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

Percentage Accurate: 99.3% → 99.3%

Time: 12.9s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

Alternative 2: 71.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+55}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ y z)))))
   (if (<= (* a 120.0) -2e+175)
     t_1
     (if (<= (* a 120.0) -2e+55)
       (+ (* a 120.0) (* x (/ -60.0 t)))
       (if (<= (* a 120.0) -1e-32)
         (+ (* a 120.0) (* 60.0 (/ y t)))
         (if (<= (* a 120.0) 5e-106)
           (* (- x y) (/ 60.0 (- z t)))
           (if (<= (* a 120.0) 2e+139)
             t_1
             (+ (* a 120.0) (/ (* 60.0 x) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if ((a * 120.0) <= -2e+175) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e+55) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= -1e-32) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-106) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 2e+139) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((-60.0d0) * (y / z))
    if ((a * 120.0d0) <= (-2d+175)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-2d+55)) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else if ((a * 120.0d0) <= (-1d-32)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= 5d-106) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if ((a * 120.0d0) <= 2d+139) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if ((a * 120.0) <= -2e+175) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e+55) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= -1e-32) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-106) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 2e+139) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (y / z))
	tmp = 0
	if (a * 120.0) <= -2e+175:
		tmp = t_1
	elif (a * 120.0) <= -2e+55:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	elif (a * 120.0) <= -1e-32:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= 5e-106:
		tmp = (x - y) * (60.0 / (z - t))
	elif (a * 120.0) <= 2e+139:
		tmp = t_1
	else:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+175)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -2e+55)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	elseif (Float64(a * 120.0) <= -1e-32)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 5e-106)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 2e+139)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * (y / z));
	tmp = 0.0;
	if ((a * 120.0) <= -2e+175)
		tmp = t_1;
	elseif ((a * 120.0) <= -2e+55)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	elseif ((a * 120.0) <= -1e-32)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= 5e-106)
		tmp = (x - y) * (60.0 / (z - t));
	elseif ((a * 120.0) <= 2e+139)
		tmp = t_1;
	else
		tmp = (a * 120.0) + ((60.0 * x) / z);
	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[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+175], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+55], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-32], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-106], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+139], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.9999999999999999e175 or 4.99999999999999983e-106 < (*.f64 a #s(literal 120 binary64)) < 2.00000000000000007e139

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 90.5%

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

      1. associate-*r/ 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in z around inf 77.3%

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

   if -1.9999999999999999e175 < (*.f64 a #s(literal 120 binary64)) < -2.00000000000000002e55

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 84.6%

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

   6. Taylor expanded in x around inf 93.8%

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

      1. associate-*r/ 93.8%

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

      2. associate-*l/ 93.8%

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

      3. *-commutative 93.8%

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

   8. Simplified 93.8%

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

   if -2.00000000000000002e55 < (*.f64 a #s(literal 120 binary64)) < -1.00000000000000006e-32

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 78.6%

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

   6. Taylor expanded in x around 0 78.7%

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

   if -1.00000000000000006e-32 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999983e-106

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 97.8%

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

      1. associate-*r/ 97.9%

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

      2. remove-double-neg 97.9%

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

      3. neg-mul-1 97.9%

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

      4. times-frac 97.8%

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

      5. metadata-eval 97.8%

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

      6. distribute-neg-frac2 97.8%

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

      7. distribute-lft-in 97.8%

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

      8. +-commutative 97.8%

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

      9. sub-neg 97.8%

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

      10. div-sub 99.7%

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

      11. associate-*r/ 99.8%

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

      12. associate-*l/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in a around 0 82.0%

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

      1. metadata-eval 82.0%

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

      2. times-frac 82.0%

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

      3. *-commutative 82.0%

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

      4. neg-mul-1 82.0%

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

      5. associate-/l* 82.0%

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

      6. distribute-neg-frac2 82.0%

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

      7. distribute-neg-frac 82.0%

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

      8. metadata-eval 82.0%

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

   10. Simplified 82.0%

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

   if 2.00000000000000007e139 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 94.7%

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

      1. associate-*r/ 94.7%

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

   7. Simplified 94.7%

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

   8. Taylor expanded in z around inf 82.9%

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

      1. associate-*r/ 82.9%

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

      2. *-commutative 82.9%

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

   10. Simplified 82.9%

       \[\leadsto \color{blue}{\frac{x \cdot 60}{z}} + a \cdot 120 \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+175}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+55}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+139}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + x \cdot \frac{-60}{t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+175}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* x (/ -60.0 t))))
        (t_2 (+ (* a 120.0) (* -60.0 (/ y z)))))
   (if (<= (* a 120.0) -2e+175)
     t_2
     (if (<= (* a 120.0) -2e+55)
       t_1
       (if (<= (* a 120.0) -1e-32)
         (+ (* a 120.0) (* 60.0 (/ y t)))
         (if (<= (* a 120.0) 5e-106)
           (* (- x y) (/ 60.0 (- z t)))
           (if (<= (* a 120.0) 2e+126) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (-60.0 / t));
	double t_2 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if ((a * 120.0) <= -2e+175) {
		tmp = t_2;
	} else if ((a * 120.0) <= -2e+55) {
		tmp = t_1;
	} else if ((a * 120.0) <= -1e-32) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-106) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 2e+126) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (x * ((-60.0d0) / t))
    t_2 = (a * 120.0d0) + ((-60.0d0) * (y / z))
    if ((a * 120.0d0) <= (-2d+175)) then
        tmp = t_2
    else if ((a * 120.0d0) <= (-2d+55)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-1d-32)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= 5d-106) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if ((a * 120.0d0) <= 2d+126) then
        tmp = t_2
    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) + (x * (-60.0 / t));
	double t_2 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if ((a * 120.0) <= -2e+175) {
		tmp = t_2;
	} else if ((a * 120.0) <= -2e+55) {
		tmp = t_1;
	} else if ((a * 120.0) <= -1e-32) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-106) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 2e+126) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (x * (-60.0 / t))
	t_2 = (a * 120.0) + (-60.0 * (y / z))
	tmp = 0
	if (a * 120.0) <= -2e+175:
		tmp = t_2
	elif (a * 120.0) <= -2e+55:
		tmp = t_1
	elif (a * 120.0) <= -1e-32:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= 5e-106:
		tmp = (x - y) * (60.0 / (z - t))
	elif (a * 120.0) <= 2e+126:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+175)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= -2e+55)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -1e-32)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 5e-106)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 2e+126)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (x * (-60.0 / t));
	t_2 = (a * 120.0) + (-60.0 * (y / z));
	tmp = 0.0;
	if ((a * 120.0) <= -2e+175)
		tmp = t_2;
	elseif ((a * 120.0) <= -2e+55)
		tmp = t_1;
	elseif ((a * 120.0) <= -1e-32)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= 5e-106)
		tmp = (x - y) * (60.0 / (z - t));
	elseif ((a * 120.0) <= 2e+126)
		tmp = t_2;
	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[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+175], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+55], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-32], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-106], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+126], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.9999999999999999e175 or 4.99999999999999983e-106 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999985e126

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 91.2%

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

      1. associate-*r/ 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in z around inf 77.7%

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

   if -1.9999999999999999e175 < (*.f64 a #s(literal 120 binary64)) < -2.00000000000000002e55 or 1.99999999999999985e126 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 78.3%

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

   6. Taylor expanded in x around inf 84.6%

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

      1. associate-*r/ 84.6%

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

      2. associate-*l/ 84.6%

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

      3. *-commutative 84.6%

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

   8. Simplified 84.6%

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

   if -2.00000000000000002e55 < (*.f64 a #s(literal 120 binary64)) < -1.00000000000000006e-32

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 78.6%

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

   6. Taylor expanded in x around 0 78.7%

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

   if -1.00000000000000006e-32 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999983e-106

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 97.8%

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

      1. associate-*r/ 97.9%

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

      2. remove-double-neg 97.9%

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

      3. neg-mul-1 97.9%

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

      4. times-frac 97.8%

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

      5. metadata-eval 97.8%

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

      6. distribute-neg-frac2 97.8%

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

      7. distribute-lft-in 97.8%

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

      8. +-commutative 97.8%

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

      9. sub-neg 97.8%

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

      10. div-sub 99.7%

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

      11. associate-*r/ 99.8%

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

      12. associate-*l/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in a around 0 82.0%

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

      1. metadata-eval 82.0%

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

      2. times-frac 82.0%

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

      3. *-commutative 82.0%

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

      4. neg-mul-1 82.0%

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

      5. associate-/l* 82.0%

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

      6. distribute-neg-frac2 82.0%

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

      7. distribute-neg-frac 82.0%

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

      8. metadata-eval 82.0%

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

   10. Simplified 82.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+175}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+55}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+126}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 1.82 \cdot 10^{+15}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+51}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-57)
   (* a 120.0)
   (if (<= (* a 120.0) 5e-106)
     (* (- x y) (/ 60.0 (- z t)))
     (if (<= (* a 120.0) 1.82e+15)
       (+ (* a 120.0) (* -60.0 (/ y z)))
       (if (<= (* a 120.0) 2e+51) (* 60.0 (/ (- x y) (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-57) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-106) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 1.82e+15) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 2e+51) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-57)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d-106) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if ((a * 120.0d0) <= 1.82d+15) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 2d+51) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-57) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-106) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 1.82e+15) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 2e+51) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-57:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e-106:
		tmp = (x - y) * (60.0 / (z - t))
	elif (a * 120.0) <= 1.82e+15:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 2e+51:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-57)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e-106)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1.82e+15)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 2e+51)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-57)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e-106)
		tmp = (x - y) * (60.0 / (z - t));
	elseif ((a * 120.0) <= 1.82e+15)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 2e+51)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-57], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-106], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1.82e+15], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+51], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999991e-57 or 2e51 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.1%

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

   if -1.99999999999999991e-57 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999983e-106

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 97.7%

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

      1. associate-*r/ 97.7%

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

      2. remove-double-neg 97.7%

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

      3. neg-mul-1 97.7%

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

      4. times-frac 97.7%

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

      5. metadata-eval 97.7%

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

      6. distribute-neg-frac2 97.7%

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

      7. distribute-lft-in 97.7%

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

      8. +-commutative 97.7%

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

      9. sub-neg 97.7%

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

      10. div-sub 99.7%

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

      11. associate-*r/ 99.8%

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

      12. associate-*l/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in a around 0 84.6%

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

      1. metadata-eval 84.6%

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

      2. times-frac 84.7%

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

      3. *-commutative 84.7%

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

      4. neg-mul-1 84.7%

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

      5. associate-/l* 84.7%

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

      6. distribute-neg-frac2 84.7%

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

      7. distribute-neg-frac 84.7%

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

      8. metadata-eval 84.7%

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

   10. Simplified 84.7%

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

   if 4.99999999999999983e-106 < (*.f64 a #s(literal 120 binary64)) < 1.82e15

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 90.1%

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

      1. associate-*r/ 90.1%

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

   7. Simplified 90.1%

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

   8. Taylor expanded in z around inf 66.2%

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

   if 1.82e15 < (*.f64 a #s(literal 120 binary64)) < 2e51

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 65.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 1.82 \cdot 10^{+15}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+51}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+90}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{-76}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -5e+90)
   (* a 120.0)
   (if (<= (- z t) 2e-76)
     (* 60.0 (/ (- x y) z))
     (if (<= (- z t) 2e+69) (* x (/ 60.0 (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+90) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e-76) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((z - t) <= 2e+69) {
		tmp = x * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z - t) <= (-5d+90)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 2d-76) then
        tmp = 60.0d0 * ((x - y) / z)
    else if ((z - t) <= 2d+69) then
        tmp = x * (60.0d0 / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+90) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e-76) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((z - t) <= 2e+69) {
		tmp = x * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -5e+90:
		tmp = a * 120.0
	elif (z - t) <= 2e-76:
		tmp = 60.0 * ((x - y) / z)
	elif (z - t) <= 2e+69:
		tmp = x * (60.0 / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -5e+90)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 2e-76)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (Float64(z - t) <= 2e+69)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -5e+90)
		tmp = a * 120.0;
	elseif ((z - t) <= 2e-76)
		tmp = 60.0 * ((x - y) / z);
	elseif ((z - t) <= 2e+69)
		tmp = x * (60.0 / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -5e+90], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 2e-76], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 2e+69], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 z t) < -5.0000000000000004e90 or 2.0000000000000001e69 < (-.f64 z t)

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.0%

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

   if -5.0000000000000004e90 < (-.f64 z t) < 1.99999999999999985e-76

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 81.3%

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

   6. Taylor expanded in z around inf 54.3%

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

   if 1.99999999999999985e-76 < (-.f64 z t) < 2.0000000000000001e69

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 78.7%

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

   6. Taylor expanded in x around inf 50.0%

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

      1. associate-*r/ 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-*r/ 71.2%

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

   8. Simplified 50.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+90}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{-76}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+90}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{-76}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{+69}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -5e+90)
   (* a 120.0)
   (if (<= (- z t) 2e-76)
     (* 60.0 (/ (- x y) z))
     (if (<= (- z t) 2e+69) (* 60.0 (/ x (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+90) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e-76) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((z - t) <= 2e+69) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z - t) <= (-5d+90)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 2d-76) then
        tmp = 60.0d0 * ((x - y) / z)
    else if ((z - t) <= 2d+69) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+90) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e-76) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((z - t) <= 2e+69) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -5e+90:
		tmp = a * 120.0
	elif (z - t) <= 2e-76:
		tmp = 60.0 * ((x - y) / z)
	elif (z - t) <= 2e+69:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -5e+90)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 2e-76)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (Float64(z - t) <= 2e+69)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -5e+90)
		tmp = a * 120.0;
	elseif ((z - t) <= 2e-76)
		tmp = 60.0 * ((x - y) / z);
	elseif ((z - t) <= 2e+69)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -5e+90], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 2e-76], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 2e+69], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 z t) < -5.0000000000000004e90 or 2.0000000000000001e69 < (-.f64 z t)

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.0%

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

   if -5.0000000000000004e90 < (-.f64 z t) < 1.99999999999999985e-76

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 81.3%

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

   6. Taylor expanded in z around inf 54.3%

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

   if 1.99999999999999985e-76 < (-.f64 z t) < 2.0000000000000001e69

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 96.0%

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

      1. associate-*r/ 96.1%

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

      2. remove-double-neg 96.1%

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

      3. neg-mul-1 96.1%

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

      4. times-frac 96.0%

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

      5. metadata-eval 96.0%

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

      6. distribute-neg-frac2 96.0%

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

      7. distribute-lft-in 96.0%

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

      8. +-commutative 96.0%

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

      9. sub-neg 96.0%

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

      10. div-sub 99.6%

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

      11. associate-*r/ 99.8%

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

      12. associate-*l/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around inf 73.2%

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

      1. associate-*r/ 73.3%

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

      2. *-commutative 73.3%

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

      3. *-commutative 73.3%

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

      4. times-frac 76.7%

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

   10. Simplified 76.7%

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

   11. Taylor expanded in x around inf 50.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+90}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{-76}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{+69}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-236}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ -60.0 t))))
   (if (<= a -2.7e-60)
     (* a 120.0)
     (if (<= a 8.2e-303)
       t_1
       (if (<= a 9e-236)
         (* 60.0 (/ (- x y) z))
         (if (<= a 1.55e-105) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (-60.0 / t);
	double tmp;
	if (a <= -2.7e-60) {
		tmp = a * 120.0;
	} else if (a <= 8.2e-303) {
		tmp = t_1;
	} else if (a <= 9e-236) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 1.55e-105) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) * ((-60.0d0) / t)
    if (a <= (-2.7d-60)) then
        tmp = a * 120.0d0
    else if (a <= 8.2d-303) then
        tmp = t_1
    else if (a <= 9d-236) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (a <= 1.55d-105) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (-60.0 / t);
	double tmp;
	if (a <= -2.7e-60) {
		tmp = a * 120.0;
	} else if (a <= 8.2e-303) {
		tmp = t_1;
	} else if (a <= 9e-236) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 1.55e-105) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * (-60.0 / t)
	tmp = 0
	if a <= -2.7e-60:
		tmp = a * 120.0
	elif a <= 8.2e-303:
		tmp = t_1
	elif a <= 9e-236:
		tmp = 60.0 * ((x - y) / z)
	elif a <= 1.55e-105:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * Float64(-60.0 / t))
	tmp = 0.0
	if (a <= -2.7e-60)
		tmp = Float64(a * 120.0);
	elseif (a <= 8.2e-303)
		tmp = t_1;
	elseif (a <= 9e-236)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (a <= 1.55e-105)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * (-60.0 / t);
	tmp = 0.0;
	if (a <= -2.7e-60)
		tmp = a * 120.0;
	elseif (a <= 8.2e-303)
		tmp = t_1;
	elseif (a <= 9e-236)
		tmp = 60.0 * ((x - y) / z);
	elseif (a <= 1.55e-105)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e-60], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 8.2e-303], t$95$1, If[LessEqual[a, 9e-236], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-105], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7e-60 or 1.55000000000000007e-105 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 71.6%

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

   if -2.7e-60 < a < 8.20000000000000037e-303 or 8.99999999999999997e-236 < a < 1.55000000000000007e-105

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 82.0%

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

   6. Taylor expanded in z around 0 55.8%

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

      1. associate-*r/ 55.9%

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

      2. *-commutative 55.9%

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

      3. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

   if 8.20000000000000037e-303 < a < 8.99999999999999997e-236

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 95.0%

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

   6. Taylor expanded in z around inf 75.5%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-303}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-236}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-105}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-57} \lor \neg \left(a \cdot 120 \leq 10^{-93}\right):\\ \;\;\;\;a \cdot 120 + x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (- z t))))
   (if (or (<= (* a 120.0) -2e-57) (not (<= (* a 120.0) 1e-93)))
     (+ (* a 120.0) (* x t_1))
     (* (- x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if (((a * 120.0) <= -2e-57) || !((a * 120.0) <= 1e-93)) {
		tmp = (a * 120.0) + (x * t_1);
	} else {
		tmp = (x - y) * 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 / (z - t)
    if (((a * 120.0d0) <= (-2d-57)) .or. (.not. ((a * 120.0d0) <= 1d-93))) then
        tmp = (a * 120.0d0) + (x * t_1)
    else
        tmp = (x - y) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if (((a * 120.0) <= -2e-57) || !((a * 120.0) <= 1e-93)) {
		tmp = (a * 120.0) + (x * t_1);
	} else {
		tmp = (x - y) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / (z - t)
	tmp = 0
	if ((a * 120.0) <= -2e-57) or not ((a * 120.0) <= 1e-93):
		tmp = (a * 120.0) + (x * t_1)
	else:
		tmp = (x - y) * t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(z - t))
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-57) || !(Float64(a * 120.0) <= 1e-93))
		tmp = Float64(Float64(a * 120.0) + Float64(x * t_1));
	else
		tmp = Float64(Float64(x - y) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / (z - t);
	tmp = 0.0;
	if (((a * 120.0) <= -2e-57) || ~(((a * 120.0) <= 1e-93)))
		tmp = (a * 120.0) + (x * t_1);
	else
		tmp = (x - y) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-57], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-93]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999991e-57 or 9.999999999999999e-94 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.0%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r/ 86.1%

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

   7. Simplified 86.1%

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

   if -1.99999999999999991e-57 < (*.f64 a #s(literal 120 binary64)) < 9.999999999999999e-94

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 97.7%

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

      1. associate-*r/ 97.8%

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

      2. remove-double-neg 97.8%

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

      3. neg-mul-1 97.8%

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

      4. times-frac 97.7%

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

      5. metadata-eval 97.7%

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

      6. distribute-neg-frac2 97.7%

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

      7. distribute-lft-in 97.7%

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

      8. +-commutative 97.7%

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

      9. sub-neg 97.7%

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

      10. div-sub 99.7%

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

      11. associate-*r/ 99.8%

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

      12. associate-*l/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in a around 0 84.1%

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

      1. metadata-eval 84.1%

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

      2. times-frac 84.2%

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

      3. *-commutative 84.2%

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

      4. neg-mul-1 84.2%

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

      5. associate-/l* 84.2%

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

      6. distribute-neg-frac2 84.2%

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

      7. distribute-neg-frac 84.2%

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

      8. metadata-eval 84.2%

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

   10. Simplified 84.2%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-57} \lor \neg \left(a \cdot 120 \leq 10^{-93}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11000000000000 \lor \neg \left(y \leq 1.9 \cdot 10^{-20}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -11000000000000.0) (not (<= y 1.9e-20)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (/ (* 60.0 x) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -11000000000000.0) || !(y <= 1.9e-20)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (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 ((y <= (-11000000000000.0d0)) .or. (.not. (y <= 1.9d-20))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (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 ((y <= -11000000000000.0) || !(y <= 1.9e-20)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -11000000000000.0) or not (y <= 1.9e-20):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -11000000000000.0) || !(y <= 1.9e-20))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -11000000000000.0) || ~((y <= 1.9e-20)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -11000000000000.0], N[Not[LessEqual[y, 1.9e-20]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e13 or 1.8999999999999999e-20 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 89.3%

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

      1. associate-*r/ 89.3%

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

   7. Simplified 89.3%

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

   if -1.1e13 < y < 1.8999999999999999e-20

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 96.4%

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

      1. associate-*r/ 96.4%

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

   7. Simplified 96.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11000000000000 \lor \neg \left(y \leq 1.9 \cdot 10^{-20}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -24000000000000 \lor \neg \left(y \leq 5.2 \cdot 10^{-21}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -24000000000000.0) (not (<= y 5.2e-21)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -24000000000000.0) || !(y <= 5.2e-21)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (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 ((y <= (-24000000000000.0d0)) .or. (.not. (y <= 5.2d-21))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (x * (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 ((y <= -24000000000000.0) || !(y <= 5.2e-21)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -24000000000000.0) or not (y <= 5.2e-21):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -24000000000000.0) || !(y <= 5.2e-21))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -24000000000000.0) || ~((y <= 5.2e-21)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -24000000000000.0], N[Not[LessEqual[y, 5.2e-21]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e13 or 5.20000000000000035e-21 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 89.3%

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

      1. associate-*r/ 89.3%

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

   7. Simplified 89.3%

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

   if -2.4e13 < y < 5.20000000000000035e-21

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 96.4%

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

      1. associate-*r/ 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-*r/ 96.4%

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

   7. Simplified 96.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -24000000000000 \lor \neg \left(y \leq 5.2 \cdot 10^{-21}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \lor \neg \left(z \leq 1.02 \cdot 10^{+69}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.1) (not (<= z 1.02e+69)))
   (+ (* a 120.0) (* -60.0 (/ 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 <= -6.1) || !(z <= 1.02e+69)) {
		tmp = (a * 120.0) + (-60.0 * (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 <= (-6.1d0)) .or. (.not. (z <= 1.02d+69))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (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 <= -6.1) || !(z <= 1.02e+69)) {
		tmp = (a * 120.0) + (-60.0 * (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 <= -6.1) or not (z <= 1.02e+69):
		tmp = (a * 120.0) + (-60.0 * (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 <= -6.1) || !(z <= 1.02e+69))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(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 <= -6.1) || ~((z <= 1.02e+69)))
		tmp = (a * 120.0) + (-60.0 * (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, -6.1], N[Not[LessEqual[z, 1.02e+69]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / 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 < -6.0999999999999996 or 1.02e69 < z

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 88.3%

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

      1. associate-*r/ 88.3%

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

   7. Simplified 88.3%

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

   8. Taylor expanded in z around inf 85.5%

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

   if -6.0999999999999996 < z < 1.02e69

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 83.3%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \lor \neg \left(z \leq 1.02 \cdot 10^{+69}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-59} \lor \neg \left(a \leq 2.65 \cdot 10^{-92}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.85e-59) (not (<= a 2.65e-92)))
   (* a 120.0)
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e-59) || !(a <= 2.65e-92)) {
		tmp = a * 120.0;
	} else {
		tmp = (x - 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 ((a <= (-1.85d-59)) .or. (.not. (a <= 2.65d-92))) then
        tmp = a * 120.0d0
    else
        tmp = (x - 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 ((a <= -1.85e-59) || !(a <= 2.65e-92)) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.85e-59) or not (a <= 2.65e-92):
		tmp = a * 120.0
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.85e-59) || !(a <= 2.65e-92))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x - 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 ((a <= -1.85e-59) || ~((a <= 2.65e-92)))
		tmp = a * 120.0;
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.85e-59], N[Not[LessEqual[a, 2.65e-92]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.85e-59 or 2.65000000000000015e-92 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.3%

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

   if -1.85e-59 < a < 2.65000000000000015e-92

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 97.7%

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

      1. associate-*r/ 97.8%

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

      2. remove-double-neg 97.8%

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

      3. neg-mul-1 97.8%

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

      4. times-frac 97.7%

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

      5. metadata-eval 97.7%

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

      6. distribute-neg-frac2 97.7%

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

      7. distribute-lft-in 97.7%

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

      8. +-commutative 97.7%

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

      9. sub-neg 97.7%

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

      10. div-sub 99.7%

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

      11. associate-*r/ 99.8%

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

      12. associate-*l/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in a around 0 84.1%

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

      1. metadata-eval 84.1%

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

      2. times-frac 84.2%

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

      3. *-commutative 84.2%

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

      4. neg-mul-1 84.2%

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

      5. associate-/l* 84.2%

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

      6. distribute-neg-frac2 84.2%

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

      7. distribute-neg-frac 84.2%

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

      8. metadata-eval 84.2%

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

   10. Simplified 84.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-59} \lor \neg \left(a \leq 2.65 \cdot 10^{-92}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-61} \lor \neg \left(a \leq 1.8 \cdot 10^{-92}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.15e-61) (not (<= a 1.8e-92)))
   (* 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 <= -1.15e-61) || !(a <= 1.8e-92)) {
		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 <= (-1.15d-61)) .or. (.not. (a <= 1.8d-92))) 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 <= -1.15e-61) || !(a <= 1.8e-92)) {
		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 <= -1.15e-61) or not (a <= 1.8e-92):
		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 <= -1.15e-61) || !(a <= 1.8e-92))
		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 <= -1.15e-61) || ~((a <= 1.8e-92)))
		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, -1.15e-61], N[Not[LessEqual[a, 1.8e-92]], $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 < -1.14999999999999996e-61 or 1.80000000000000008e-92 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.3%

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

   if -1.14999999999999996e-61 < a < 1.80000000000000008e-92

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 84.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-61} \lor \neg \left(a \leq 1.8 \cdot 10^{-92}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+195} \lor \neg \left(x \leq 1.6 \cdot 10^{+179}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.55e+195) (not (<= x 1.6e+179)))
   (* 60.0 (/ x (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.55e+195) || !(x <= 1.6e+179)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.55d+195)) .or. (.not. (x <= 1.6d+179))) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.55e+195) || !(x <= 1.6e+179)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.55e+195) or not (x <= 1.6e+179):
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.55e+195) || !(x <= 1.6e+179))
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.55e+195) || ~((x <= 1.6e+179)))
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.55e+195], N[Not[LessEqual[x, 1.6e+179]], $MachinePrecision]], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5500000000000001e195 or 1.6000000000000001e179 < x

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 96.3%

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

      1. associate-*r/ 96.4%

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

      2. remove-double-neg 96.4%

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

      3. neg-mul-1 96.4%

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

      4. times-frac 96.3%

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

      5. metadata-eval 96.3%

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

      6. distribute-neg-frac2 96.3%

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

      7. distribute-lft-in 96.3%

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

      8. +-commutative 96.3%

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

      9. sub-neg 96.3%

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

      10. div-sub 99.8%

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

      11. associate-*r/ 99.9%

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

      12. associate-*l/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around inf 83.6%

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

      1. associate-*r/ 83.7%

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

      2. *-commutative 83.7%

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

      3. *-commutative 83.7%

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

      4. times-frac 83.5%

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

   10. Simplified 83.5%

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

   11. Taylor expanded in x around inf 67.9%

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

   if -1.5500000000000001e195 < x < 1.6000000000000001e179

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+195} \lor \neg \left(x \leq 1.6 \cdot 10^{+179}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+198} \lor \neg \left(x \leq 1.38 \cdot 10^{+172}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.35e+198) (not (<= x 1.38e+172)))
   (* -60.0 (/ x t))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.35e+198) || !(x <= 1.38e+172)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.35d+198)) .or. (.not. (x <= 1.38d+172))) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.35e+198) || !(x <= 1.38e+172)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.35e+198) or not (x <= 1.38e+172):
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.35e+198) || !(x <= 1.38e+172))
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.35e+198) || ~((x <= 1.38e+172)))
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.35e+198], N[Not[LessEqual[x, 1.38e+172]], $MachinePrecision]], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3500000000000001e198 or 1.38000000000000002e172 < x

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 80.1%

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

   6. Taylor expanded in x around inf 67.9%

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

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*r/ 87.6%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in z around 0 56.0%

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

   if -2.3500000000000001e198 < x < 1.38000000000000002e172

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.7%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+198} \lor \neg \left(x \leq 1.38 \cdot 10^{+172}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+194}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+183}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.2e+194)
   (* -60.0 (/ x t))
   (if (<= x 1.1e+183) (* a 120.0) (* x (/ -60.0 t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.2e+194) {
		tmp = -60.0 * (x / t);
	} else if (x <= 1.1e+183) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.2d+194)) then
        tmp = (-60.0d0) * (x / t)
    else if (x <= 1.1d+183) then
        tmp = a * 120.0d0
    else
        tmp = x * ((-60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.2e+194) {
		tmp = -60.0 * (x / t);
	} else if (x <= 1.1e+183) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.2e+194:
		tmp = -60.0 * (x / t)
	elif x <= 1.1e+183:
		tmp = a * 120.0
	else:
		tmp = x * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.2e+194)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (x <= 1.1e+183)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.2e+194)
		tmp = -60.0 * (x / t);
	elseif (x <= 1.1e+183)
		tmp = a * 120.0;
	else
		tmp = x * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.2e+194], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+183], N[(a * 120.0), $MachinePrecision], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.1999999999999999e194

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 77.6%

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

   6. Taylor expanded in x around inf 70.2%

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

      1. associate-*r/ 92.2%

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

      2. *-commutative 92.2%

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

      3. associate-*r/ 92.2%

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

   8. Simplified 70.2%

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

   9. Taylor expanded in z around 0 62.3%

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

   if -6.1999999999999999e194 < x < 1.09999999999999995e183

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.7%

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

   if 1.09999999999999995e183 < x

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 82.1%

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

   6. Taylor expanded in x around inf 66.1%

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

      1. associate-*r/ 84.0%

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

      2. *-commutative 84.0%

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

      3. associate-*r/ 83.9%

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

   8. Simplified 66.2%

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

   9. Taylor expanded in z around 0 50.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+194}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+183}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((x - y) * (60.0d0 / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 99.0%

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

   1. associate-*r/ 99.0%

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

   2. remove-double-neg 99.0%

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

   3. neg-mul-1 99.0%

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

   4. times-frac 99.0%

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

   5. metadata-eval 99.0%

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

   6. distribute-neg-frac2 99.0%

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

   7. distribute-lft-in 99.0%

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

   8. +-commutative 99.0%

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

   9. sub-neg 99.0%

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

   10. div-sub 99.8%

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

   11. associate-*r/ 99.8%

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

   12. associate-*l/ 99.8%

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

7. Simplified 99.8%

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

8. Final simplification 99.8%

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

Alternative 18: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (60.0d0 * ((x - y) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

   \[\leadsto a \cdot 120 + 60 \cdot \frac{x - y}{z - t} \]
6. Add Preprocessing

Alternative 19: 50.7% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 51.1%

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

6. Final simplification 51.1%

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

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 2024091 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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