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

Percentage Accurate: 99.4% → 99.8%

Time: 16.9s

Alternatives: 16

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: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

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(Float64(60.0 / Float64(z - t)) * Float64(x - y)))
end

Wolfram

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

Derivation

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 99.8%

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

   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%

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

Alternative 2: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.05:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 200000000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+73}:\\ \;\;\;\;a \cdot 120 - x \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -0.05)
   (- (* a 120.0) (* 60.0 (/ x t)))
   (if (<= (* a 120.0) 200000000.0)
     (* (/ 60.0 (- z t)) (- x y))
     (if (<= (* a 120.0) 1e+73)
       (- (* a 120.0) (* x (/ -60.0 z)))
       (+ (* a 120.0) (* y (/ 60.0 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -0.05) {
		tmp = (a * 120.0) - (60.0 * (x / t));
	} else if ((a * 120.0) <= 200000000.0) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((a * 120.0) <= 1e+73) {
		tmp = (a * 120.0) - (x * (-60.0 / z));
	} else {
		tmp = (a * 120.0) + (y * (60.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-0.05d0)) then
        tmp = (a * 120.0d0) - (60.0d0 * (x / t))
    else if ((a * 120.0d0) <= 200000000.0d0) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else if ((a * 120.0d0) <= 1d+73) then
        tmp = (a * 120.0d0) - (x * ((-60.0d0) / z))
    else
        tmp = (a * 120.0d0) + (y * (60.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -0.05) {
		tmp = (a * 120.0) - (60.0 * (x / t));
	} else if ((a * 120.0) <= 200000000.0) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((a * 120.0) <= 1e+73) {
		tmp = (a * 120.0) - (x * (-60.0 / z));
	} else {
		tmp = (a * 120.0) + (y * (60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -0.05:
		tmp = (a * 120.0) - (60.0 * (x / t))
	elif (a * 120.0) <= 200000000.0:
		tmp = (60.0 / (z - t)) * (x - y)
	elif (a * 120.0) <= 1e+73:
		tmp = (a * 120.0) - (x * (-60.0 / z))
	else:
		tmp = (a * 120.0) + (y * (60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -0.05)
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 200000000.0)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (Float64(a * 120.0) <= 1e+73)
		tmp = Float64(Float64(a * 120.0) - Float64(x * Float64(-60.0 / z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -0.05)
		tmp = (a * 120.0) - (60.0 * (x / t));
	elseif ((a * 120.0) <= 200000000.0)
		tmp = (60.0 / (z - t)) * (x - y);
	elseif ((a * 120.0) <= 1e+73)
		tmp = (a * 120.0) - (x * (-60.0 / z));
	else
		tmp = (a * 120.0) + (y * (60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -0.05], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 200000000.0], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+73], N[(N[(a * 120.0), $MachinePrecision] - N[(x * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -0.050000000000000003

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      3. frac-2neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. div-inv 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 78.0%

      \[\leadsto \left(-\frac{x - y}{\color{blue}{0.016666666666666666 \cdot t}}\right) + a \cdot 120 \]
   5. Step-by-step derivation

      1. *-commutative 78.0%

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

   6. Simplified 78.0%

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

   7. Taylor expanded in y around 0 81.2%

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

   if -0.050000000000000003 < (*.f64 a 120) < 2e8

   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%

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

      2. associate-/l* 99.6%

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

      3. frac-2neg 99.6%

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

      4. distribute-frac-neg 99.6%

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

      5. div-inv 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]
   4. Step-by-step derivation

      1. +-commutative 99.6%

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

      2. unsub-neg 99.6%

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

      3. div-inv 99.5%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 76.2%

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

      1. associate-*r/ 76.2%

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

      2. associate-/l* 76.3%

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

      3. associate-/r/ 76.3%

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

   8. Simplified 76.3%

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

   if 2e8 < (*.f64 a 120) < 9.99999999999999983e72

   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%

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

      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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. unsub-neg 99.8%

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

      3. div-inv 100.0%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 100.0%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.9%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 93.3%

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

   7. Taylor expanded in x around inf 93.6%

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

      1. associate-*r/ 93.3%

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

      2. associate-*l/ 93.6%

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

      3. *-commutative 93.6%

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

   9. Simplified 93.6%

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

   if 9.99999999999999983e72 < (*.f64 a 120)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.4%

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

      1. associate-*r/ 95.4%

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

   4. Simplified 95.4%

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

   5. Taylor expanded in z around 0 84.1%

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

      1. associate-*r/ 84.2%

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

      2. metadata-eval 84.2%

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

      3. distribute-lft-neg-in 84.2%

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

      4. *-commutative 84.2%

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

      5. distribute-neg-frac 84.2%

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

      6. associate-*r/ 84.2%

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

      7. distribute-rgt-neg-in 84.2%

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

      8. distribute-neg-frac 84.2%

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

      9. metadata-eval 84.2%

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

   7. Simplified 84.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.05:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 200000000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+73}:\\ \;\;\;\;a \cdot 120 - x \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t}\\ \end{array} \]

Alternative 3: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.05:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 200000000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+73}:\\ \;\;\;\;a \cdot 120 - x \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -0.05)
   (- (* a 120.0) (* 60.0 (/ x t)))
   (if (<= (* a 120.0) 200000000.0)
     (/ 60.0 (/ (- z t) (- x y)))
     (if (<= (* a 120.0) 1e+73)
       (- (* a 120.0) (* x (/ -60.0 z)))
       (+ (* a 120.0) (* y (/ 60.0 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -0.05) {
		tmp = (a * 120.0) - (60.0 * (x / t));
	} else if ((a * 120.0) <= 200000000.0) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((a * 120.0) <= 1e+73) {
		tmp = (a * 120.0) - (x * (-60.0 / z));
	} else {
		tmp = (a * 120.0) + (y * (60.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-0.05d0)) then
        tmp = (a * 120.0d0) - (60.0d0 * (x / t))
    else if ((a * 120.0d0) <= 200000000.0d0) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if ((a * 120.0d0) <= 1d+73) then
        tmp = (a * 120.0d0) - (x * ((-60.0d0) / z))
    else
        tmp = (a * 120.0d0) + (y * (60.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -0.05) {
		tmp = (a * 120.0) - (60.0 * (x / t));
	} else if ((a * 120.0) <= 200000000.0) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((a * 120.0) <= 1e+73) {
		tmp = (a * 120.0) - (x * (-60.0 / z));
	} else {
		tmp = (a * 120.0) + (y * (60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -0.05:
		tmp = (a * 120.0) - (60.0 * (x / t))
	elif (a * 120.0) <= 200000000.0:
		tmp = 60.0 / ((z - t) / (x - y))
	elif (a * 120.0) <= 1e+73:
		tmp = (a * 120.0) - (x * (-60.0 / z))
	else:
		tmp = (a * 120.0) + (y * (60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -0.05)
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 200000000.0)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (Float64(a * 120.0) <= 1e+73)
		tmp = Float64(Float64(a * 120.0) - Float64(x * Float64(-60.0 / z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -0.05)
		tmp = (a * 120.0) - (60.0 * (x / t));
	elseif ((a * 120.0) <= 200000000.0)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif ((a * 120.0) <= 1e+73)
		tmp = (a * 120.0) - (x * (-60.0 / z));
	else
		tmp = (a * 120.0) + (y * (60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -0.05], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 200000000.0], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+73], N[(N[(a * 120.0), $MachinePrecision] - N[(x * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -0.050000000000000003

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      3. frac-2neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. div-inv 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 78.0%

      \[\leadsto \left(-\frac{x - y}{\color{blue}{0.016666666666666666 \cdot t}}\right) + a \cdot 120 \]
   5. Step-by-step derivation

      1. *-commutative 78.0%

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

   6. Simplified 78.0%

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

   7. Taylor expanded in y around 0 81.2%

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

   if -0.050000000000000003 < (*.f64 a 120) < 2e8

   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/ 99.7%

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

   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 76.2%

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

      1. clear-num 76.1%

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

      2. un-div-inv 76.3%

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

   8. Applied egg-rr 76.3%

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

   if 2e8 < (*.f64 a 120) < 9.99999999999999983e72

   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%

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

      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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. unsub-neg 99.8%

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

      3. div-inv 100.0%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 100.0%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.9%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 93.3%

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

   7. Taylor expanded in x around inf 93.6%

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

      1. associate-*r/ 93.3%

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

      2. associate-*l/ 93.6%

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

      3. *-commutative 93.6%

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

   9. Simplified 93.6%

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

   if 9.99999999999999983e72 < (*.f64 a 120)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.4%

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

      1. associate-*r/ 95.4%

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

   4. Simplified 95.4%

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

   5. Taylor expanded in z around 0 84.1%

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

      1. associate-*r/ 84.2%

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

      2. metadata-eval 84.2%

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

      3. distribute-lft-neg-in 84.2%

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

      4. *-commutative 84.2%

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

      5. distribute-neg-frac 84.2%

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

      6. associate-*r/ 84.2%

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

      7. distribute-rgt-neg-in 84.2%

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

      8. distribute-neg-frac 84.2%

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

      9. metadata-eval 84.2%

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

   7. Simplified 84.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.05:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 200000000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+73}:\\ \;\;\;\;a \cdot 120 - x \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t}\\ \end{array} \]

Alternative 4: 58.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ t_2 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -8.4 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 900:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ (- x y) t))) (t_2 (* 60.0 (/ (- x y) z))))
   (if (<= a -8.4e-10)
     (* a 120.0)
     (if (<= a -1.85e-271)
       t_2
       (if (<= a 3.8e-205)
         t_1
         (if (<= a 6e-168)
           t_2
           (if (<= a 4.2e-55) t_1 (if (<= a 900.0) t_2 (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double t_2 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -8.4e-10) {
		tmp = a * 120.0;
	} else if (a <= -1.85e-271) {
		tmp = t_2;
	} else if (a <= 3.8e-205) {
		tmp = t_1;
	} else if (a <= 6e-168) {
		tmp = t_2;
	} else if (a <= 4.2e-55) {
		tmp = t_1;
	} else if (a <= 900.0) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * ((x - y) / t)
    t_2 = 60.0d0 * ((x - y) / z)
    if (a <= (-8.4d-10)) then
        tmp = a * 120.0d0
    else if (a <= (-1.85d-271)) then
        tmp = t_2
    else if (a <= 3.8d-205) then
        tmp = t_1
    else if (a <= 6d-168) then
        tmp = t_2
    else if (a <= 4.2d-55) then
        tmp = t_1
    else if (a <= 900.0d0) then
        tmp = t_2
    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) / t);
	double t_2 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -8.4e-10) {
		tmp = a * 120.0;
	} else if (a <= -1.85e-271) {
		tmp = t_2;
	} else if (a <= 3.8e-205) {
		tmp = t_1;
	} else if (a <= 6e-168) {
		tmp = t_2;
	} else if (a <= 4.2e-55) {
		tmp = t_1;
	} else if (a <= 900.0) {
		tmp = t_2;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * ((x - y) / t)
	t_2 = 60.0 * ((x - y) / z)
	tmp = 0
	if a <= -8.4e-10:
		tmp = a * 120.0
	elif a <= -1.85e-271:
		tmp = t_2
	elif a <= 3.8e-205:
		tmp = t_1
	elif a <= 6e-168:
		tmp = t_2
	elif a <= 4.2e-55:
		tmp = t_1
	elif a <= 900.0:
		tmp = t_2
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(Float64(x - y) / t))
	t_2 = Float64(60.0 * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (a <= -8.4e-10)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.85e-271)
		tmp = t_2;
	elseif (a <= 3.8e-205)
		tmp = t_1;
	elseif (a <= 6e-168)
		tmp = t_2;
	elseif (a <= 4.2e-55)
		tmp = t_1;
	elseif (a <= 900.0)
		tmp = t_2;
	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) / t);
	t_2 = 60.0 * ((x - y) / z);
	tmp = 0.0;
	if (a <= -8.4e-10)
		tmp = a * 120.0;
	elseif (a <= -1.85e-271)
		tmp = t_2;
	elseif (a <= 3.8e-205)
		tmp = t_1;
	elseif (a <= 6e-168)
		tmp = t_2;
	elseif (a <= 4.2e-55)
		tmp = t_1;
	elseif (a <= 900.0)
		tmp = t_2;
	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] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.4e-10], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.85e-271], t$95$2, If[LessEqual[a, 3.8e-205], t$95$1, If[LessEqual[a, 6e-168], t$95$2, If[LessEqual[a, 4.2e-55], t$95$1, If[LessEqual[a, 900.0], t$95$2, N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.3999999999999999e-10 or 900 < 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 79.5%

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

   if -8.3999999999999999e-10 < a < -1.85000000000000011e-271 or 3.79999999999999992e-205 < a < 5.99999999999999983e-168 or 4.2000000000000003e-55 < a < 900

   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/ 99.7%

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

   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 78.5%

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

   7. Taylor expanded in z around inf 56.3%

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

   if -1.85000000000000011e-271 < a < 3.79999999999999992e-205 or 5.99999999999999983e-168 < a < 4.2000000000000003e-55

   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 99.7%

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

      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 72.5%

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

   7. Taylor expanded in z around 0 50.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-271}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-205}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-168}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-55}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 900:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -3.85 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-136}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-225}:\\ \;\;\;\;a \cdot 120 - x \cdot \frac{-60}{z}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 - \frac{60 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ (- x y) t)))))
   (if (<= t -3.85e+62)
     t_1
     (if (<= t -3.7e-136)
       (/ 60.0 (/ (- z t) (- x y)))
       (if (<= t 1.15e-225)
         (- (* a 120.0) (* x (/ -60.0 z)))
         (if (<= t 4.2e-48) (- (* a 120.0) (/ (* 60.0 y) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * ((x - y) / t));
	double tmp;
	if (t <= -3.85e+62) {
		tmp = t_1;
	} else if (t <= -3.7e-136) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t <= 1.15e-225) {
		tmp = (a * 120.0) - (x * (-60.0 / z));
	} else if (t <= 4.2e-48) {
		tmp = (a * 120.0) - ((60.0 * y) / z);
	} 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 = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    if (t <= (-3.85d+62)) then
        tmp = t_1
    else if (t <= (-3.7d-136)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (t <= 1.15d-225) then
        tmp = (a * 120.0d0) - (x * ((-60.0d0) / z))
    else if (t <= 4.2d-48) then
        tmp = (a * 120.0d0) - ((60.0d0 * y) / z)
    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 = (a * 120.0) + (-60.0 * ((x - y) / t));
	double tmp;
	if (t <= -3.85e+62) {
		tmp = t_1;
	} else if (t <= -3.7e-136) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t <= 1.15e-225) {
		tmp = (a * 120.0) - (x * (-60.0 / z));
	} else if (t <= 4.2e-48) {
		tmp = (a * 120.0) - ((60.0 * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * ((x - y) / t))
	tmp = 0
	if t <= -3.85e+62:
		tmp = t_1
	elif t <= -3.7e-136:
		tmp = 60.0 / ((z - t) / (x - y))
	elif t <= 1.15e-225:
		tmp = (a * 120.0) - (x * (-60.0 / z))
	elif t <= 4.2e-48:
		tmp = (a * 120.0) - ((60.0 * y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -3.85e+62)
		tmp = t_1;
	elseif (t <= -3.7e-136)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (t <= 1.15e-225)
		tmp = Float64(Float64(a * 120.0) - Float64(x * Float64(-60.0 / z)));
	elseif (t <= 4.2e-48)
		tmp = Float64(Float64(a * 120.0) - Float64(Float64(60.0 * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * ((x - y) / t));
	tmp = 0.0;
	if (t <= -3.85e+62)
		tmp = t_1;
	elseif (t <= -3.7e-136)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (t <= 1.15e-225)
		tmp = (a * 120.0) - (x * (-60.0 / z));
	elseif (t <= 4.2e-48)
		tmp = (a * 120.0) - ((60.0 * y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.85e+62], t$95$1, If[LessEqual[t, -3.7e-136], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-225], N[(N[(a * 120.0), $MachinePrecision] - N[(x * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-48], N[(N[(a * 120.0), $MachinePrecision] - N[(N[(60.0 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.8500000000000001e62 or 4.19999999999999977e-48 < t

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 88.2%

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

   if -3.8500000000000001e62 < t < -3.7e-136

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      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/ 99.7%

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

   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 73.7%

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

      1. clear-num 73.7%

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

      2. un-div-inv 73.9%

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

   8. Applied egg-rr 73.9%

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

   if -3.7e-136 < t < 1.1499999999999999e-225

   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%

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

      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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. unsub-neg 99.8%

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

      3. div-inv 99.7%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 92.6%

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

   7. Taylor expanded in x around inf 76.6%

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

      1. associate-*r/ 76.6%

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

      2. associate-*l/ 76.6%

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

      3. *-commutative 76.6%

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

   9. Simplified 76.6%

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

   if 1.1499999999999999e-225 < t < 4.19999999999999977e-48

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.7%

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

      3. frac-2neg 99.7%

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

      4. distribute-frac-neg 99.7%

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

      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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. unsub-neg 99.8%

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

      3. div-inv 99.7%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 89.0%

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

   7. Taylor expanded in x around 0 81.7%

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

      1. associate-*r/ 81.9%

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

   9. Simplified 81.9%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.85 \cdot 10^{+62}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-136}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-225}:\\ \;\;\;\;a \cdot 120 - x \cdot \frac{-60}{z}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 - \frac{60 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 6: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-35}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+119}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ (- x y) z)))))
   (if (<= z -9.6e-135)
     t_1
     (if (<= z 1e-35)
       (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
       (if (<= z 2.5e+119) (+ (* a 120.0) (* y (/ -60.0 (- z t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	double tmp;
	if (z <= -9.6e-135) {
		tmp = t_1;
	} else if (z <= 1e-35) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else if (z <= 2.5e+119) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - 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) :: tmp
    t_1 = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    if (z <= (-9.6d-135)) then
        tmp = t_1
    else if (z <= 1d-35) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else if (z <= 2.5d+119) then
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (z - 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 = (a * 120.0) + (60.0 * ((x - y) / z));
	double tmp;
	if (z <= -9.6e-135) {
		tmp = t_1;
	} else if (z <= 1e-35) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else if (z <= 2.5e+119) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * ((x - y) / z))
	tmp = 0
	if z <= -9.6e-135:
		tmp = t_1
	elif z <= 1e-35:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	elif z <= 2.5e+119:
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)))
	tmp = 0.0
	if (z <= -9.6e-135)
		tmp = t_1;
	elseif (z <= 1e-35)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	elseif (z <= 2.5e+119)
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	tmp = 0.0;
	if (z <= -9.6e-135)
		tmp = t_1;
	elseif (z <= 1e-35)
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	elseif (z <= 2.5e+119)
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e-135], t$95$1, If[LessEqual[z, 1e-35], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+119], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5999999999999994e-135 or 2.5e119 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 85.2%

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

   if -9.5999999999999994e-135 < z < 1.00000000000000001e-35

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 90.7%

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

   if 1.00000000000000001e-35 < z < 2.5e119

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 82.7%

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

      1. associate-*r/ 82.6%

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

   4. Simplified 82.6%

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

      1. associate-/l* 82.6%

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

      2. associate-/r/ 82.6%

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

   6. Applied egg-rr 82.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-135}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 10^{-35}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+119}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 7: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.05 \lor \neg \left(a \cdot 120 \leq 200000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -0.05) (not (<= (* a 120.0) 200000000.0)))
   (* a 120.0)
   (* (/ 60.0 (- z t)) (- x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -0.05) || !((a * 120.0) <= 200000000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-0.05d0)) .or. (.not. ((a * 120.0d0) <= 200000000.0d0))) then
        tmp = a * 120.0d0
    else
        tmp = (60.0d0 / (z - t)) * (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -0.05) || !((a * 120.0) <= 200000000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -0.05) or not ((a * 120.0) <= 200000000.0):
		tmp = a * 120.0
	else:
		tmp = (60.0 / (z - t)) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -0.05) || !(Float64(a * 120.0) <= 200000000.0))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -0.05) || ~(((a * 120.0) <= 200000000.0)))
		tmp = a * 120.0;
	else
		tmp = (60.0 / (z - t)) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -0.05], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 200000000.0]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -0.050000000000000003 or 2e8 < (*.f64 a 120)

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 80.1%

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

   if -0.050000000000000003 < (*.f64 a 120) < 2e8

   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%

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

      2. associate-/l* 99.6%

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

      3. frac-2neg 99.6%

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

      4. distribute-frac-neg 99.6%

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

      5. div-inv 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]
   4. Step-by-step derivation

      1. +-commutative 99.6%

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

      2. unsub-neg 99.6%

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

      3. div-inv 99.5%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 76.2%

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

      1. associate-*r/ 76.2%

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

      2. associate-/l* 76.3%

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

      3. associate-/r/ 76.3%

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

   8. Simplified 76.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.05 \lor \neg \left(a \cdot 120 \leq 200000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 8: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.05:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 200000000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -0.05)
   (- (* a 120.0) (* 60.0 (/ x t)))
   (if (<= (* a 120.0) 200000000.0) (* (/ 60.0 (- z t)) (- x y)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -0.05) {
		tmp = (a * 120.0) - (60.0 * (x / t));
	} else if ((a * 120.0) <= 200000000.0) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-0.05d0)) then
        tmp = (a * 120.0d0) - (60.0d0 * (x / t))
    else if ((a * 120.0d0) <= 200000000.0d0) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -0.05) {
		tmp = (a * 120.0) - (60.0 * (x / t));
	} else if ((a * 120.0) <= 200000000.0) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -0.05:
		tmp = (a * 120.0) - (60.0 * (x / t))
	elif (a * 120.0) <= 200000000.0:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -0.05)
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 200000000.0)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -0.05)
		tmp = (a * 120.0) - (60.0 * (x / t));
	elseif ((a * 120.0) <= 200000000.0)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -0.05], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 200000000.0], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -0.050000000000000003

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      3. frac-2neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. div-inv 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 78.0%

      \[\leadsto \left(-\frac{x - y}{\color{blue}{0.016666666666666666 \cdot t}}\right) + a \cdot 120 \]
   5. Step-by-step derivation

      1. *-commutative 78.0%

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

   6. Simplified 78.0%

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

   7. Taylor expanded in y around 0 81.2%

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

   if -0.050000000000000003 < (*.f64 a 120) < 2e8

   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%

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

      2. associate-/l* 99.6%

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

      3. frac-2neg 99.6%

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

      4. distribute-frac-neg 99.6%

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

      5. div-inv 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]
   4. Step-by-step derivation

      1. +-commutative 99.6%

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

      2. unsub-neg 99.6%

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

      3. div-inv 99.5%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 76.2%

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

      1. associate-*r/ 76.2%

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

      2. associate-/l* 76.3%

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

      3. associate-/r/ 76.3%

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

   8. Simplified 76.3%

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

   if 2e8 < (*.f64 a 120)

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 79.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.05:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 200000000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 57.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 35000:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -4.4e+112)
     t_1
     (if (<= y 7.2e-46)
       (* a 120.0)
       (if (<= y 35000.0)
         (* (/ 60.0 (- z t)) x)
         (if (<= y 4.6e+200) (* 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 tmp;
	if (y <= -4.4e+112) {
		tmp = t_1;
	} else if (y <= 7.2e-46) {
		tmp = a * 120.0;
	} else if (y <= 35000.0) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 4.6e+200) {
		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) * (y / (z - t))
    if (y <= (-4.4d+112)) then
        tmp = t_1
    else if (y <= 7.2d-46) then
        tmp = a * 120.0d0
    else if (y <= 35000.0d0) then
        tmp = (60.0d0 / (z - t)) * x
    else if (y <= 4.6d+200) 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 tmp;
	if (y <= -4.4e+112) {
		tmp = t_1;
	} else if (y <= 7.2e-46) {
		tmp = a * 120.0;
	} else if (y <= 35000.0) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 4.6e+200) {
		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))
	tmp = 0
	if y <= -4.4e+112:
		tmp = t_1
	elif y <= 7.2e-46:
		tmp = a * 120.0
	elif y <= 35000.0:
		tmp = (60.0 / (z - t)) * x
	elif y <= 4.6e+200:
		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)))
	tmp = 0.0
	if (y <= -4.4e+112)
		tmp = t_1;
	elseif (y <= 7.2e-46)
		tmp = Float64(a * 120.0);
	elseif (y <= 35000.0)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (y <= 4.6e+200)
		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));
	tmp = 0.0;
	if (y <= -4.4e+112)
		tmp = t_1;
	elseif (y <= 7.2e-46)
		tmp = a * 120.0;
	elseif (y <= 35000.0)
		tmp = (60.0 / (z - t)) * x;
	elseif (y <= 4.6e+200)
		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]}, If[LessEqual[y, -4.4e+112], t$95$1, If[LessEqual[y, 7.2e-46], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 35000.0], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 4.6e+200], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3999999999999999e112 or 4.60000000000000006e200 < 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%

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

      2. associate-/l* 99.7%

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

      3. frac-2neg 99.7%

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

      4. distribute-frac-neg 99.7%

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

      5. div-inv 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. metadata-eval 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]
   4. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-inv 99.6%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.6%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 65.8%

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

      1. *-commutative 65.8%

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

   8. Simplified 65.8%

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

   if -4.3999999999999999e112 < y < 7.2e-46 or 35000 < y < 4.60000000000000006e200

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 62.5%

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

   if 7.2e-46 < y < 35000

   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* 99.1%

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

      3. frac-2neg 99.1%

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

      4. distribute-frac-neg 99.1%

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

      5. div-inv 99.3%

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

      6. distribute-rgt-neg-in 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]
   4. Step-by-step derivation

      1. +-commutative 99.3%

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

      2. unsub-neg 99.3%

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

      3. div-inv 99.7%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 74.1%

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

      1. associate-*r/ 74.2%

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

   8. Simplified 74.2%

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

      1. associate-/l* 74.5%

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

      2. associate-/r/ 74.5%

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

   10. Applied egg-rr 74.5%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+112}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 35000:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 10: 80.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-135} \lor \neg \left(z \leq 2.35 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.6e-135) (not (<= z 2.35e+119)))
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))
   (+ (* a 120.0) (* -60.0 (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.6e-135) || !(z <= 2.35e+119)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (-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 ((z <= (-9.6d-135)) .or. (.not. (z <= 2.35d+119))) then
        tmp = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    else
        tmp = (a * 120.0d0) + ((-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 ((z <= -9.6e-135) || !(z <= 2.35e+119)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.6e-135) or not (z <= 2.35e+119):
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	else:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.6e-135) || !(z <= 2.35e+119))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)));
	else
		tmp = Float64(Float64(a * 120.0) + 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 ((z <= -9.6e-135) || ~((z <= 2.35e+119)))
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	else
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.6e-135], N[Not[LessEqual[z, 2.35e+119]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5999999999999994e-135 or 2.35000000000000004e119 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 85.2%

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

   if -9.5999999999999994e-135 < z < 2.35000000000000004e119

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 85.4%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-135} \lor \neg \left(z \leq 2.35 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 11: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+78} \lor \neg \left(x \leq 145000\right):\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.52e+78) (not (<= x 145000.0)))
   (+ (* a 120.0) (/ (* 60.0 x) (- z t)))
   (+ (* a 120.0) (* y (/ -60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.52e+78) || !(x <= 145000.0)) {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (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 ((x <= (-1.52d+78)) .or. (.not. (x <= 145000.0d0))) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (z - t))
    else
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (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 ((x <= -1.52e+78) || !(x <= 145000.0)) {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.52e+78) or not (x <= 145000.0):
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	else:
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.52e+78) || !(x <= 145000.0))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.52e+78) || ~((x <= 145000.0)))
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	else
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.52e+78], N[Not[LessEqual[x, 145000.0]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.52e78 or 145000 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 89.1%

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

      1. associate-*r/ 89.2%

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

   4. Simplified 89.2%

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

   if -1.52e78 < x < 145000

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 95.9%

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

      1. associate-*r/ 95.9%

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

   4. Simplified 95.9%

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

      1. associate-/l* 95.9%

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

      2. associate-/r/ 95.9%

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

   6. Applied egg-rr 95.9%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+78} \lor \neg \left(x \leq 145000\right):\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \]

Alternative 12: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-9} \lor \neg \left(a \leq 600000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.35e-9) (not (<= a 600000000.0)))
   (* 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 <= -1.35e-9) || !(a <= 600000000.0)) {
		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 <= (-1.35d-9)) .or. (.not. (a <= 600000000.0d0))) 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 <= -1.35e-9) || !(a <= 600000000.0)) {
		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 <= -1.35e-9) or not (a <= 600000000.0):
		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 <= -1.35e-9) || !(a <= 600000000.0))
		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 <= -1.35e-9) || ~((a <= 600000000.0)))
		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, -1.35e-9], N[Not[LessEqual[a, 600000000.0]], $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 < -1.3500000000000001e-9 or 6e8 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 80.1%

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

   if -1.3500000000000001e-9 < a < 6e8

   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/ 99.7%

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

   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 76.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-9} \lor \neg \left(a \leq 600000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

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(Float64(60.0 / 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[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

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

Alternative 14: 58.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-114} \lor \neg \left(a \leq 950000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.55e-114) (not (<= a 950000.0)))
   (* 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 <= -1.55e-114) || !(a <= 950000.0)) {
		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 <= (-1.55d-114)) .or. (.not. (a <= 950000.0d0))) 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 <= -1.55e-114) || !(a <= 950000.0)) {
		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 <= -1.55e-114) or not (a <= 950000.0):
		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 <= -1.55e-114) || !(a <= 950000.0))
		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 <= -1.55e-114) || ~((a <= 950000.0)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.55e-114], N[Not[LessEqual[a, 950000.0]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e-114 or 9.5e5 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 74.2%

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

   if -1.55e-114 < a < 9.5e5

   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/ 99.7%

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

   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 78.1%

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

   7. Taylor expanded in z around 0 39.1%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-114} \lor \neg \left(a \leq 950000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 15: 52.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+243}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1e+243) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1e+243) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / 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 (x <= 1d+243) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / 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 (x <= 1e+243) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1e+243:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 1e+243)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 1e+243)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 1e+243], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.0000000000000001e243

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 53.4%

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

   if 1.0000000000000001e243 < x

   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* 99.5%

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

      3. frac-2neg 99.5%

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

      4. distribute-frac-neg 99.5%

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

      5. div-inv 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 71.2%

      \[\leadsto \left(-\frac{x - y}{\color{blue}{0.016666666666666666 \cdot t}}\right) + a \cdot 120 \]
   5. Step-by-step derivation

      1. *-commutative 71.2%

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

   6. Simplified 71.2%

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

   7. Taylor expanded in x around inf 54.3%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+243}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 16: 51.4% 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 99.7%

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

2. Taylor expanded in z around inf 51.5%

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

3. Final simplification 51.5%

   \[\leadsto a \cdot 120 \]

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 2023306 
(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)))