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

Percentage Accurate: 99.4% → 99.4%

Time: 13.3s

Alternatives: 17

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% 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 99.8%

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

   1. +-commutative N/A

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

   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 99.8

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

4. Applied egg-rr 99.8%

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

Alternative 2: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -0.05:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t \cdot -0.016666666666666666}\right)\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -0.05)
     (/ (- x y) (* (- z t) 0.016666666666666666))
     (if (<= t_1 5e-92)
       (* a 120.0)
       (if (<= t_1 4e+55)
         (fma a 120.0 (/ x (* t -0.016666666666666666)))
         (* 60.0 (/ (- x y) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -0.05) {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	} else if (t_1 <= 5e-92) {
		tmp = a * 120.0;
	} else if (t_1 <= 4e+55) {
		tmp = fma(a, 120.0, (x / (t * -0.016666666666666666)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -0.05)
		tmp = Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666));
	elseif (t_1 <= 5e-92)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 4e+55)
		tmp = fma(a, 120.0, Float64(x / Float64(t * -0.016666666666666666)));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.05], N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-92], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 4e+55], N[(a * 120.0 + N[(x / N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -0.050000000000000003

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 78.6

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

   5. Simplified 78.6%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 78.6

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

   7. Applied egg-rr 78.6%

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

      1. associate-/r/ N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. div-inv N/A

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

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

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

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

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

      10. metadata-eval 78.6

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

   9. Applied egg-rr 78.6%

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

   if -0.050000000000000003 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000011e-92

   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 83.5

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

   5. Simplified 83.5%

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

   if 5.00000000000000011e-92 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.00000000000000004e55

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   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 89.2

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

   5. Simplified 89.2%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. *-lowering-*.f64 68.2

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

   8. Simplified 68.2%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

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

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

      7. div-inv N/A

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

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

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

      9. metadata-eval 68.2

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

   10. Applied egg-rr 68.2%

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

   if 4.00000000000000004e55 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 88.2

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

   5. Simplified 88.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 88.3

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

   7. Applied egg-rr 88.3%

      \[\leadsto \color{blue}{\frac{x - y}{z - t} \cdot 60} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -0.05:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{-92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t \cdot -0.016666666666666666}\right)\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -0.05:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;t\_1 \leq 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -0.05)
     (/ (- x y) (* (- z t) 0.016666666666666666))
     (if (<= t_1 1e-39) (* a 120.0) (* 60.0 (/ (- x y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -0.05) {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	} else if (t_1 <= 1e-39) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-0.05d0)) then
        tmp = (x - y) / ((z - t) * 0.016666666666666666d0)
    else if (t_1 <= 1d-39) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -0.05) {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	} else if (t_1 <= 1e-39) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -0.05:
		tmp = (x - y) / ((z - t) * 0.016666666666666666)
	elif t_1 <= 1e-39:
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -0.05)
		tmp = Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666));
	elseif (t_1 <= 1e-39)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -0.05)
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	elseif (t_1 <= 1e-39)
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.05], N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-39], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -0.050000000000000003

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 78.6

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

   5. Simplified 78.6%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 78.6

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

   7. Applied egg-rr 78.6%

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

      1. associate-/r/ N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. div-inv N/A

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

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

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

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

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

      10. metadata-eval 78.6

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

   9. Applied egg-rr 78.6%

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

   if -0.050000000000000003 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999929e-40

   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 81.9

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

   5. Simplified 81.9%

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

   if 9.99999999999999929e-40 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 76.6

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

   5. Simplified 76.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 76.7

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

   7. Applied egg-rr 76.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -0.05:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -0.05)
     t_1
     (if (<= t_1 1e-39) (* a 120.0) (* 60.0 (/ (- x y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -0.05) {
		tmp = t_1;
	} else if (t_1 <= 1e-39) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-0.05d0)) then
        tmp = t_1
    else if (t_1 <= 1d-39) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -0.05) {
		tmp = t_1;
	} else if (t_1 <= 1e-39) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -0.05:
		tmp = t_1
	elif t_1 <= 1e-39:
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -0.05)
		tmp = t_1;
	elseif (t_1 <= 1e-39)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -0.05)
		tmp = t_1;
	elseif (t_1 <= 1e-39)
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.05], t$95$1, If[LessEqual[t$95$1, 1e-39], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -0.050000000000000003

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 78.6

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

   5. Simplified 78.6%

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

   if -0.050000000000000003 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999929e-40

   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 81.9

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

   5. Simplified 81.9%

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

   if 9.99999999999999929e-40 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 76.6

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

   5. Simplified 76.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 76.7

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

   7. Applied egg-rr 76.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -0.05:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -0.05) t_1 (if (<= t_2 1e-39) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -0.05) {
		tmp = t_1;
	} else if (t_2 <= 1e-39) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-0.05d0)) then
        tmp = t_1
    else if (t_2 <= 1d-39) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -0.05) {
		tmp = t_1;
	} else if (t_2 <= 1e-39) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -0.05:
		tmp = t_1
	elif t_2 <= 1e-39:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -0.05)
		tmp = t_1;
	elseif (t_2 <= 1e-39)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -0.05)
		tmp = t_1;
	elseif (t_2 <= 1e-39)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $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, -0.05], t$95$1, If[LessEqual[t$95$2, 1e-39], 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)) < -0.050000000000000003 or 9.99999999999999929e-40 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 77.5

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

   5. Simplified 77.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 77.5

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

   7. Applied egg-rr 77.5%

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

   if -0.050000000000000003 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999929e-40

   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 81.9

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

   5. Simplified 81.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -0.05:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z - t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ 60.0 (- z t)))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -0.05) t_1 (if (<= t_2 1e-39) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (60.0 / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -0.05) {
		tmp = t_1;
	} else if (t_2 <= 1e-39) {
		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 - y) * (60.0d0 / (z - t))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-0.05d0)) then
        tmp = t_1
    else if (t_2 <= 1d-39) 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 - y) * (60.0 / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -0.05) {
		tmp = t_1;
	} else if (t_2 <= 1e-39) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * (60.0 / (z - t))
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -0.05:
		tmp = t_1
	elif t_2 <= 1e-39:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -0.05)
		tmp = t_1;
	elseif (t_2 <= 1e-39)
		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 - y) * (60.0 / (z - t));
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -0.05)
		tmp = t_1;
	elseif (t_2 <= 1e-39)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $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, -0.05], t$95$1, If[LessEqual[t$95$2, 1e-39], 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)) < -0.050000000000000003 or 9.99999999999999929e-40 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 77.5

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

   5. Simplified 77.5%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 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

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

      5. --lowering--.f64 77.5

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

   7. Applied egg-rr 77.5%

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

   if -0.050000000000000003 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999929e-40

   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 81.9

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

   5. Simplified 81.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -0.05:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+88) t_1 (if (<= t_2 4e+55) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+88) {
		tmp = t_1;
	} else if (t_2 <= 4e+55) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+88)) then
        tmp = t_1
    else if (t_2 <= 4d+55) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+88) {
		tmp = t_1;
	} else if (t_2 <= 4e+55) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+88:
		tmp = t_1
	elif t_2 <= 4e+55:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+88)
		tmp = t_1;
	elseif (t_2 <= 4e+55)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+88)
		tmp = t_1;
	elseif (t_2 <= 4e+55)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+88], t$95$1, If[LessEqual[t$95$2, 4e+55], 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)) < -1.99999999999999992e88 or 4.00000000000000004e55 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 87.1

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

   5. Simplified 87.1%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 87.1

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

   7. Applied egg-rr 87.1%

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

   8. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 57.9

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

   10. Simplified 57.9%

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

   if -1.99999999999999992e88 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.00000000000000004e55

   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 70.6

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

   5. Simplified 70.6%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+88}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{+55}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+88) t_1 (if (<= t_2 4e+55) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+88) {
		tmp = t_1;
	} else if (t_2 <= 4e+55) {
		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) * (y / (z - t))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+88)) then
        tmp = t_1
    else if (t_2 <= 4d+55) 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 * (y / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+88) {
		tmp = t_1;
	} else if (t_2 <= 4e+55) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+88:
		tmp = t_1
	elif t_2 <= 4e+55:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+88)
		tmp = t_1;
	elseif (t_2 <= 4e+55)
		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 * (y / (z - t));
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+88)
		tmp = t_1;
	elseif (t_2 <= 4e+55)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $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+88], t$95$1, If[LessEqual[t$95$2, 4e+55], 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)) < -1.99999999999999992e88 or 4.00000000000000004e55 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-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 44.7

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

   5. Simplified 44.7%

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

   if -1.99999999999999992e88 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.00000000000000004e55

   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 70.6

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

   5. Simplified 70.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+88}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{+55}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+186}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y z))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+159) t_1 (if (<= t_2 1e+186) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+159) {
		tmp = t_1;
	} else if (t_2 <= 1e+186) {
		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) * (y / z)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+159)) then
        tmp = t_1
    else if (t_2 <= 1d+186) 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 * (y / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+159) {
		tmp = t_1;
	} else if (t_2 <= 1e+186) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / z)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+159:
		tmp = t_1
	elif t_2 <= 1e+186:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / z))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+159)
		tmp = t_1;
	elseif (t_2 <= 1e+186)
		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 * (y / z);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+159)
		tmp = t_1;
	elseif (t_2 <= 1e+186)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / 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+159], t$95$1, If[LessEqual[t$95$2, 1e+186], 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)) < -9.9999999999999993e158 or 9.9999999999999998e185 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   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 55.1

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

   5. Simplified 55.1%

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

   6. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 42.1

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

   8. Simplified 42.1%

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

   if -9.9999999999999993e158 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999998e185

   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 59.5

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

   5. Simplified 59.5%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+159}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+186}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{\left(x - y\right) \cdot -60}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e-81)
   (fma a 120.0 (/ (* 60.0 (- x y)) z))
   (if (<= z 3.9e-47)
     (fma a 120.0 (/ (* (- x y) -60.0) t))
     (fma 60.0 (/ (- x y) z) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e-81) {
		tmp = fma(a, 120.0, ((60.0 * (x - y)) / z));
	} else if (z <= 3.9e-47) {
		tmp = fma(a, 120.0, (((x - y) * -60.0) / t));
	} else {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e-81)
		tmp = fma(a, 120.0, Float64(Float64(60.0 * Float64(x - y)) / z));
	elseif (z <= 3.9e-47)
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) * -60.0) / t));
	else
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e-81], N[(a * 120.0 + N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-47], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.8000000000000006e-81

   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

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

      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 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 88.0

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

   7. Simplified 88.0%

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

   if -9.8000000000000006e-81 < z < 3.89999999999999978e-47

   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

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

      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 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 89.8

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

   7. Simplified 89.8%

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

   if 3.89999999999999978e-47 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 89.3

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

   5. Simplified 89.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{\left(x - y\right) \cdot -60}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e-79)
   (fma a 120.0 (/ (* 60.0 (- x y)) z))
   (if (<= z 1.5e-46)
     (fma -60.0 (/ (- x y) t) (* a 120.0))
     (fma 60.0 (/ (- x y) z) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e-79) {
		tmp = fma(a, 120.0, ((60.0 * (x - y)) / z));
	} else if (z <= 1.5e-46) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e-79)
		tmp = fma(a, 120.0, Float64(Float64(60.0 * Float64(x - y)) / z));
	elseif (z <= 1.5e-46)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	else
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e-79], N[(a * 120.0 + N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-46], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e-79

   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

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

      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 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 88.0

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

   7. Simplified 88.0%

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

   if -1e-79 < z < 1.49999999999999994e-46

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. 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 89.8

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

   5. Simplified 89.8%

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

   if 1.49999999999999994e-46 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 89.3

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

   5. Simplified 89.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ (- x y) z) (* a 120.0))))
   (if (<= z -3.2e-80)
     t_1
     (if (<= z 7.2e-47) (fma -60.0 (/ (- x y) t) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(60.0, ((x - y) / z), (a * 120.0));
	double tmp;
	if (z <= -3.2e-80) {
		tmp = t_1;
	} else if (z <= 7.2e-47) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0))
	tmp = 0.0
	if (z <= -3.2e-80)
		tmp = t_1;
	elseif (z <= 7.2e-47)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-80], t$95$1, If[LessEqual[z, 7.2e-47], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999999e-80 or 7.19999999999999982e-47 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. 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 88.5

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

   5. Simplified 88.5%

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

   if -3.1999999999999999e-80 < z < 7.19999999999999982e-47

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. 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 89.8

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

   5. Simplified 89.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-80}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ x z) (* a 120.0))))
   (if (<= z -9.5e-81)
     t_1
     (if (<= z 5.5e-47) (fma -60.0 (/ (- x y) t) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(60.0, (x / z), (a * 120.0));
	double tmp;
	if (z <= -9.5e-81) {
		tmp = t_1;
	} else if (z <= 5.5e-47) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(x / z), Float64(a * 120.0))
	tmp = 0.0
	if (z <= -9.5e-81)
		tmp = t_1;
	elseif (z <= 5.5e-47)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-81], t$95$1, If[LessEqual[z, 5.5e-47], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.49999999999999917e-81 or 5.5000000000000002e-47 < z

   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

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   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 80.7

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

   5. Simplified 80.7%

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

   6. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 74.3

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

   8. Simplified 74.3%

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

   if -9.49999999999999917e-81 < z < 5.5000000000000002e-47

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. 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 89.8

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

   5. Simplified 89.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot x}{z}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+138}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+266}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 x) z)))
   (if (<= x -9.5e+111)
     t_1
     (if (<= x 2.3e+138)
       (* a 120.0)
       (if (<= x 9.2e+266) t_1 (* x (/ -60.0 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * x) / z;
	double tmp;
	if (x <= -9.5e+111) {
		tmp = t_1;
	} else if (x <= 2.3e+138) {
		tmp = a * 120.0;
	} else if (x <= 9.2e+266) {
		tmp = t_1;
	} else {
		tmp = x * (-60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * x) / z
    if (x <= (-9.5d+111)) then
        tmp = t_1
    else if (x <= 2.3d+138) then
        tmp = a * 120.0d0
    else if (x <= 9.2d+266) then
        tmp = t_1
    else
        tmp = x * ((-60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * x) / z;
	double tmp;
	if (x <= -9.5e+111) {
		tmp = t_1;
	} else if (x <= 2.3e+138) {
		tmp = a * 120.0;
	} else if (x <= 9.2e+266) {
		tmp = t_1;
	} else {
		tmp = x * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * x) / z
	tmp = 0
	if x <= -9.5e+111:
		tmp = t_1
	elif x <= 2.3e+138:
		tmp = a * 120.0
	elif x <= 9.2e+266:
		tmp = t_1
	else:
		tmp = x * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * x) / z)
	tmp = 0.0
	if (x <= -9.5e+111)
		tmp = t_1;
	elseif (x <= 2.3e+138)
		tmp = Float64(a * 120.0);
	elseif (x <= 9.2e+266)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * x) / z;
	tmp = 0.0;
	if (x <= -9.5e+111)
		tmp = t_1;
	elseif (x <= 2.3e+138)
		tmp = a * 120.0;
	elseif (x <= 9.2e+266)
		tmp = t_1;
	else
		tmp = x * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -9.5e+111], t$95$1, If[LessEqual[x, 2.3e+138], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 9.2e+266], t$95$1, N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000019e111 or 2.30000000000000008e138 < x < 9.2000000000000004e266

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 82.0

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 55.1

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

   8. Simplified 55.1%

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

   9. Taylor expanded in x around inf

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

   11. Simplified 51.0%

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

   if -9.50000000000000019e111 < x < 2.30000000000000008e138

   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 60.6

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

   5. Simplified 60.6%

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

   if 9.2000000000000004e266 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 74.4

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

   5. Simplified 74.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
   7. 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 64.4

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

   8. Simplified 64.4%

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

   9. Taylor expanded in x around inf

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

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

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

       2. /-lowering-/.f64 65.3

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

   11. Simplified 65.3%

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

       1. *-commutative N/A

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

       2. metadata-eval N/A

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

       3. times-frac N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

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

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

       7. *-commutative N/A

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

       8. associate-/r* N/A

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

       9. metadata-eval N/A

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

       10. /-lowering-/.f64 65.6

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

   13. Applied egg-rr 65.6%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+138}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+266}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+140}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= x -1.5e+111) t_1 (if (<= x 2.4e+140) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (x <= -1.5e+111) {
		tmp = t_1;
	} else if (x <= 2.4e+140) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    if (x <= (-1.5d+111)) then
        tmp = t_1
    else if (x <= 2.4d+140) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (x <= -1.5e+111) {
		tmp = t_1;
	} else if (x <= 2.4e+140) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	tmp = 0
	if x <= -1.5e+111:
		tmp = t_1
	elif x <= 2.4e+140:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (x <= -1.5e+111)
		tmp = t_1;
	elseif (x <= 2.4e+140)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / (z - t));
	tmp = 0.0;
	if (x <= -1.5e+111)
		tmp = t_1;
	elseif (x <= 2.4e+140)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+111], t$95$1, If[LessEqual[x, 2.4e+140], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e111 or 2.4e140 < x

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf

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

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

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

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

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

      3. --lowering--.f64 67.5

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

   7. Simplified 67.5%

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

   if -1.5e111 < x < 2.4e140

   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 60.6

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

   5. Simplified 60.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+140}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+252}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))))
   (if (<= x -4.1e+157) t_1 (if (<= x 2.3e+252) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (x <= -4.1e+157) {
		tmp = t_1;
	} else if (x <= 2.3e+252) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / t)
    if (x <= (-4.1d+157)) then
        tmp = t_1
    else if (x <= 2.3d+252) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (x <= -4.1e+157) {
		tmp = t_1;
	} else if (x <= 2.3e+252) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	tmp = 0
	if x <= -4.1e+157:
		tmp = t_1
	elif x <= 2.3e+252:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	tmp = 0.0
	if (x <= -4.1e+157)
		tmp = t_1;
	elseif (x <= 2.3e+252)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / t);
	tmp = 0.0;
	if (x <= -4.1e+157)
		tmp = t_1;
	elseif (x <= 2.3e+252)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.1e+157], t$95$1, If[LessEqual[x, 2.3e+252], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.10000000000000016e157 or 2.3e252 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 84.8

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

   5. Simplified 84.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
   7. 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 57.5

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

   8. Simplified 57.5%

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

   9. Taylor expanded in x around inf

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

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

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

       2. /-lowering-/.f64 50.7

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

   11. Simplified 50.7%

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

   if -4.10000000000000016e157 < x < 2.3e252

   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 54.3

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

   5. Simplified 54.3%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+157}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+252}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.6% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around inf

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

   1. *-lowering-*.f64 47.9

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

5. Simplified 47.9%

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

6. Final simplification 47.9%

   \[\leadsto a \cdot 120 \]
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 2024199 
(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)))