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

Percentage Accurate: 99.3% → 99.8%

Time: 13.9s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
4. Add Preprocessing
5. 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 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 68.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot y}{t} + a \cdot 120\\ \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-134}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y - x}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (* 60.0 y) t) (* a 120.0))))
   (if (<= (* a 120.0) -4e-112)
     t_1
     (if (<= (* a 120.0) 5e-134)
       (/ 60.0 (/ (- t z) (- y x)))
       (if (<= (* a 120.0) 5e+33) t_1 (+ (* x (/ 60.0 z)) (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((60.0 * y) / t) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -4e-112) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-134) {
		tmp = 60.0 / ((t - z) / (y - x));
	} else if ((a * 120.0) <= 5e+33) {
		tmp = t_1;
	} else {
		tmp = (x * (60.0 / z)) + (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 * y) / t) + (a * 120.0d0)
    if ((a * 120.0d0) <= (-4d-112)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d-134) then
        tmp = 60.0d0 / ((t - z) / (y - x))
    else if ((a * 120.0d0) <= 5d+33) then
        tmp = t_1
    else
        tmp = (x * (60.0d0 / z)) + (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 * y) / t) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -4e-112) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-134) {
		tmp = 60.0 / ((t - z) / (y - x));
	} else if ((a * 120.0) <= 5e+33) {
		tmp = t_1;
	} else {
		tmp = (x * (60.0 / z)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((60.0 * y) / t) + (a * 120.0)
	tmp = 0
	if (a * 120.0) <= -4e-112:
		tmp = t_1
	elif (a * 120.0) <= 5e-134:
		tmp = 60.0 / ((t - z) / (y - x))
	elif (a * 120.0) <= 5e+33:
		tmp = t_1
	else:
		tmp = (x * (60.0 / z)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(60.0 * y) / t) + Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-112)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e-134)
		tmp = Float64(60.0 / Float64(Float64(t - z) / Float64(y - x)));
	elseif (Float64(a * 120.0) <= 5e+33)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(60.0 / z)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((60.0 * y) / t) + (a * 120.0);
	tmp = 0.0;
	if ((a * 120.0) <= -4e-112)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e-134)
		tmp = 60.0 / ((t - z) / (y - x));
	elseif ((a * 120.0) <= 5e+33)
		tmp = t_1;
	else
		tmp = (x * (60.0 / z)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-112], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-134], N[(60.0 / N[(N[(t - z), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+33], t$95$1, N[(N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -3.9999999999999998e-112 or 5.0000000000000003e-134 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999973e33

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 87.6%

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

   4. Taylor expanded in z around 0 74.4%

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

      1. associate-*r/ 74.4%

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

      2. *-commutative 74.4%

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

   6. Simplified 74.4%

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

   if -3.9999999999999998e-112 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000003e-134

   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%

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

      2. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 85.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   6. 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%

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

   7. Applied egg-rr 85.7%

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

   if 4.99999999999999973e33 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.4%

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

      1. *-commutative 98.4%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 88.8%

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

   6. Taylor expanded in z around inf 82.4%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-112}:\\ \;\;\;\;\frac{60 \cdot y}{t} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-134}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y - x}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+33}:\\ \;\;\;\;\frac{60 \cdot y}{t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot y}{t} + a \cdot 120\\ \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-134}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (* 60.0 y) t) (* a 120.0))))
   (if (<= (* a 120.0) -4e-112)
     t_1
     (if (<= (* a 120.0) 5e-134)
       (* (- x y) (/ 60.0 (- z t)))
       (if (<= (* a 120.0) 5e+33) t_1 (+ (* x (/ 60.0 z)) (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((60.0 * y) / t) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -4e-112) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-134) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 5e+33) {
		tmp = t_1;
	} else {
		tmp = (x * (60.0 / z)) + (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 * y) / t) + (a * 120.0d0)
    if ((a * 120.0d0) <= (-4d-112)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d-134) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if ((a * 120.0d0) <= 5d+33) then
        tmp = t_1
    else
        tmp = (x * (60.0d0 / z)) + (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 * y) / t) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -4e-112) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-134) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 5e+33) {
		tmp = t_1;
	} else {
		tmp = (x * (60.0 / z)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((60.0 * y) / t) + (a * 120.0)
	tmp = 0
	if (a * 120.0) <= -4e-112:
		tmp = t_1
	elif (a * 120.0) <= 5e-134:
		tmp = (x - y) * (60.0 / (z - t))
	elif (a * 120.0) <= 5e+33:
		tmp = t_1
	else:
		tmp = (x * (60.0 / z)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(60.0 * y) / t) + Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-112)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e-134)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 5e+33)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(60.0 / z)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((60.0 * y) / t) + (a * 120.0);
	tmp = 0.0;
	if ((a * 120.0) <= -4e-112)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e-134)
		tmp = (x - y) * (60.0 / (z - t));
	elseif ((a * 120.0) <= 5e+33)
		tmp = t_1;
	else
		tmp = (x * (60.0 / z)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-112], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-134], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+33], t$95$1, N[(N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -3.9999999999999998e-112 or 5.0000000000000003e-134 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999973e33

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 87.6%

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

   4. Taylor expanded in z around 0 74.4%

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

      1. associate-*r/ 74.4%

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

      2. *-commutative 74.4%

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

   6. Simplified 74.4%

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

   if -3.9999999999999998e-112 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000003e-134

   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 85.6%

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

      1. associate-*r/ 85.6%

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

      2. associate-*l/ 85.6%

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

      3. *-commutative 85.6%

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

   9. Simplified 85.6%

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

   if 4.99999999999999973e33 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.4%

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

      1. *-commutative 98.4%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 88.8%

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

   6. Taylor expanded in z around inf 82.4%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-112}:\\ \;\;\;\;\frac{60 \cdot y}{t} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-134}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+33}:\\ \;\;\;\;\frac{60 \cdot y}{t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-134}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-48}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e+52)
   (* a 120.0)
   (if (<= (* a 120.0) 5e-134)
     (* (- x y) (/ 60.0 (- z t)))
     (if (<= (* a 120.0) 1e-48)
       (* a 120.0)
       (+ (* x (/ 60.0 z)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e+52) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-134) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 1e-48) {
		tmp = a * 120.0;
	} else {
		tmp = (x * (60.0 / z)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-1d+52)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d-134) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if ((a * 120.0d0) <= 1d-48) then
        tmp = a * 120.0d0
    else
        tmp = (x * (60.0d0 / z)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e+52) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-134) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 1e-48) {
		tmp = a * 120.0;
	} else {
		tmp = (x * (60.0 / z)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e+52:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e-134:
		tmp = (x - y) * (60.0 / (z - t))
	elif (a * 120.0) <= 1e-48:
		tmp = a * 120.0
	else:
		tmp = (x * (60.0 / z)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e+52)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e-134)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1e-48)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x * Float64(60.0 / z)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e+52)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e-134)
		tmp = (x - y) * (60.0 / (z - t));
	elseif ((a * 120.0) <= 1e-48)
		tmp = a * 120.0;
	else
		tmp = (x * (60.0 / z)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e+52], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-134], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-48], N[(a * 120.0), $MachinePrecision], N[(N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.9999999999999999e51 or 5.0000000000000003e-134 < (*.f64 a #s(literal 120 binary64)) < 9.9999999999999997e-49

   1. Initial program 98.7%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 81.9%

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

   if -9.9999999999999999e51 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000003e-134

   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 78.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   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/ 78.1%

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

      3. *-commutative 78.1%

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

   9. Simplified 78.1%

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

   if 9.9999999999999997e-49 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 83.7%

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

   6. Taylor expanded in z around inf 78.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-134}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-48}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t}\\ \mathbf{if}\;z - t \leq -2 \cdot 10^{+65} \lor \neg \left(z - t \leq 4 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot t\_1 + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (- z t))))
   (if (or (<= (- z t) -2e+65) (not (<= (- z t) 4e-47)))
     (+ (* x t_1) (* a 120.0))
     (* (- x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if (((z - t) <= -2e+65) || !((z - t) <= 4e-47)) {
		tmp = (x * t_1) + (a * 120.0);
	} else {
		tmp = (x - y) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 / (z - t)
    if (((z - t) <= (-2d+65)) .or. (.not. ((z - t) <= 4d-47))) then
        tmp = (x * t_1) + (a * 120.0d0)
    else
        tmp = (x - y) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if (((z - t) <= -2e+65) || !((z - t) <= 4e-47)) {
		tmp = (x * t_1) + (a * 120.0);
	} else {
		tmp = (x - y) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / (z - t)
	tmp = 0
	if ((z - t) <= -2e+65) or not ((z - t) <= 4e-47):
		tmp = (x * t_1) + (a * 120.0)
	else:
		tmp = (x - y) * t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(z - t))
	tmp = 0.0
	if ((Float64(z - t) <= -2e+65) || !(Float64(z - t) <= 4e-47))
		tmp = Float64(Float64(x * t_1) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(x - y) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / (z - t);
	tmp = 0.0;
	if (((z - t) <= -2e+65) || ~(((z - t) <= 4e-47)))
		tmp = (x * t_1) + (a * 120.0);
	else
		tmp = (x - y) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(z - t), $MachinePrecision], -2e+65], N[Not[LessEqual[N[(z - t), $MachinePrecision], 4e-47]], $MachinePrecision]], N[(N[(x * t$95$1), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -2e65 or 3.9999999999999999e-47 < (-.f64 z t)

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 88.9%

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

   if -2e65 < (-.f64 z t) < 3.9999999999999999e-47

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. 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. Taylor expanded in a around 0 81.5%

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

      1. associate-*r/ 81.6%

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

      2. associate-*l/ 81.6%

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

      3. *-commutative 81.6%

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

   9. Simplified 81.6%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+65} \lor \neg \left(z - t \leq 4 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t}\\ \mathbf{if}\;z - t \leq -2 \cdot 10^{+65}:\\ \;\;\;\;x \cdot t\_1 + a \cdot 120\\ \mathbf{elif}\;z - t \leq 4 \cdot 10^{-47}:\\ \;\;\;\;\left(x - y\right) \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{t - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (- z t))))
   (if (<= (- z t) -2e+65)
     (+ (* x t_1) (* a 120.0))
     (if (<= (- z t) 4e-47)
       (* (- x y) t_1)
       (- (* a 120.0) (/ 60.0 (/ (- t z) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if ((z - t) <= -2e+65) {
		tmp = (x * t_1) + (a * 120.0);
	} else if ((z - t) <= 4e-47) {
		tmp = (x - y) * t_1;
	} else {
		tmp = (a * 120.0) - (60.0 / ((t - z) / 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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 / (z - t)
    if ((z - t) <= (-2d+65)) then
        tmp = (x * t_1) + (a * 120.0d0)
    else if ((z - t) <= 4d-47) then
        tmp = (x - y) * t_1
    else
        tmp = (a * 120.0d0) - (60.0d0 / ((t - z) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if ((z - t) <= -2e+65) {
		tmp = (x * t_1) + (a * 120.0);
	} else if ((z - t) <= 4e-47) {
		tmp = (x - y) * t_1;
	} else {
		tmp = (a * 120.0) - (60.0 / ((t - z) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / (z - t)
	tmp = 0
	if (z - t) <= -2e+65:
		tmp = (x * t_1) + (a * 120.0)
	elif (z - t) <= 4e-47:
		tmp = (x - y) * t_1
	else:
		tmp = (a * 120.0) - (60.0 / ((t - z) / x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(z - t))
	tmp = 0.0
	if (Float64(z - t) <= -2e+65)
		tmp = Float64(Float64(x * t_1) + Float64(a * 120.0));
	elseif (Float64(z - t) <= 4e-47)
		tmp = Float64(Float64(x - y) * t_1);
	else
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 / Float64(Float64(t - z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / (z - t);
	tmp = 0.0;
	if ((z - t) <= -2e+65)
		tmp = (x * t_1) + (a * 120.0);
	elseif ((z - t) <= 4e-47)
		tmp = (x - y) * t_1;
	else
		tmp = (a * 120.0) - (60.0 / ((t - z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z - t), $MachinePrecision], -2e+65], N[(N[(x * t$95$1), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 4e-47], N[(N[(x - y), $MachinePrecision] * t$95$1), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 z t) < -2e65

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 89.2%

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

   if -2e65 < (-.f64 z t) < 3.9999999999999999e-47

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. 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. Taylor expanded in a around 0 81.5%

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

      1. associate-*r/ 81.6%

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

      2. associate-*l/ 81.6%

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

      3. *-commutative 81.6%

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

   9. Simplified 81.6%

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

   if 3.9999999999999999e-47 < (-.f64 z t)

   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. 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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 88.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;z - t \leq 4 \cdot 10^{-47}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{t - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+52} \lor \neg \left(a \cdot 120 \leq 10^{+97}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -1e+52) (not (<= (* a 120.0) 1e+97)))
   (* 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) <= -1e+52) || !((a * 120.0) <= 1e+97)) {
		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) <= (-1d+52)) .or. (.not. ((a * 120.0d0) <= 1d+97))) 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) <= -1e+52) || !((a * 120.0) <= 1e+97)) {
		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) <= -1e+52) or not ((a * 120.0) <= 1e+97):
		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) <= -1e+52) || !(Float64(a * 120.0) <= 1e+97))
		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) <= -1e+52) || ~(((a * 120.0) <= 1e+97)))
		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], -1e+52], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+97]], $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)) < -9.9999999999999999e51 or 1.0000000000000001e97 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.0%

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

      1. associate-/l* 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 85.1%

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

   if -9.9999999999999999e51 < (*.f64 a #s(literal 120 binary64)) < 1.0000000000000001e97

   1. Initial program 99.0%

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

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

      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. Taylor expanded in a around 0 70.3%

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

      1. associate-*r/ 69.7%

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

      2. associate-*l/ 70.4%

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

      3. *-commutative 70.4%

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

   9. Simplified 70.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+52} \lor \neg \left(a \cdot 120 \leq 10^{+97}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-38} \lor \neg \left(x \leq 3.2 \cdot 10^{+142}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.1e-38) (not (<= x 3.2e+142)))
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))
   (+ (/ (* y -60.0) (- z t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.1e-38) || !(x <= 3.2e+142)) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.1d-38)) .or. (.not. (x <= 3.2d+142))) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.1e-38) || !(x <= 3.2e+142)) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.1e-38) or not (x <= 3.2e+142):
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	else:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.1e-38) || !(x <= 3.2e+142))
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.1e-38) || ~((x <= 3.2e+142)))
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	else
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.1e-38], N[Not[LessEqual[x, 3.2e+142]], $MachinePrecision]], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000013e-38 or 3.20000000000000005e142 < x

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 91.0%

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

   if -2.10000000000000013e-38 < x < 3.20000000000000005e142

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 95.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-38} \lor \neg \left(x \leq 3.2 \cdot 10^{+142}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-38}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{+142}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4e-38)
   (+ (/ (* 60.0 x) (- z t)) (* a 120.0))
   (if (<= x 4.7e+142)
     (+ (/ 60.0 (/ (- t z) y)) (* a 120.0))
     (+ (* x (/ 60.0 (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e-38) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else if (x <= 4.7e+142) {
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	} else {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-4d-38)) then
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    else if (x <= 4.7d+142) then
        tmp = (60.0d0 / ((t - z) / y)) + (a * 120.0d0)
    else
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e-38) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else if (x <= 4.7e+142) {
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	} else {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4e-38:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	elif x <= 4.7e+142:
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0)
	else:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4e-38)
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	elseif (x <= 4.7e+142)
		tmp = Float64(Float64(60.0 / Float64(Float64(t - z) / y)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4e-38)
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	elseif (x <= 4.7e+142)
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	else
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4e-38], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.7e+142], N[(N[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9999999999999998e-38

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 89.7%

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

      1. associate-*r/ 89.8%

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

   7. Simplified 89.8%

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

   if -3.9999999999999998e-38 < x < 4.7e142

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. 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 0 96.0%

      \[\leadsto \frac{60}{\frac{z - t}{\color{blue}{-1 \cdot y}}} + a \cdot 120 \]
   8. Step-by-step derivation

      1. neg-mul-1 96.0%

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

   9. Simplified 96.0%

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

   if 4.7e142 < x

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 94.1%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-38}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{+142}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+142}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.4e-38)
   (+ (/ (* 60.0 x) (- z t)) (* a 120.0))
   (if (<= x 3.4e+142)
     (+ (/ (* y -60.0) (- z t)) (* a 120.0))
     (+ (* x (/ 60.0 (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.4e-38) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else if (x <= 3.4e+142) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3.4d-38)) then
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    else if (x <= 3.4d+142) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.4e-38) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else if (x <= 3.4e+142) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.4e-38:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	elif x <= 3.4e+142:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.4e-38)
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	elseif (x <= 3.4e+142)
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.4e-38)
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	elseif (x <= 3.4e+142)
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.4e-38], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+142], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4000000000000002e-38

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 89.7%

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

      1. associate-*r/ 89.8%

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

   7. Simplified 89.8%

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

   if -3.4000000000000002e-38 < x < 3.3999999999999998e142

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 95.9%

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

   if 3.3999999999999998e142 < x

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 94.1%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+142}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+48} \lor \neg \left(a \leq 4.8 \cdot 10^{+94}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e+48) (not (<= a 4.8e+94)))
   (* a 120.0)
   (* 60.0 (/ (- y x) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e+48) || !(a <= 4.8e+94)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((y - x) / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.8d+48)) .or. (.not. (a <= 4.8d+94))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((y - x) / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e+48) || !(a <= 4.8e+94)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((y - x) / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e+48) or not (a <= 4.8e+94):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((y - x) / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e+48) || !(a <= 4.8e+94))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(y - x) / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e+48) || ~((a <= 4.8e+94)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((y - x) / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e+48], N[Not[LessEqual[a, 4.8e+94]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(y - x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8000000000000002e48 or 4.79999999999999965e94 < a

   1. Initial program 99.0%

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

      1. associate-/l* 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 85.1%

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

   if -4.8000000000000002e48 < a < 4.79999999999999965e94

   1. Initial program 99.0%

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

      1. associate-/l* 99.6%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 70.3%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+48} \lor \neg \left(a \leq 4.8 \cdot 10^{+94}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-115} \lor \neg \left(a \leq 2.1 \cdot 10^{-132}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.85e-115) (not (<= a 2.1e-132)))
   (* a 120.0)
   (/ (* x -60.0) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e-115) || !(a <= 2.1e-132)) {
		tmp = a * 120.0;
	} else {
		tmp = (x * -60.0) / (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.85d-115)) .or. (.not. (a <= 2.1d-132))) then
        tmp = a * 120.0d0
    else
        tmp = (x * (-60.0d0)) / (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e-115) || !(a <= 2.1e-132)) {
		tmp = a * 120.0;
	} else {
		tmp = (x * -60.0) / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.85e-115) or not (a <= 2.1e-132):
		tmp = a * 120.0
	else:
		tmp = (x * -60.0) / (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.85e-115) || !(a <= 2.1e-132))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x * -60.0) / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.85e-115) || ~((a <= 2.1e-132)))
		tmp = a * 120.0;
	else
		tmp = (x * -60.0) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.85e-115], N[Not[LessEqual[a, 2.1e-132]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(x * -60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.85e-115 or 2.1000000000000001e-132 < a

   1. Initial program 98.8%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 71.6%

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

   if -1.85e-115 < a < 2.1000000000000001e-132

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 90.9%

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

   6. Taylor expanded in x around inf 51.2%

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

      1. associate-*r/ 51.3%

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

   8. Simplified 51.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-115} \lor \neg \left(a \leq 2.1 \cdot 10^{-132}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-114} \lor \neg \left(a \leq 2.4 \cdot 10^{-131}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.2e-114) (not (<= a 2.4e-131)))
   (* a 120.0)
   (/ -60.0 (/ (- t z) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.2e-114) || !(a <= 2.4e-131)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((t - z) / 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 ((a <= (-1.2d-114)) .or. (.not. (a <= 2.4d-131))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / ((t - z) / 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 ((a <= -1.2e-114) || !(a <= 2.4e-131)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((t - z) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.2e-114) or not (a <= 2.4e-131):
		tmp = a * 120.0
	else:
		tmp = -60.0 / ((t - z) / x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.2e-114) || !(a <= 2.4e-131))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(Float64(t - z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.2e-114) || ~((a <= 2.4e-131)))
		tmp = a * 120.0;
	else
		tmp = -60.0 / ((t - z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.2e-114], N[Not[LessEqual[a, 2.4e-131]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2000000000000001e-114 or 2.4e-131 < a

   1. Initial program 98.8%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 71.6%

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

   if -1.2000000000000001e-114 < a < 2.4e-131

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 90.9%

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

   6. Taylor expanded in x around inf 51.2%

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

      1. clear-num 51.2%

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

      2. un-div-inv 51.3%

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

   8. Applied egg-rr 51.3%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-114} \lor \neg \left(a \leq 2.4 \cdot 10^{-131}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-115} \lor \neg \left(a \leq 4.6 \cdot 10^{-132}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.4e-115) (not (<= a 4.6e-132)))
   (* a 120.0)
   (* x (/ -60.0 (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.4e-115) || !(a <= 4.6e-132)) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.4d-115)) .or. (.not. (a <= 4.6d-132))) then
        tmp = a * 120.0d0
    else
        tmp = x * ((-60.0d0) / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.4e-115) || !(a <= 4.6e-132)) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.4e-115) or not (a <= 4.6e-132):
		tmp = a * 120.0
	else:
		tmp = x * (-60.0 / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.4e-115) || !(a <= 4.6e-132))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(-60.0 / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.4e-115) || ~((a <= 4.6e-132)))
		tmp = a * 120.0;
	else
		tmp = x * (-60.0 / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.4e-115], N[Not[LessEqual[a, 4.6e-132]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(x * N[(-60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.3999999999999999e-115 or 4.60000000000000006e-132 < a

   1. Initial program 98.8%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 71.6%

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

   if -4.3999999999999999e-115 < a < 4.60000000000000006e-132

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 90.9%

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

   6. Taylor expanded in x around inf 51.2%

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

      1. clear-num 51.2%

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

      2. un-div-inv 51.3%

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

   8. Applied egg-rr 51.3%

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

      1. associate-/r/ 51.2%

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

   10. Simplified 51.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-115} \lor \neg \left(a \leq 4.6 \cdot 10^{-132}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-115} \lor \neg \left(a \leq 10^{-130}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.5e-115) (not (<= a 1e-130)))
   (* a 120.0)
   (* -60.0 (/ x (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.5e-115) || !(a <= 1e-130)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6.5d-115)) .or. (.not. (a <= 1d-130))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.5e-115) || !(a <= 1e-130)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.5e-115) or not (a <= 1e-130):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.5e-115) || !(a <= 1e-130))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.5e-115) || ~((a <= 1e-130)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.5e-115], N[Not[LessEqual[a, 1e-130]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.50000000000000033e-115 or 1.0000000000000001e-130 < a

   1. Initial program 98.8%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 71.6%

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

   if -6.50000000000000033e-115 < a < 1.0000000000000001e-130

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 90.9%

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

   6. Taylor expanded in x around inf 51.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-115} \lor \neg \left(a \leq 10^{-130}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-116} \lor \neg \left(a \leq 1.8 \cdot 10^{-220}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.65e-116) (not (<= a 1.8e-220)))
   (* a 120.0)
   (/ -60.0 (/ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.65e-116) || !(a <= 1.8e-220)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (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 ((a <= (-1.65d-116)) .or. (.not. (a <= 1.8d-220))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / (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 ((a <= -1.65e-116) || !(a <= 1.8e-220)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.65e-116) or not (a <= 1.8e-220):
		tmp = a * 120.0
	else:
		tmp = -60.0 / (t / x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.65e-116) || !(a <= 1.8e-220))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(t / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.65e-116) || ~((a <= 1.8e-220)))
		tmp = a * 120.0;
	else
		tmp = -60.0 / (t / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.65e-116], N[Not[LessEqual[a, 1.8e-220]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.65e-116 or 1.8000000000000001e-220 < a

   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%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 65.7%

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

   if -1.65e-116 < a < 1.8000000000000001e-220

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.5%

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

      3. fma-define 99.5%

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

      4. sub-neg 99.5%

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

      5. +-commutative 99.5%

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

      6. neg-sub0 99.5%

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

      7. associate-+l- 99.5%

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

      8. sub0-neg 99.5%

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

      9. distribute-frac-neg2 99.5%

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

      10. distribute-neg-frac 99.5%

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

      11. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 92.1%

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

   6. Taylor expanded in x around inf 59.0%

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

      1. clear-num 59.1%

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

      2. un-div-inv 59.1%

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

   8. Applied egg-rr 59.1%

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

   9. Taylor expanded in t around inf 35.0%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-116} \lor \neg \left(a \leq 1.8 \cdot 10^{-220}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-117} \lor \neg \left(a \leq 1.75 \cdot 10^{-220}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.35e-117) (not (<= a 1.75e-220)))
   (* a 120.0)
   (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e-117) || !(a <= 1.75e-220)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.35d-117)) .or. (.not. (a <= 1.75d-220))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e-117) || !(a <= 1.75e-220)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.35e-117) or not (a <= 1.75e-220):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.35e-117) || !(a <= 1.75e-220))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.35e-117) || ~((a <= 1.75e-220)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.35e-117], N[Not[LessEqual[a, 1.75e-220]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.35000000000000001e-117 or 1.74999999999999994e-220 < a

   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%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 65.7%

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

   if -1.35000000000000001e-117 < a < 1.74999999999999994e-220

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.5%

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

      3. fma-define 99.5%

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

      4. sub-neg 99.5%

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

      5. +-commutative 99.5%

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

      6. neg-sub0 99.5%

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

      7. associate-+l- 99.5%

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

      8. sub0-neg 99.5%

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

      9. distribute-frac-neg2 99.5%

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

      10. distribute-neg-frac 99.5%

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

      11. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 92.1%

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

   6. Taylor expanded in x around inf 59.0%

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

   7. Taylor expanded in t around inf 35.0%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-117} \lor \neg \left(a \leq 1.75 \cdot 10^{-220}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 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 99.0%

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

   1. *-commutative 99.0%

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

   2. associate-/l* 99.8%

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

4. Applied egg-rr 99.8%

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

Alternative 19: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 20: 51.3% 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 99.0%

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

   1. associate-/l* 99.8%

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

   2. fma-define 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 54.7%

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

6. Final simplification 54.7%

   \[\leadsto a \cdot 120 \]
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 2024172 
(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)))