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

Percentage Accurate: 99.5% → 99.8%

Time: 14.4s

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: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. clear-num 99.7%

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

   2. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-define 99.8%

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

   3. associate-/r/ 99.8%

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

   4. div-inv 99.7%

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

   5. *-commutative 99.7%

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

   6. div-inv 99.8%

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

8. Applied egg-rr 99.8%

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

Alternative 2: 59.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-100}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))))
   (if (<= a -2.3e-38)
     (* a 120.0)
     (if (<= a -6.2e-103)
       t_1
       (if (<= a 9e-100)
         (* 60.0 (/ (- y x) t))
         (if (<= a 1.9e-75) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -2.3e-38) {
		tmp = a * 120.0;
	} else if (a <= -6.2e-103) {
		tmp = t_1;
	} else if (a <= 9e-100) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 1.9e-75) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    if (a <= (-2.3d-38)) then
        tmp = a * 120.0d0
    else if (a <= (-6.2d-103)) then
        tmp = t_1
    else if (a <= 9d-100) then
        tmp = 60.0d0 * ((y - x) / t)
    else if (a <= 1.9d-75) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -2.3e-38) {
		tmp = a * 120.0;
	} else if (a <= -6.2e-103) {
		tmp = t_1;
	} else if (a <= 9e-100) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 1.9e-75) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	tmp = 0
	if a <= -2.3e-38:
		tmp = a * 120.0
	elif a <= -6.2e-103:
		tmp = t_1
	elif a <= 9e-100:
		tmp = 60.0 * ((y - x) / t)
	elif a <= 1.9e-75:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (a <= -2.3e-38)
		tmp = Float64(a * 120.0);
	elseif (a <= -6.2e-103)
		tmp = t_1;
	elseif (a <= 9e-100)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	elseif (a <= 1.9e-75)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	tmp = 0.0;
	if (a <= -2.3e-38)
		tmp = a * 120.0;
	elseif (a <= -6.2e-103)
		tmp = t_1;
	elseif (a <= 9e-100)
		tmp = 60.0 * ((y - x) / t);
	elseif (a <= 1.9e-75)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-38], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6.2e-103], t$95$1, If[LessEqual[a, 9e-100], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-75], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.30000000000000002e-38 or 1.89999999999999997e-75 < a

   1. Initial program 99.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 70.7%

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

   if -2.30000000000000002e-38 < a < -6.2000000000000003e-103 or 9.0000000000000002e-100 < a < 1.89999999999999997e-75

   1. Initial program 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 86.0%

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

   8. Taylor expanded in z around inf 79.0%

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

   if -6.2000000000000003e-103 < a < 9.0000000000000002e-100

   1. Initial program 99.5%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 79.9%

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

   8. Taylor expanded in z around 0 49.0%

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

      1. associate-*r/ 60.0%

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

      2. neg-mul-1 60.0%

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

      3. neg-sub0 60.0%

         \[\leadsto 60 \cdot \frac{\color{blue}{0 - \left(x - y\right)}}{t} + a \cdot 120 \]

      4. sub-neg 60.0%

         \[\leadsto 60 \cdot \frac{0 - \color{blue}{\left(x + \left(-y\right)\right)}}{t} + a \cdot 120 \]

      5. +-commutative 60.0%

         \[\leadsto 60 \cdot \frac{0 - \color{blue}{\left(\left(-y\right) + x\right)}}{t} + a \cdot 120 \]

      6. associate--r+ 60.0%

         \[\leadsto 60 \cdot \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{t} + a \cdot 120 \]

      7. neg-sub0 60.0%

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

      8. remove-double-neg 60.0%

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

   10. Simplified 49.0%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-103}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-100}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-75}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32} \lor \neg \left(a \cdot 120 \leq 10^{+40}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-32) (not (<= (* a 120.0) 1e+40)))
   (* 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 * 120.0) <= -2e-32) || !((a * 120.0) <= 1e+40)) {
		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 * 120.0d0) <= (-2d-32)) .or. (.not. ((a * 120.0d0) <= 1d+40))) 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 * 120.0) <= -2e-32) || !((a * 120.0) <= 1e+40)) {
		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 * 120.0) <= -2e-32) or not ((a * 120.0) <= 1e+40):
		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 ((Float64(a * 120.0) <= -2e-32) || !(Float64(a * 120.0) <= 1e+40))
		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 * 120.0) <= -2e-32) || ~(((a * 120.0) <= 1e+40)))
		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[N[(a * 120.0), $MachinePrecision], -2e-32], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+40]], $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 (*.f64 a #s(literal 120 binary64)) < -2.00000000000000011e-32 or 1.00000000000000003e40 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 75.3%

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

   if -2.00000000000000011e-32 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000003e40

   1. Initial program 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 78.2%

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

      1. associate-*r/ 78.1%

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

      2. associate-*l/ 78.2%

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

      3. *-commutative 78.2%

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

   9. Simplified 78.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32} \lor \neg \left(a \cdot 120 \leq 10^{+40}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+29}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot 60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-32)
   (* a 120.0)
   (if (<= (* a 120.0) 5e+29)
     (/ 60.0 (/ (- z t) (- x y)))
     (+ (* a 120.0) (/ (* y 60.0) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-32) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e+29) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + ((y * 60.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-32)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d+29) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = (a * 120.0d0) + ((y * 60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-32) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e+29) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + ((y * 60.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-32:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e+29:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (a * 120.0) + ((y * 60.0) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-32)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e+29)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * 60.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-32)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e+29)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (a * 120.0) + ((y * 60.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-32], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+29], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2.00000000000000011e-32

   1. Initial program 98.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 77.3%

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

   if -2.00000000000000011e-32 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000001e29

   1. Initial program 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 78.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   9. Applied egg-rr 78.6%

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

   if 5.0000000000000001e29 < (*.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* 99.8%

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

   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 87.1%

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

      1. associate-*r/ 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in z around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. *-commutative 78.0%

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

   10. Simplified 78.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+29}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot 60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+29}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot 60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-32)
   (* a 120.0)
   (if (<= (* a 120.0) 5e+29)
     (* (- x y) (/ 60.0 (- z t)))
     (+ (* a 120.0) (/ (* y 60.0) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-32) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e+29) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + ((y * 60.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-32)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d+29) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = (a * 120.0d0) + ((y * 60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-32) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e+29) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + ((y * 60.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-32:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e+29:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = (a * 120.0) + ((y * 60.0) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-32)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e+29)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * 60.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-32)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e+29)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = (a * 120.0) + ((y * 60.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-32], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+29], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2.00000000000000011e-32

   1. Initial program 98.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 77.3%

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

   if -2.00000000000000011e-32 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000001e29

   1. Initial program 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 78.6%

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

      1. associate-*r/ 78.5%

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

      2. associate-*l/ 78.6%

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

      3. *-commutative 78.6%

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

   9. Simplified 78.6%

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

   if 5.0000000000000001e29 < (*.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* 99.8%

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

   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 87.1%

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

      1. associate-*r/ 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in z around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. *-commutative 78.0%

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

   10. Simplified 78.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+29}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot 60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+34} \lor \neg \left(z \leq 45000000000\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e+34) (not (<= z 45000000000.0)))
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))
   (+ (* a 120.0) (* 60.0 (/ (- y x) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e+34) || !(z <= 45000000000.0)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.75d+34)) .or. (.not. (z <= 45000000000.0d0))) then
        tmp = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    else
        tmp = (a * 120.0d0) + (60.0d0 * ((y - x) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e+34) || !(z <= 45000000000.0)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.75e+34) or not (z <= 45000000000.0):
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	else:
		tmp = (a * 120.0) + (60.0 * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.75e+34) || !(z <= 45000000000.0))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.75e+34) || ~((z <= 45000000000.0)))
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	else
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.75e+34], N[Not[LessEqual[z, 45000000000.0]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7499999999999998e34 or 4.5e10 < z

   1. Initial program 98.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 z around inf 94.8%

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

   if -2.7499999999999998e34 < z < 4.5e10

   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* 99.7%

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

   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%

      \[\leadsto 60 \cdot \color{blue}{\left(-1 \cdot \frac{x - y}{t}\right)} + a \cdot 120 \]
   6. Step-by-step derivation

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

      3. neg-sub0 83.3%

         \[\leadsto 60 \cdot \frac{\color{blue}{0 - \left(x - y\right)}}{t} + a \cdot 120 \]

      4. sub-neg 83.3%

         \[\leadsto 60 \cdot \frac{0 - \color{blue}{\left(x + \left(-y\right)\right)}}{t} + a \cdot 120 \]

      5. +-commutative 83.3%

         \[\leadsto 60 \cdot \frac{0 - \color{blue}{\left(\left(-y\right) + x\right)}}{t} + a \cdot 120 \]

      6. associate--r+ 83.3%

         \[\leadsto 60 \cdot \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{t} + a \cdot 120 \]

      7. neg-sub0 83.3%

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

      8. remove-double-neg 83.3%

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

   7. Simplified 83.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+34} \lor \neg \left(z \leq 45000000000\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+54}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+115}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.45e+54)
   (+ (* a 120.0) (* 60.0 (/ x (- z t))))
   (if (<= x 1.05e+115)
     (+ (* a 120.0) (/ (* y -60.0) (- z t)))
     (+ (* a 120.0) (/ 60.0 (/ (- z t) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.45e+54) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else if (x <= 1.05e+115) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	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 <= (-1.45d+54)) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    else if (x <= 1.05d+115) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    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 <= -1.45e+54) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else if (x <= 1.05e+115) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.45e+54:
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	elif x <= 1.05e+115:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.45e+54)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	elseif (x <= 1.05e+115)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.45e+54)
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	elseif (x <= 1.05e+115)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.45e+54], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+115], 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[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4499999999999999e54

   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 x around inf 86.2%

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

   if -1.4499999999999999e54 < x < 1.05000000000000002e115

   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* 99.7%

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

   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 93.2%

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

      1. associate-*r/ 93.2%

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

   7. Simplified 93.2%

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

   if 1.05000000000000002e115 < x

   1. Initial program 96.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 91.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+54}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+115}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+34}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 126000000000:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+34)
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))
   (if (<= z 126000000000.0)
     (+ (* a 120.0) (* 60.0 (/ (- y x) t)))
     (+ (* a 120.0) (/ 60.0 (/ z (- x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+34) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else if (z <= 126000000000.0) {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+34)) then
        tmp = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    else if (z <= 126000000000.0d0) then
        tmp = (a * 120.0d0) + (60.0d0 * ((y - x) / t))
    else
        tmp = (a * 120.0d0) + (60.0d0 / (z / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+34) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else if (z <= 126000000000.0) {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+34:
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	elif z <= 126000000000.0:
		tmp = (a * 120.0) + (60.0 * ((y - x) / t))
	else:
		tmp = (a * 120.0) + (60.0 / (z / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+34)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)));
	elseif (z <= 126000000000.0)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+34)
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	elseif (z <= 126000000000.0)
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	else
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+34], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 126000000000.0], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4500000000000001e34

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 inf 93.2%

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

   if -1.4500000000000001e34 < z < 1.26e11

   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* 99.7%

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

   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%

      \[\leadsto 60 \cdot \color{blue}{\left(-1 \cdot \frac{x - y}{t}\right)} + a \cdot 120 \]
   6. Step-by-step derivation

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

      3. neg-sub0 83.3%

         \[\leadsto 60 \cdot \frac{\color{blue}{0 - \left(x - y\right)}}{t} + a \cdot 120 \]

      4. sub-neg 83.3%

         \[\leadsto 60 \cdot \frac{0 - \color{blue}{\left(x + \left(-y\right)\right)}}{t} + a \cdot 120 \]

      5. +-commutative 83.3%

         \[\leadsto 60 \cdot \frac{0 - \color{blue}{\left(\left(-y\right) + x\right)}}{t} + a \cdot 120 \]

      6. associate--r+ 83.3%

         \[\leadsto 60 \cdot \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{t} + a \cdot 120 \]

      7. neg-sub0 83.3%

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

      8. remove-double-neg 83.3%

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

   7. Simplified 83.3%

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

   if 1.26e11 < z

   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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 96.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+34}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 126000000000:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+156}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 4.45 \cdot 10^{+105}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.3e+156)
   (* (- x y) (/ 60.0 (- z t)))
   (if (<= y 4.45e+105)
     (+ (* a 120.0) (* 60.0 (/ x (- z t))))
     (* 60.0 (/ (- x y) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.3e+156) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (y <= 4.45e+105) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} 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 (y <= (-4.3d+156)) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if (y <= 4.45d+105) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    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 (y <= -4.3e+156) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (y <= 4.45e+105) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.3e+156:
		tmp = (x - y) * (60.0 / (z - t))
	elif y <= 4.45e+105:
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.3e+156)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (y <= 4.45e+105)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	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 (y <= -4.3e+156)
		tmp = (x - y) * (60.0 / (z - t));
	elseif (y <= 4.45e+105)
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.3e+156], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.45e+105], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.29999999999999985e156

   1. Initial program 99.6%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 80.2%

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

      1. associate-*r/ 80.3%

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

      2. associate-*l/ 80.5%

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

      3. *-commutative 80.5%

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

   9. Simplified 80.5%

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

   if -4.29999999999999985e156 < y < 4.44999999999999987e105

   1. Initial program 99.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 88.4%

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

   if 4.44999999999999987e105 < y

   1. Initial program 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 79.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+156}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 4.45 \cdot 10^{+105}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+145}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- x y) -1e+145)
   (* 60.0 (/ x (- z t)))
   (if (<= (- x y) 2e+148) (* a 120.0) (* y (/ -60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x - y) <= -1e+145) {
		tmp = 60.0 * (x / (z - t));
	} else if ((x - y) <= 2e+148) {
		tmp = a * 120.0;
	} else {
		tmp = y * (-60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x - y) <= (-1d+145)) then
        tmp = 60.0d0 * (x / (z - t))
    else if ((x - y) <= 2d+148) then
        tmp = a * 120.0d0
    else
        tmp = y * ((-60.0d0) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x - y) <= -1e+145) {
		tmp = 60.0 * (x / (z - t));
	} else if ((x - y) <= 2e+148) {
		tmp = a * 120.0;
	} else {
		tmp = y * (-60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x - y) <= -1e+145:
		tmp = 60.0 * (x / (z - t))
	elif (x - y) <= 2e+148:
		tmp = a * 120.0
	else:
		tmp = y * (-60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x - y) <= -1e+145)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (Float64(x - y) <= 2e+148)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x - y) <= -1e+145)
		tmp = 60.0 * (x / (z - t));
	elseif ((x - y) <= 2e+148)
		tmp = a * 120.0;
	else
		tmp = y * (-60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x - y), $MachinePrecision], -1e+145], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 2e+148], N[(a * 120.0), $MachinePrecision], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x y) < -9.9999999999999999e144

   1. Initial program 99.6%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-/r/ 99.7%

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

      4. div-inv 99.6%

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

      5. *-commutative 99.6%

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

      6. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around inf 56.9%

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

   if -9.9999999999999999e144 < (-.f64 x y) < 2.0000000000000001e148

   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 67.8%

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

   if 2.0000000000000001e148 < (-.f64 x y)

   1. Initial program 98.0%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.8%

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

      3. associate-/r/ 99.8%

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

      4. div-inv 99.6%

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

      5. *-commutative 99.6%

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

      6. div-inv 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in y around inf 51.8%

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

       1. associate-*r/ 51.8%

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

       2. *-commutative 51.8%

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

   11. Simplified 51.8%

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

       1. associate-/l* 51.9%

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

   13. Applied egg-rr 51.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+145}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{-34} \lor \neg \left(a \leq 8.2 \cdot 10^{+37}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.28e-34) (not (<= a 8.2e+37)))
   (* 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 <= -1.28e-34) || !(a <= 8.2e+37)) {
		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 <= (-1.28d-34)) .or. (.not. (a <= 8.2d+37))) 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 <= -1.28e-34) || !(a <= 8.2e+37)) {
		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 <= -1.28e-34) or not (a <= 8.2e+37):
		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 <= -1.28e-34) || !(a <= 8.2e+37))
		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 <= -1.28e-34) || ~((a <= 8.2e+37)))
		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, -1.28e-34], N[Not[LessEqual[a, 8.2e+37]], $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 < -1.2799999999999999e-34 or 8.1999999999999996e37 < a

   1. Initial program 99.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 75.3%

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

   if -1.2799999999999999e-34 < a < 8.1999999999999996e37

   1. Initial program 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 78.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{-34} \lor \neg \left(a \leq 8.2 \cdot 10^{+37}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+186}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+116}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.55e+186)
   (* 60.0 (/ x z))
   (if (<= x -1.1e+116) (/ (* x -60.0) t) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.55e+186) {
		tmp = 60.0 * (x / z);
	} else if (x <= -1.1e+116) {
		tmp = (x * -60.0) / 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+186)) then
        tmp = 60.0d0 * (x / z)
    else if (x <= (-1.1d+116)) then
        tmp = (x * (-60.0d0)) / 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+186) {
		tmp = 60.0 * (x / z);
	} else if (x <= -1.1e+116) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.55e+186:
		tmp = 60.0 * (x / z)
	elif x <= -1.1e+116:
		tmp = (x * -60.0) / t
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.55e+186)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (x <= -1.1e+116)
		tmp = Float64(Float64(x * -60.0) / 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+186)
		tmp = 60.0 * (x / z);
	elseif (x <= -1.1e+116)
		tmp = (x * -60.0) / t;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.55e+186], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.1e+116], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5500000000000001e186

   1. Initial program 99.6%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.8%

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

      3. associate-/r/ 99.7%

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

      4. div-inv 99.6%

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

      5. *-commutative 99.6%

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

      6. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around inf 82.3%

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

   10. Taylor expanded in z around inf 55.5%

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

   if -1.5500000000000001e186 < x < -1.1e116

   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. Step-by-step derivation

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-/r/ 99.7%

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

      4. div-inv 99.7%

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

      5. *-commutative 99.7%

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

      6. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around inf 61.0%

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

   10. Taylor expanded in z around 0 56.0%

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

       1. associate-*r/ 56.1%

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

   12. Simplified 56.1%

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

   if -1.1e116 < x

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 inf 55.1%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+186}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+116}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+186}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+114}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.15e+186)
   (* 60.0 (/ x z))
   (if (<= x -3e+114) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.15e+186) {
		tmp = 60.0 * (x / z);
	} else if (x <= -3e+114) {
		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 <= (-1.15d+186)) then
        tmp = 60.0d0 * (x / z)
    else if (x <= (-3d+114)) 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 <= -1.15e+186) {
		tmp = 60.0 * (x / z);
	} else if (x <= -3e+114) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.15e+186:
		tmp = 60.0 * (x / z)
	elif x <= -3e+114:
		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 <= -1.15e+186)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (x <= -3e+114)
		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 <= -1.15e+186)
		tmp = 60.0 * (x / z);
	elseif (x <= -3e+114)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.15e+186], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e+114], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15000000000000007e186

   1. Initial program 99.6%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.8%

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

      3. associate-/r/ 99.7%

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

      4. div-inv 99.6%

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

      5. *-commutative 99.6%

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

      6. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around inf 82.3%

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

   10. Taylor expanded in z around inf 55.5%

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

   if -1.15000000000000007e186 < x < -3e114

   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. Step-by-step derivation

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-/r/ 99.7%

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

      4. div-inv 99.7%

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

      5. *-commutative 99.7%

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

      6. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around inf 61.0%

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

   10. Taylor expanded in z around 0 56.0%

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

   if -3e114 < x

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 inf 55.1%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+186}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+114}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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]

Derivation

1. Initial program 99.3%

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

   1. clear-num 99.7%

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

   2. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 15: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. *-commutative 99.3%

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

   2. associate-/l* 99.7%

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

4. Applied egg-rr 99.7%

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

Alternative 16: 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 99.3%

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

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

Alternative 17: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+115}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.55e+115) (* 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+115) {
		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+115)) 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+115) {
		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+115:
		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+115)
		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+115)
		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[x, -1.55e+115], 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 < -1.55000000000000002e115

   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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.8%

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

      3. associate-/r/ 99.7%

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

      4. div-inv 99.6%

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

      5. *-commutative 99.6%

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

      6. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around inf 75.1%

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

   if -1.55000000000000002e115 < x

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 inf 55.1%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+115}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+116}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.1e+116) (* -60.0 (/ x t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e+116) {
		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 <= (-1.1d+116)) 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 <= -1.1e+116) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.1e+116:
		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 <= -1.1e+116)
		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 <= -1.1e+116)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.1e+116], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e116

   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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.8%

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

      3. associate-/r/ 99.7%

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

      4. div-inv 99.6%

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

      5. *-commutative 99.6%

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

      6. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around inf 75.1%

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

   10. Taylor expanded in z around 0 45.0%

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

   if -1.1e116 < x

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 inf 55.1%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+116}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.6% 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 99.3%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 inf 48.3%

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

6. Final simplification 48.3%

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

Developer Target 1: 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 2024118 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

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