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

Percentage Accurate: 99.3% → 99.8%

Time: 14.1s

Alternatives: 18

Speedup: 1.0×

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: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. fma-def 99.5%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. fma-def 99.5%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 73.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t_2 \leq -400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{-33}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;t_2 \leq 200000000:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+21}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+45}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -400000000.0)
     t_1
     (if (<= t_2 2e-76)
       (* a 120.0)
       (if (<= t_2 4e-33)
         (/ 60.0 (/ (- z t) (- x y)))
         (if (<= t_2 200000000.0)
           (+ (* a 120.0) (* 60.0 (/ y t)))
           (if (<= t_2 5e+21)
             (+ (* a 120.0) (* 60.0 (/ x z)))
             (if (<= t_2 5e+45) (+ (* a 120.0) (* -60.0 (/ x t))) 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 <= -400000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2e-76) {
		tmp = a * 120.0;
	} else if (t_2 <= 4e-33) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t_2 <= 200000000.0) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (t_2 <= 5e+21) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if (t_2 <= 5e+45) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} 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 <= (-400000000.0d0)) then
        tmp = t_1
    else if (t_2 <= 2d-76) then
        tmp = a * 120.0d0
    else if (t_2 <= 4d-33) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (t_2 <= 200000000.0d0) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if (t_2 <= 5d+21) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if (t_2 <= 5d+45) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    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 <= -400000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2e-76) {
		tmp = a * 120.0;
	} else if (t_2 <= 4e-33) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t_2 <= 200000000.0) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (t_2 <= 5e+21) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if (t_2 <= 5e+45) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} 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 <= -400000000.0:
		tmp = t_1
	elif t_2 <= 2e-76:
		tmp = a * 120.0
	elif t_2 <= 4e-33:
		tmp = 60.0 / ((z - t) / (x - y))
	elif t_2 <= 200000000.0:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif t_2 <= 5e+21:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif t_2 <= 5e+45:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	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 <= -400000000.0)
		tmp = t_1;
	elseif (t_2 <= 2e-76)
		tmp = Float64(a * 120.0);
	elseif (t_2 <= 4e-33)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (t_2 <= 200000000.0)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (t_2 <= 5e+21)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (t_2 <= 5e+45)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	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 <= -400000000.0)
		tmp = t_1;
	elseif (t_2 <= 2e-76)
		tmp = a * 120.0;
	elseif (t_2 <= 4e-33)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (t_2 <= 200000000.0)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif (t_2 <= 5e+21)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif (t_2 <= 5e+45)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	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, -400000000.0], t$95$1, If[LessEqual[t$95$2, 2e-76], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$2, 4e-33], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 200000000.0], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+21], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+45], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -4e8 or 5e45 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 98.9%

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

      3. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 82.1%

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

   if -4e8 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 1.99999999999999985e-76

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 85.7%

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

   if 1.99999999999999985e-76 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 4.0000000000000002e-33

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-def 99.6%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 99.3%

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

      1. clear-num 99.1%

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

      2. un-div-inv 99.6%

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

   8. Applied egg-rr 99.6%

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

   if 4.0000000000000002e-33 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 2e8

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 79.1%

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

   3. Taylor expanded in x around 0 79.7%

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

   if 2e8 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 5e21

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 74.5%

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

   3. Taylor expanded in x around inf 74.5%

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

   if 5e21 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 5e45

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in x around inf 89.8%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} + a \cdot 120 \]
3. Recombined 6 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -400000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{-76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{-33}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 200000000:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+21}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+45}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 4: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+60} \lor \neg \left(t_1 \leq 4 \cdot 10^{+177}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (or (<= t_1 -5e+60) (not (<= t_1 4e+177)))
     (/ 60.0 (/ (- z t) (- x y)))
     (+ (* -60.0 (/ y (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e+60) || !(t_1 <= 4e+177)) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if ((t_1 <= (-5d+60)) .or. (.not. (t_1 <= 4d+177))) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = ((-60.0d0) * (y / (z - t))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e+60) || !(t_1 <= 4e+177)) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if (t_1 <= -5e+60) or not (t_1 <= 4e+177):
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -5e+60) || !(t_1 <= 4e+177))
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(-60.0 * Float64(y / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if ((t_1 <= -5e+60) || ~((t_1 <= 4e+177)))
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	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[Or[LessEqual[t$95$1, -5e+60], N[Not[LessEqual[t$95$1, 4e+177]], $MachinePrecision]], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -4.99999999999999975e60 or 4e177 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. fma-def 98.4%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 91.1%

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

      1. clear-num 91.1%

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

      2. un-div-inv 91.2%

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

   8. Applied egg-rr 91.2%

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

   if -4.99999999999999975e60 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 4e177

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 87.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+60} \lor \neg \left(\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{+177}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 5: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -2e+53)
     (* a 120.0)
     (if (<= (* a 120.0) -1e-100)
       (+ (* a 120.0) (* 60.0 (/ x z)))
       (if (<= (* a 120.0) 2e-148)
         t_1
         (if (<= (* a 120.0) 5e-125)
           (+ (* a 120.0) (* -60.0 (/ x t)))
           (if (<= (* a 120.0) 1000000.0) t_1 (* a 120.0))))))))

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 ((a * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-2d+53)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-1d-100)) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if ((a * 120.0d0) <= 2d-148) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d-125) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else if ((a * 120.0d0) <= 1000000.0d0) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -2e+53:
		tmp = a * 120.0
	elif (a * 120.0) <= -1e-100:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif (a * 120.0) <= 2e-148:
		tmp = t_1
	elif (a * 120.0) <= 5e-125:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	elif (a * 120.0) <= 1000000.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+53)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -1e-100)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (Float64(a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e-125)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 1000000.0)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	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 ((a * 120.0) <= -2e+53)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -1e-100)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif ((a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e-125)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	elseif ((a * 120.0) <= 1000000.0)
		tmp = t_1;
	else
		tmp = a * 120.0;
	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]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-100], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-148], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-125], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1000000.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -2e53 or 1e6 < (*.f64 a 120)

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 84.2%

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

   if -2e53 < (*.f64 a 120) < -1e-100

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 67.7%

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

   3. Taylor expanded in x around inf 69.5%

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

   if -1e-100 < (*.f64 a 120) < 1.99999999999999987e-148 or 4.99999999999999967e-125 < (*.f64 a 120) < 1e6

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 98.8%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 83.0%

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

   if 1.99999999999999987e-148 < (*.f64 a 120) < 4.99999999999999967e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 88.6%

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

   3. Taylor expanded in x around inf 88.6%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -2e+53)
     (* a 120.0)
     (if (<= (* a 120.0) -1e-100)
       (+ (* a 120.0) (* 60.0 (/ x z)))
       (if (<= (* a 120.0) 2e-152)
         t_1
         (if (<= (* a 120.0) 5e-125)
           (+ (* a 120.0) (* 60.0 (/ y t)))
           (if (<= (* a 120.0) 1000000.0) t_1 (* a 120.0))))))))

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 ((a * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 2e-152) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-2d+53)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-1d-100)) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if ((a * 120.0d0) <= 2d-152) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d-125) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= 1000000.0d0) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 2e-152) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -2e+53:
		tmp = a * 120.0
	elif (a * 120.0) <= -1e-100:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif (a * 120.0) <= 2e-152:
		tmp = t_1
	elif (a * 120.0) <= 5e-125:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= 1000000.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+53)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -1e-100)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (Float64(a * 120.0) <= 2e-152)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e-125)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 1000000.0)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	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 ((a * 120.0) <= -2e+53)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -1e-100)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif ((a * 120.0) <= 2e-152)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e-125)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= 1000000.0)
		tmp = t_1;
	else
		tmp = a * 120.0;
	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]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-100], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-152], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-125], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1000000.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -2e53 or 1e6 < (*.f64 a 120)

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 84.2%

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

   if -2e53 < (*.f64 a 120) < -1e-100

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 67.7%

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

   3. Taylor expanded in x around inf 69.5%

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

   if -1e-100 < (*.f64 a 120) < 2.00000000000000013e-152 or 4.99999999999999967e-125 < (*.f64 a 120) < 1e6

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 98.8%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 82.7%

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

   if 2.00000000000000013e-152 < (*.f64 a 120) < 4.99999999999999967e-125

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 90.8%

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

   3. Taylor expanded in x around 0 94.1%

      \[\leadsto \color{blue}{60 \cdot \frac{y}{t}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-152}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -1e-10)
     (* a 120.0)
     (if (<= (* a 120.0) 2e-148)
       t_1
       (if (<= (* a 120.0) 5e-125)
         (+ (* a 120.0) (* -60.0 (/ x t)))
         (if (<= (* a 120.0) 1000000.0) t_1 (* a 120.0)))))))

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 ((a * 120.0) <= -1e-10) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-1d-10)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d-148) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d-125) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else if ((a * 120.0d0) <= 1000000.0d0) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -1e-10) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -1e-10:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e-148:
		tmp = t_1
	elif (a * 120.0) <= 5e-125:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	elif (a * 120.0) <= 1000000.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-10)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e-125)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 1000000.0)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	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 ((a * 120.0) <= -1e-10)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e-125)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	elseif ((a * 120.0) <= 1000000.0)
		tmp = t_1;
	else
		tmp = a * 120.0;
	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]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-10], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-148], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-125], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1000000.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -1.00000000000000004e-10 or 1e6 < (*.f64 a 120)

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.7%

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

   if -1.00000000000000004e-10 < (*.f64 a 120) < 1.99999999999999987e-148 or 4.99999999999999967e-125 < (*.f64 a 120) < 1e6

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-def 99.0%

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

      3. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 79.6%

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

   if 1.99999999999999987e-148 < (*.f64 a 120) < 4.99999999999999967e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 88.6%

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

   3. Taylor expanded in x around inf 88.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-119} \lor \neg \left(a \leq 10^{-149}\right) \land \left(a \leq 3.3 \cdot 10^{-133} \lor \neg \left(a \leq 6.2 \cdot 10^{-40}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.5e-119)
         (and (not (<= a 1e-149)) (or (<= a 3.3e-133) (not (<= a 6.2e-40)))))
   (* a 120.0)
   (* -60.0 (/ y (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.5e-119) || (!(a <= 1e-149) && ((a <= 3.3e-133) || !(a <= 6.2e-40)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (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) :: tmp
    if ((a <= (-1.5d-119)) .or. (.not. (a <= 1d-149)) .and. (a <= 3.3d-133) .or. (.not. (a <= 6.2d-40))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (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 tmp;
	if ((a <= -1.5e-119) || (!(a <= 1e-149) && ((a <= 3.3e-133) || !(a <= 6.2e-40)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.5e-119) or (not (a <= 1e-149) and ((a <= 3.3e-133) or not (a <= 6.2e-40))):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.5e-119) || (!(a <= 1e-149) && ((a <= 3.3e-133) || !(a <= 6.2e-40))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.5e-119) || (~((a <= 1e-149)) && ((a <= 3.3e-133) || ~((a <= 6.2e-40)))))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.5e-119], And[N[Not[LessEqual[a, 1e-149]], $MachinePrecision], Or[LessEqual[a, 3.3e-133], N[Not[LessEqual[a, 6.2e-40]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5000000000000001e-119 or 9.99999999999999979e-150 < a < 3.30000000000000009e-133 or 6.20000000000000021e-40 < a

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 74.2%

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

   if -1.5000000000000001e-119 < a < 9.99999999999999979e-150 or 3.30000000000000009e-133 < a < 6.20000000000000021e-40

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 88.3%

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

      1. clear-num 88.2%

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

      2. un-div-inv 88.4%

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

   8. Applied egg-rr 88.4%

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

   9. Taylor expanded in x around 0 54.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-119} \lor \neg \left(a \leq 10^{-149}\right) \land \left(a \leq 3.3 \cdot 10^{-133} \lor \neg \left(a \leq 6.2 \cdot 10^{-40}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 9: 57.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-150}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.46 \cdot 10^{-132} \lor \neg \left(a \leq 3.8 \cdot 10^{-38}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.02e-112)
   (* a 120.0)
   (if (<= a 9.4e-150)
     (* -60.0 (/ y (- z t)))
     (if (or (<= a 2.46e-132) (not (<= a 3.8e-38)))
       (* a 120.0)
       (* -60.0 (/ (- x y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.02e-112) {
		tmp = a * 120.0;
	} else if (a <= 9.4e-150) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a <= 2.46e-132) || !(a <= 3.8e-38)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.02d-112)) then
        tmp = a * 120.0d0
    else if (a <= 9.4d-150) then
        tmp = (-60.0d0) * (y / (z - t))
    else if ((a <= 2.46d-132) .or. (.not. (a <= 3.8d-38))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.02e-112) {
		tmp = a * 120.0;
	} else if (a <= 9.4e-150) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a <= 2.46e-132) || !(a <= 3.8e-38)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.02e-112:
		tmp = a * 120.0
	elif a <= 9.4e-150:
		tmp = -60.0 * (y / (z - t))
	elif (a <= 2.46e-132) or not (a <= 3.8e-38):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.02e-112)
		tmp = Float64(a * 120.0);
	elseif (a <= 9.4e-150)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif ((a <= 2.46e-132) || !(a <= 3.8e-38))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.02e-112)
		tmp = a * 120.0;
	elseif (a <= 9.4e-150)
		tmp = -60.0 * (y / (z - t));
	elseif ((a <= 2.46e-132) || ~((a <= 3.8e-38)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.02e-112], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 9.4e-150], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 2.46e-132], N[Not[LessEqual[a, 3.8e-38]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.01999999999999996e-112 or 9.3999999999999998e-150 < a < 2.45999999999999998e-132 or 3.8e-38 < a

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 74.2%

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

   if -1.01999999999999996e-112 < a < 9.3999999999999998e-150

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 89.7%

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

      1. clear-num 89.6%

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

      2. un-div-inv 89.8%

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

   8. Applied egg-rr 89.8%

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

   9. Taylor expanded in x around 0 58.1%

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

   if 2.45999999999999998e-132 < a < 3.8e-38

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-def 99.6%

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

      3. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 84.6%

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

   7. Taylor expanded in z around 0 54.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-150}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.46 \cdot 10^{-132} \lor \neg \left(a \leq 3.8 \cdot 10^{-38}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 10: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-114}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-149}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-132} \lor \neg \left(a \leq 2.1 \cdot 10^{-41}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e-114)
   (* a 120.0)
   (if (<= a 1.25e-149)
     (/ 60.0 (/ (- t z) y))
     (if (or (<= a 5e-132) (not (<= a 2.1e-41)))
       (* a 120.0)
       (* -60.0 (/ (- x y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e-114) {
		tmp = a * 120.0;
	} else if (a <= 1.25e-149) {
		tmp = 60.0 / ((t - z) / y);
	} else if ((a <= 5e-132) || !(a <= 2.1e-41)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.4d-114)) then
        tmp = a * 120.0d0
    else if (a <= 1.25d-149) then
        tmp = 60.0d0 / ((t - z) / y)
    else if ((a <= 5d-132) .or. (.not. (a <= 2.1d-41))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e-114) {
		tmp = a * 120.0;
	} else if (a <= 1.25e-149) {
		tmp = 60.0 / ((t - z) / y);
	} else if ((a <= 5e-132) || !(a <= 2.1e-41)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e-114:
		tmp = a * 120.0
	elif a <= 1.25e-149:
		tmp = 60.0 / ((t - z) / y)
	elif (a <= 5e-132) or not (a <= 2.1e-41):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e-114)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.25e-149)
		tmp = Float64(60.0 / Float64(Float64(t - z) / y));
	elseif ((a <= 5e-132) || !(a <= 2.1e-41))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.4e-114)
		tmp = a * 120.0;
	elseif (a <= 1.25e-149)
		tmp = 60.0 / ((t - z) / y);
	elseif ((a <= 5e-132) || ~((a <= 2.1e-41)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e-114], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.25e-149], N[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 5e-132], N[Not[LessEqual[a, 2.1e-41]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.39999999999999981e-114 or 1.24999999999999992e-149 < a < 4.9999999999999999e-132 or 2.10000000000000013e-41 < a

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 74.2%

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

   if -3.39999999999999981e-114 < a < 1.24999999999999992e-149

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 89.7%

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

      1. clear-num 89.6%

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

      2. un-div-inv 89.8%

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

   8. Applied egg-rr 89.8%

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

   9. Taylor expanded in x around 0 58.1%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{z - t}{y}}} \]
   10. Step-by-step derivation

       1. associate-*r/ 58.1%

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

       2. neg-mul-1 58.1%

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

   11. Simplified 58.1%

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

   if 4.9999999999999999e-132 < a < 2.10000000000000013e-41

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-def 99.6%

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

      3. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 84.6%

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

   7. Taylor expanded in z around 0 54.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-114}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-149}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-132} \lor \neg \left(a \leq 2.1 \cdot 10^{-41}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 11: 87.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+75} \lor \neg \left(x \leq 2.5 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.7e+75) (not (<= x 2.5e+175)))
   (+ (/ (* 60.0 x) (- z t)) (* a 120.0))
   (+ (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.7e+75) || !(x <= 2.5e+175)) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.7d+75)) .or. (.not. (x <= 2.5d+175))) then
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    else
        tmp = ((-60.0d0) * (y / (z - t))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.7e+75) || !(x <= 2.5e+175)) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.7e+75) or not (x <= 2.5e+175):
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	else:
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.7e+75) || !(x <= 2.5e+175))
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(-60.0 * Float64(y / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.7e+75) || ~((x <= 2.5e+175)))
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	else
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.7e+75], N[Not[LessEqual[x, 2.5e+175]], $MachinePrecision]], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.69999999999999984e75 or 2.5e175 < x

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 93.3%

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

      1. associate-*r/ 92.0%

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

   4. Simplified 92.0%

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

   if -4.69999999999999984e75 < x < 2.5e175

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 92.3%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+75} \lor \neg \left(x \leq 2.5 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 12: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-16} \lor \neg \left(a \leq 38000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.25e-16) (not (<= a 38000000.0)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.25e-16) || !(a <= 38000000.0)) {
		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) :: tmp
    if ((a <= (-1.25d-16)) .or. (.not. (a <= 38000000.0d0))) 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 tmp;
	if ((a <= -1.25e-16) || !(a <= 38000000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.25e-16) or not (a <= 38000000.0):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.25e-16) || !(a <= 38000000.0))
		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)
	tmp = 0.0;
	if ((a <= -1.25e-16) || ~((a <= 38000000.0)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.25e-16], N[Not[LessEqual[a, 38000000.0]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2500000000000001e-16 or 3.8e7 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.7%

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

   if -1.2500000000000001e-16 < a < 3.8e7

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-def 99.0%

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

      3. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 76.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-16} \lor \neg \left(a \leq 38000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((x - y) * (60.0 / (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 = ((x - y) * (60.0d0 / (z - t))) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-*l/ 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 14: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((y - x) / ((z - t) * -0.016666666666666666)) + (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 = ((y - x) / ((z - t) * (-0.016666666666666666d0))) + (a * 120.0d0)
end function

Java

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

Python

def code(x, y, z, t, a):
	return ((y - x) / ((z - t) * -0.016666666666666666)) + (a * 120.0)

Julia

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((y - x) / ((z - t) * -0.016666666666666666)) + (a * 120.0);
end

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 99.8%

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

   3. frac-2neg 99.8%

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

   4. distribute-frac-neg 99.8%

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

   5. div-inv 99.8%

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

   6. distribute-rgt-neg-in 99.8%

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

   7. metadata-eval 99.8%

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

   8. metadata-eval 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \frac{y - x}{\left(z - t\right) \cdot -0.016666666666666666} + a \cdot 120 \]

Alternative 15: 52.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-183} \lor \neg \left(a \leq 6.5 \cdot 10^{-206}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e-183) (not (<= a 6.5e-206))) (* a 120.0) (* 60.0 (/ x z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-183) || !(a <= 6.5e-206)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.8d-183)) .or. (.not. (a <= 6.5d-206))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-183) || !(a <= 6.5e-206)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e-183) or not (a <= 6.5e-206):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e-183) || !(a <= 6.5e-206))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e-183) || ~((a <= 6.5e-206)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e-183], N[Not[LessEqual[a, 6.5e-206]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8000000000000001e-183 or 6.4999999999999996e-206 < a

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 61.5%

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

   if -1.8000000000000001e-183 < a < 6.4999999999999996e-206

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 51.6%

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

   3. Taylor expanded in x around inf 25.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-183} \lor \neg \left(a \leq 6.5 \cdot 10^{-206}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 16: 52.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.3 \cdot 10^{-187} \lor \neg \left(a \leq 5.8 \cdot 10^{-207}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.3e-187) (not (<= a 5.8e-207))) (* a 120.0) (* x (/ 60.0 z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.3e-187) || !(a <= 5.8e-207)) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.3d-187)) .or. (.not. (a <= 5.8d-207))) then
        tmp = a * 120.0d0
    else
        tmp = x * (60.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.3e-187) || !(a <= 5.8e-207)) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.3e-187) or not (a <= 5.8e-207):
		tmp = a * 120.0
	else:
		tmp = x * (60.0 / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.3e-187) || !(a <= 5.8e-207))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(60.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.3e-187) || ~((a <= 5.8e-207)))
		tmp = a * 120.0;
	else
		tmp = x * (60.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.3e-187], N[Not[LessEqual[a, 5.8e-207]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.2999999999999995e-187 or 5.80000000000000022e-207 < a

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 61.5%

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

   if -8.2999999999999995e-187 < a < 5.80000000000000022e-207

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 51.6%

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

   3. Taylor expanded in x around inf 28.1%

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

   4. Taylor expanded in x around inf 25.7%

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

      1. associate-*r/ 25.8%

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

      2. associate-*l/ 25.8%

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

   6. Simplified 25.8%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.3 \cdot 10^{-187} \lor \neg \left(a \leq 5.8 \cdot 10^{-207}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \]

Alternative 17: 51.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{+193}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \left(-\frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 9.5e+193) (* a 120.0) (* 60.0 (- (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 9.5e+193) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * -(y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 9.5d+193) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * -(y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 9.5e+193) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * -(y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 9.5e+193:
		tmp = a * 120.0
	else:
		tmp = 60.0 * -(y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 9.5e+193)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(-Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 9.5e+193)
		tmp = a * 120.0;
	else
		tmp = 60.0 * -(y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 9.5e+193], N[(a * 120.0), $MachinePrecision], N[(60.0 * (-N[(y / z), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.4999999999999997e193

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 57.6%

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

   if 9.4999999999999997e193 < y

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 79.4%

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

   7. Taylor expanded in z around inf 45.7%

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

   8. Taylor expanded in x around 0 41.9%

      \[\leadsto 60 \cdot \color{blue}{\left(-1 \cdot \frac{y}{z}\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 41.9%

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

   10. Simplified 41.9%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{+193}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \left(-\frac{y}{z}\right)\\ \end{array} \]

Alternative 18: 50.7% accurate, 4.3× 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 99.4%

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

2. Taylor expanded in z around inf 52.8%

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

3. Final simplification 52.8%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% accurate, 1.0× 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 2023336 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))