering-*.f64 55.5

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

   5. Simplified 55.5%

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

   if 9.999999999999999e258 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 92.4%

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

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 62.0

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

   5. Simplified 62.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 61.8

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

   7. Applied egg-rr 61.8%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. /-lowering-/.f64 61.9

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

   10. Simplified 61.9%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

       3. /-lowering-/.f64 N/A

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

       4. div-inv N/A

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

       5. *-lowering-*.f64 N/A

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

       6. metadata-eval 62.0

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

   12. Applied egg-rr 62.0%

       \[\leadsto \color{blue}{\frac{x}{z \cdot 0.016666666666666666}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+252}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+259}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+252}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+259}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -2e+252)
     t_1
     (if (<= t_2 -5e+129)
       (* y (/ 60.0 t))
       (if (<= t_2 1e+259) (* 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 <= -2e+252) {
		tmp = t_1;
	} else if (t_2 <= -5e+129) {
		tmp = y * (60.0 / t);
	} else if (t_2 <= 1e+259) {
		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 <= (-2d+252)) then
        tmp = t_1
    else if (t_2 <= (-5d+129)) then
        tmp = y * (60.0d0 / t)
    else if (t_2 <= 1d+259) 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 <= -2e+252) {
		tmp = t_1;
	} else if (t_2 <= -5e+129) {
		tmp = y * (60.0 / t);
	} else if (t_2 <= 1e+259) {
		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 <= -2e+252:
		tmp = t_1
	elif t_2 <= -5e+129:
		tmp = y * (60.0 / t)
	elif t_2 <= 1e+259:
		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 <= -2e+252)
		tmp = t_1;
	elseif (t_2 <= -5e+129)
		tmp = Float64(y * Float64(60.0 / t));
	elseif (t_2 <= 1e+259)
		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 <= -2e+252)
		tmp = t_1;
	elseif (t_2 <= -5e+129)
		tmp = y * (60.0 / t);
	elseif (t_2 <= 1e+259)
		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, -2e+252], t$95$1, If[LessEqual[t$95$2, -5e+129], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+259], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000002e252 or 9.999999999999999e258 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 93.4%

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

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 64.1

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

   5. Simplified 64.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 67.2

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

   7. Applied egg-rr 67.2%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. /-lowering-/.f64 54.5

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

   10. Simplified 54.5%

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

   if -2.0000000000000002e252 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000003e129

   1. Initial program 99.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.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. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 84.1

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

   7. Simplified 84.1%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 47.6

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

   10. Simplified 47.6%

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

   11. Taylor expanded in x around 0

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

       1. *-lft-identity N/A

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

       2. associate-*l/ N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 N/A

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

       6. associate-*r/ N/A

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

       7. metadata-eval N/A

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

       8. /-lowering-/.f64 34.5

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

   13. Simplified 34.5%

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

   if -5.0000000000000003e129 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.999999999999999e258

   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. *-lowering-*.f64 55.5

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

   5. Simplified 55.5%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+252}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+259}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+75}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e-52) t_1 (if (<= t_2 5e+75) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e-52) {
		tmp = t_1;
	} else if (t_2 <= 5e+75) {
		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 / (z - t)) * (x - y)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d-52)) then
        tmp = t_1
    else if (t_2 <= 5d+75) 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 / (z - t)) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e-52) {
		tmp = t_1;
	} else if (t_2 <= 5e+75) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / (z - t)) * (x - y)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e-52:
		tmp = t_1
	elif t_2 <= 5e+75:
		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(z - t)) * Float64(x - y))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e-52)
		tmp = t_1;
	elseif (t_2 <= 5e+75)
		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 / (z - t)) * (x - y);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e-52)
		tmp = t_1;
	elseif (t_2 <= 5e+75)
		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[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-52], t$95$1, If[LessEqual[t$95$2, 5e+75], 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)) < -5e-52 or 5.0000000000000002e75 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.3%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.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. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 79.5

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

   7. Simplified 79.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 80.9

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

   9. Applied egg-rr 80.9%

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

   if -5e-52 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000002e75

   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. *-lowering-*.f64 76.8

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

   5. Simplified 76.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{-52}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+75}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+259}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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+276) t_1 (if (<= t_2 1e+259) (* 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+276) {
		tmp = t_1;
	} else if (t_2 <= 1e+259) {
		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+276)) then
        tmp = t_1
    else if (t_2 <= 1d+259) 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+276) {
		tmp = t_1;
	} else if (t_2 <= 1e+259) {
		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+276:
		tmp = t_1
	elif t_2 <= 1e+259:
		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+276)
		tmp = t_1;
	elseif (t_2 <= 1e+259)
		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+276)
		tmp = t_1;
	elseif (t_2 <= 1e+259)
		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+276], t$95$1, If[LessEqual[t$95$2, 1e+259], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.0000000000000001e276 or 9.999999999999999e258 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 92.7%

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

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 67.5

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

   5. Simplified 67.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 70.9

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

   7. Applied egg-rr 70.9%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. /-lowering-/.f64 60.2

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

   10. Simplified 60.2%

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

   if -1.0000000000000001e276 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.999999999999999e258

   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. *-lowering-*.f64 50.5

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

   5. Simplified 50.5%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+276}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+259}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-167}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-52}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-54)
   (* a 120.0)
   (if (<= (* a 120.0) -4e-167)
     (/ (* y -60.0) (- z t))
     (if (<= (* a 120.0) 2e-52) (* -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) <= -1e-54) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e-167) {
		tmp = (y * -60.0) / (z - t);
	} else if ((a * 120.0) <= 2e-52) {
		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) <= (-1d-54)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-4d-167)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if ((a * 120.0d0) <= 2d-52) 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) <= -1e-54) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e-167) {
		tmp = (y * -60.0) / (z - t);
	} else if ((a * 120.0) <= 2e-52) {
		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) <= -1e-54:
		tmp = a * 120.0
	elif (a * 120.0) <= -4e-167:
		tmp = (y * -60.0) / (z - t)
	elif (a * 120.0) <= 2e-52:
		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) <= -1e-54)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -4e-167)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (Float64(a * 120.0) <= 2e-52)
		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) <= -1e-54)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -4e-167)
		tmp = (y * -60.0) / (z - t);
	elseif ((a * 120.0) <= 2e-52)
		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], -1e-54], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-167], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-52], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e-54 or 2e-52 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 67.5

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

   5. Simplified 67.5%

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

   if -1e-54 < (*.f64 a #s(literal 120 binary64)) < -4.00000000000000001e-167

   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. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 99.6

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 62.5

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

   7. Simplified 62.5%

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

   if -4.00000000000000001e-167 < (*.f64 a #s(literal 120 binary64)) < 2e-52

   1. Initial program 97.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.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. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 80.1

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 55.7

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

   10. Simplified 55.7%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 N/A

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

       5. --lowering--.f64 55.7

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

   12. Applied egg-rr 55.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-167}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-52}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-167}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-52}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-54)
   (* a 120.0)
   (if (<= (* a 120.0) -4e-167)
     (* -60.0 (/ y (- z t)))
     (if (<= (* a 120.0) 2e-52) (* -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) <= -1e-54) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e-167) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a * 120.0) <= 2e-52) {
		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) <= (-1d-54)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-4d-167)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if ((a * 120.0d0) <= 2d-52) 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) <= -1e-54) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e-167) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a * 120.0) <= 2e-52) {
		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) <= -1e-54:
		tmp = a * 120.0
	elif (a * 120.0) <= -4e-167:
		tmp = -60.0 * (y / (z - t))
	elif (a * 120.0) <= 2e-52:
		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) <= -1e-54)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -4e-167)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 2e-52)
		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) <= -1e-54)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -4e-167)
		tmp = -60.0 * (y / (z - t));
	elseif ((a * 120.0) <= 2e-52)
		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], -1e-54], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-167], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-52], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e-54 or 2e-52 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 67.5

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

   5. Simplified 67.5%

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

   if -1e-54 < (*.f64 a #s(literal 120 binary64)) < -4.00000000000000001e-167

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 62.3

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

   5. Simplified 62.3%

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

   if -4.00000000000000001e-167 < (*.f64 a #s(literal 120 binary64)) < 2e-52

   1. Initial program 97.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.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. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 80.1

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 55.7

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

   10. Simplified 55.7%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 N/A

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

       5. --lowering--.f64 55.7

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

   12. Applied egg-rr 55.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-167}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-52}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{+22}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-54)
   (* a 120.0)
   (if (<= (* a 120.0) 4e+22) (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e-54) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 4e+22) {
		tmp = -60.0 * (y / (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) <= (-1d-54)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 4d+22) then
        tmp = (-60.0d0) * (y / (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) <= -1e-54) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 4e+22) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e-54:
		tmp = a * 120.0
	elif (a * 120.0) <= 4e+22:
		tmp = -60.0 * (y / (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) <= -1e-54)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 4e+22)
		tmp = Float64(-60.0 * Float64(y / 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) <= -1e-54)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 4e+22)
		tmp = -60.0 * (y / (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], -1e-54], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e+22], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e-54 or 4e22 < (*.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. *-lowering-*.f64 73.2

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

   5. Simplified 73.2%

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

   if -1e-54 < (*.f64 a #s(literal 120 binary64)) < 4e22

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 47.0

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

   5. Simplified 47.0%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{+22}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot x\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-40}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* (/ 60.0 (- z t)) x))))
   (if (<= x -3.3e+113)
     t_1
     (if (<= x 2e-40) (fma a 120.0 (/ (* y -60.0) (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((60.0 / (z - t)) * x));
	double tmp;
	if (x <= -3.3e+113) {
		tmp = t_1;
	} else if (x <= 2e-40) {
		tmp = fma(a, 120.0, ((y * -60.0) / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(60.0 / Float64(z - t)) * x))
	tmp = 0.0
	if (x <= -3.3e+113)
		tmp = t_1;
	elseif (x <= 2e-40)
		tmp = fma(a, 120.0, Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+113], t$95$1, If[LessEqual[x, 2e-40], N[(a * 120.0 + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3000000000000003e113 or 1.9999999999999999e-40 < x

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 85.5

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

   5. Simplified 85.5%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. --lowering--.f64 86.4

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

   7. Applied egg-rr 86.4%

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

   if -3.3000000000000003e113 < x < 1.9999999999999999e-40

   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. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 99.8

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

   4. Applied egg-rr 99.8%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. div-inv N/A

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

      9. *-lowering-*.f64 N/A

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

      10. --lowering--.f64 N/A

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

      11. metadata-eval 99.8

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 95.1

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

   9. Simplified 95.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot x\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-40}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* a 120.0))))
   (if (<= t -7e-7)
     t_1
     (if (<= t 1.95e+37) (fma 60.0 (/ (- x y) z) (* 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 - y) / t), (a * 120.0));
	double tmp;
	if (t <= -7e-7) {
		tmp = t_1;
	} else if (t <= 1.95e+37) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0))
	tmp = 0.0
	if (t <= -7e-7)
		tmp = t_1;
	elseif (t <= 1.95e+37)
		tmp = fma(60.0, Float64(Float64(x - y) / z), 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[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-7], t$95$1, If[LessEqual[t, 1.95e+37], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.99999999999999968e-7 or 1.9499999999999999e37 < t

   1. Initial program 99.0%

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

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 86.6

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

   5. Simplified 86.6%

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

   if -6.99999999999999968e-7 < t < 1.9499999999999999e37

   1. Initial program 99.0%

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

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 85.4

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

   5. Simplified 85.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-60}{t}\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+253}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ -60.0 t))))
   (if (<= x -5.8e+204) t_1 (if (<= x 2.15e+253) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-60.0 / t);
	double tmp;
	if (x <= -5.8e+204) {
		tmp = t_1;
	} else if (x <= 2.15e+253) {
		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) / t)
    if (x <= (-5.8d+204)) then
        tmp = t_1
    else if (x <= 2.15d+253) 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 / t);
	double tmp;
	if (x <= -5.8e+204) {
		tmp = t_1;
	} else if (x <= 2.15e+253) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (-60.0 / t)
	tmp = 0
	if x <= -5.8e+204:
		tmp = t_1
	elif x <= 2.15e+253:
		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 / t))
	tmp = 0.0
	if (x <= -5.8e+204)
		tmp = t_1;
	elseif (x <= 2.15e+253)
		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 / t);
	tmp = 0.0;
	if (x <= -5.8e+204)
		tmp = t_1;
	elseif (x <= 2.15e+253)
		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 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+204], t$95$1, If[LessEqual[x, 2.15e+253], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.80000000000000007e204 or 2.1499999999999999e253 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in 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. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 74.3

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

   5. Simplified 74.3%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 52.4

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

   8. Simplified 52.4%

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

   if -5.80000000000000007e204 < x < 2.1499999999999999e253

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 49.4

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

   5. Simplified 49.4%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+253}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. /-lowering-/.f64 N/A

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

   6. --lowering--.f64 N/A

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

   7. --lowering--.f64 N/A

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

   8. *-lowering-*.f64 99.8

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

4. Applied egg-rr 99.8%

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

   1. +-commutative N/A

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

   2. accelerator-lowering-fma.f64 N/A

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

   3. *-commutative N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. /-lowering-/.f64 N/A

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

   7. --lowering--.f64 N/A

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

   8. div-inv N/A

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

   9. *-lowering-*.f64 N/A

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

   10. --lowering--.f64 N/A

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

   11. metadata-eval 99.8

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

6. Applied egg-rr 99.8%

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

Alternative 14: 99.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. +-commutative N/A

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

   2. accelerator-lowering-fma.f64 N/A

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

   3. /-lowering-/.f64 N/A

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

   4. *-lowering-*.f64 N/A

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

   5. --lowering--.f64 N/A

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

   6. --lowering--.f64 99.0

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

4. Applied egg-rr 99.0%

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

Alternative 15: 51.0% 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 99.0%

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

3. Taylor expanded in z around inf

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

   1. *-lowering-*.f64 45.4

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

5. Simplified 45.4%

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

6. Final simplification 45.4%

   \[\leadsto a \cdot 120 \]
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 2024204 
(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)))