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

Percentage Accurate: 99.4% → 99.8%

Time: 12.7s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 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 98.0%

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

   1. *-commutative 98.0%

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

   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 2: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;t\_1 \leq 3.3 \cdot 10^{-151}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+31}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+17)
     (/ 60.0 (/ (- z t) (- x y)))
     (if (<= t_1 3.3e-151)
       (* a 120.0)
       (if (<= t_1 5e+31)
         (+ (* a 120.0) (* x (/ -60.0 t)))
         (* 60.0 (/ (- x y) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+17) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t_1 <= 3.3e-151) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+31) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-2d+17)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (t_1 <= 3.3d-151) then
        tmp = a * 120.0d0
    else if (t_1 <= 5d+31) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+17) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t_1 <= 3.3e-151) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+31) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -2e+17:
		tmp = 60.0 / ((z - t) / (x - y))
	elif t_1 <= 3.3e-151:
		tmp = a * 120.0
	elif t_1 <= 5e+31:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+17)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (t_1 <= 3.3e-151)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 5e+31)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+17)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (t_1 <= 3.3e-151)
		tmp = a * 120.0;
	elseif (t_1 <= 5e+31)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+17], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 3.3e-151], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+31], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2e17

   1. Initial program 95.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 82.5%

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

      1. clear-num 82.5%

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

      2. un-div-inv 82.6%

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

   7. Applied egg-rr 82.6%

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

   if -2e17 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 3.2999999999999999e-151

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      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 82.0%

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

   if 3.2999999999999999e-151 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000027e31

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.9%

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

   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 82.1%

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

   6. Taylor expanded in z around 0 63.4%

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

   if 5.00000000000000027e31 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 94.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 83.6%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+17}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 3.3 \cdot 10^{-151}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+31}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-177}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-235}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-56}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* x (/ -60.0 t)))))
   (if (<= t -1.8e-6)
     t_1
     (if (<= t -1.7e-177)
       (* 60.0 (/ (- x y) (- z t)))
       (if (<= t -1.9e-235)
         (+ (* a 120.0) (/ (* x 60.0) z))
         (if (<= t 1.75e-56) (+ (* a 120.0) (* -60.0 (/ y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (-60.0 / t));
	double tmp;
	if (t <= -1.8e-6) {
		tmp = t_1;
	} else if (t <= -1.7e-177) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t <= -1.9e-235) {
		tmp = (a * 120.0) + ((x * 60.0) / z);
	} else if (t <= 1.75e-56) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (x * ((-60.0d0) / t))
    if (t <= (-1.8d-6)) then
        tmp = t_1
    else if (t <= (-1.7d-177)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t <= (-1.9d-235)) then
        tmp = (a * 120.0d0) + ((x * 60.0d0) / z)
    else if (t <= 1.75d-56) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (-60.0 / t));
	double tmp;
	if (t <= -1.8e-6) {
		tmp = t_1;
	} else if (t <= -1.7e-177) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t <= -1.9e-235) {
		tmp = (a * 120.0) + ((x * 60.0) / z);
	} else if (t <= 1.75e-56) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (x * (-60.0 / t))
	tmp = 0
	if t <= -1.8e-6:
		tmp = t_1
	elif t <= -1.7e-177:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t <= -1.9e-235:
		tmp = (a * 120.0) + ((x * 60.0) / z)
	elif t <= 1.75e-56:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)))
	tmp = 0.0
	if (t <= -1.8e-6)
		tmp = t_1;
	elseif (t <= -1.7e-177)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t <= -1.9e-235)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * 60.0) / z));
	elseif (t <= 1.75e-56)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (x * (-60.0 / t));
	tmp = 0.0;
	if (t <= -1.8e-6)
		tmp = t_1;
	elseif (t <= -1.7e-177)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t <= -1.9e-235)
		tmp = (a * 120.0) + ((x * 60.0) / z);
	elseif (t <= 1.75e-56)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e-6], t$95$1, If[LessEqual[t, -1.7e-177], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e-235], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * 60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-56], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.79999999999999992e-6 or 1.7499999999999999e-56 < t

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      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. Taylor expanded in x around inf 80.7%

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

   6. Taylor expanded in z around 0 72.9%

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

   if -1.79999999999999992e-6 < t < -1.7e-177

   1. Initial program 96.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 79.8%

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

   if -1.7e-177 < t < -1.90000000000000013e-235

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 90.8%

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

   4. Taylor expanded in x around inf 85.2%

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

   if -1.90000000000000013e-235 < t < 1.7499999999999999e-56

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. remove-double-neg 89.5%

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

      3. neg-mul-1 89.5%

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

      4. times-frac 89.5%

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

      5. metadata-eval 89.5%

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

      6. neg-sub0 89.5%

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

      7. sub-neg 89.5%

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

      8. +-commutative 89.5%

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

      9. associate--r+ 89.5%

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

      10. neg-sub0 89.5%

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

      11. remove-double-neg 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in t around 0 85.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-6}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-177}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-235}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-56}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-179}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-236}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* x (/ -60.0 t)))))
   (if (<= t -5.6e-5)
     t_1
     (if (<= t -1.3e-179)
       (* 60.0 (/ (- x y) (- z t)))
       (if (<= t -8e-236)
         (+ (* a 120.0) (* x (/ 60.0 z)))
         (if (<= t 5.8e-57) (+ (* a 120.0) (* -60.0 (/ y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (-60.0 / t));
	double tmp;
	if (t <= -5.6e-5) {
		tmp = t_1;
	} else if (t <= -1.3e-179) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t <= -8e-236) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if (t <= 5.8e-57) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (x * ((-60.0d0) / t))
    if (t <= (-5.6d-5)) then
        tmp = t_1
    else if (t <= (-1.3d-179)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t <= (-8d-236)) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / z))
    else if (t <= 5.8d-57) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (-60.0 / t));
	double tmp;
	if (t <= -5.6e-5) {
		tmp = t_1;
	} else if (t <= -1.3e-179) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t <= -8e-236) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if (t <= 5.8e-57) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (x * (-60.0 / t))
	tmp = 0
	if t <= -5.6e-5:
		tmp = t_1
	elif t <= -1.3e-179:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t <= -8e-236:
		tmp = (a * 120.0) + (x * (60.0 / z))
	elif t <= 5.8e-57:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)))
	tmp = 0.0
	if (t <= -5.6e-5)
		tmp = t_1;
	elseif (t <= -1.3e-179)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t <= -8e-236)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / z)));
	elseif (t <= 5.8e-57)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (x * (-60.0 / t));
	tmp = 0.0;
	if (t <= -5.6e-5)
		tmp = t_1;
	elseif (t <= -1.3e-179)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t <= -8e-236)
		tmp = (a * 120.0) + (x * (60.0 / z));
	elseif (t <= 5.8e-57)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e-5], t$95$1, If[LessEqual[t, -1.3e-179], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e-236], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-57], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.59999999999999992e-5 or 5.8000000000000005e-57 < t

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      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. Taylor expanded in x around inf 80.7%

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

   6. Taylor expanded in z around 0 72.9%

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

   if -5.59999999999999992e-5 < t < -1.30000000000000003e-179

   1. Initial program 96.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 79.8%

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

   if -1.30000000000000003e-179 < t < -8.0000000000000004e-236

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      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. Taylor expanded in x around inf 80.3%

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

   6. Taylor expanded in z around inf 85.1%

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

   if -8.0000000000000004e-236 < t < 5.8000000000000005e-57

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. remove-double-neg 89.5%

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

      3. neg-mul-1 89.5%

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

      4. times-frac 89.5%

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

      5. metadata-eval 89.5%

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

      6. neg-sub0 89.5%

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

      7. sub-neg 89.5%

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

      8. +-commutative 89.5%

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

      9. associate--r+ 89.5%

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

      10. neg-sub0 89.5%

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

      11. remove-double-neg 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in t around 0 85.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-5}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-179}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-236}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-57}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+22} \lor \neg \left(x - y \leq 10^{+156}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- x y) -5e+22) (not (<= (- x y) 1e+156)))
   (* 60.0 (/ (- x y) (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x - y) <= -5e+22) || !((x - y) <= 1e+156)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x - y) <= (-5d+22)) .or. (.not. ((x - y) <= 1d+156))) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x - y) <= -5e+22) || !((x - y) <= 1e+156)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x - y) <= -5e+22) or not ((x - y) <= 1e+156):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x - y) <= -5e+22) || !(Float64(x - y) <= 1e+156))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x - y) <= -5e+22) || ~(((x - y) <= 1e+156)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x - y), $MachinePrecision], -5e+22], N[Not[LessEqual[N[(x - y), $MachinePrecision], 1e+156]], $MachinePrecision]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x y) < -4.9999999999999996e22 or 9.9999999999999998e155 < (-.f64 x y)

   1. Initial program 96.5%

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

      1. associate-/l* 99.7%

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

      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 72.0%

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

   if -4.9999999999999996e22 < (-.f64 x y) < 9.9999999999999998e155

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      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 78.5%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+22} \lor \neg \left(x - y \leq 10^{+156}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-71}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-65}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-71)
   (* a 120.0)
   (if (<= (* a 120.0) 5e-65)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* -60.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e-71) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-65) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-1d-71)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d-65) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e-71) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-65) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e-71:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e-65:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-71)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e-65)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e-71)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e-65)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (-60.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-71], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-65], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.9999999999999992e-72

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      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 72.5%

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

   if -9.9999999999999992e-72 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999983e-65

   1. Initial program 97.1%

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

      1. associate-/l* 99.7%

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

      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 78.9%

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

   if 4.99999999999999983e-65 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 97.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 87.5%

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

      1. associate-*r/ 86.2%

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

      2. remove-double-neg 86.2%

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

      3. neg-mul-1 86.2%

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

      4. times-frac 87.5%

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

      5. metadata-eval 87.5%

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

      6. neg-sub0 87.5%

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

      7. sub-neg 87.5%

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

      8. +-commutative 87.5%

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

      9. associate--r+ 87.5%

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

      10. neg-sub0 87.5%

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

      11. remove-double-neg 87.5%

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

   7. Simplified 87.5%

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

   8. Taylor expanded in t around 0 71.8%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-71}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-65}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+28} \lor \neg \left(y \leq 1.25 \cdot 10^{+27}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.3e+28) (not (<= y 1.25e+27)))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.3e+28) || !(y <= 1.25e+27)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.3d+28)) .or. (.not. (y <= 1.25d+27))) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    else
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.3e+28) || !(y <= 1.25e+27)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.3e+28) or not (y <= 1.25e+27):
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.3e+28) || !(y <= 1.25e+27))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.3e+28) || ~((y <= 1.25e+27)))
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.3e+28], N[Not[LessEqual[y, 1.25e+27]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e28 or 1.24999999999999995e27 < y

   1. Initial program 96.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 89.4%

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

      1. associate-*r/ 86.9%

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

      2. remove-double-neg 86.9%

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

      3. neg-mul-1 86.9%

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

      4. times-frac 89.4%

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

      5. metadata-eval 89.4%

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

      6. neg-sub0 89.4%

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

      7. sub-neg 89.4%

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

      8. +-commutative 89.4%

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

      9. associate--r+ 89.4%

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

      10. neg-sub0 89.4%

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

      11. remove-double-neg 89.4%

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

   7. Simplified 89.4%

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

   if -3.3e28 < y < 1.24999999999999995e27

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      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 96.3%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+28} \lor \neg \left(y \leq 1.25 \cdot 10^{+27}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+141} \lor \neg \left(x \leq 3.6 \cdot 10^{+163}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4e+141) (not (<= x 3.6e+163)))
   (/ 60.0 (/ (- z t) (- x y)))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4e+141) || !(x <= 3.6e+163)) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (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 ((x <= (-4d+141)) .or. (.not. (x <= 3.6d+163))) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (y / (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 ((x <= -4e+141) || !(x <= 3.6e+163)) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4e+141) or not (x <= 3.6e+163):
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4e+141) || !(x <= 3.6e+163))
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4e+141) || ~((x <= 3.6e+163)))
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4e+141], N[Not[LessEqual[x, 3.6e+163]], $MachinePrecision]], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000007e141 or 3.59999999999999978e163 < x

   1. Initial program 93.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 82.3%

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

      1. clear-num 82.4%

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

      2. un-div-inv 82.4%

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

   7. Applied egg-rr 82.4%

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

   if -4.00000000000000007e141 < x < 3.59999999999999978e163

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 90.1%

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

      1. associate-*r/ 89.6%

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

      2. remove-double-neg 89.6%

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

      3. neg-mul-1 89.6%

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

      4. times-frac 90.1%

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

      5. metadata-eval 90.1%

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

      6. neg-sub0 90.1%

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

      7. sub-neg 90.1%

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

      8. +-commutative 90.1%

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

      9. associate--r+ 90.1%

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

      10. neg-sub0 90.1%

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

      11. remove-double-neg 90.1%

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

   7. Simplified 90.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+141} \lor \neg \left(x \leq 3.6 \cdot 10^{+163}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.1e+30)
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))
   (if (<= y 1.8e+27)
     (+ (* a 120.0) (* x (/ 60.0 (- z t))))
     (+ (* a 120.0) (* y (/ 60.0 (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.1e+30) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else if (y <= 1.8e+27) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + (y * (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 (y <= (-2.1d+30)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    else if (y <= 1.8d+27) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    else
        tmp = (a * 120.0d0) + (y * (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 (y <= -2.1e+30) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else if (y <= 1.8e+27) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + (y * (60.0 / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.1e+30:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	elif y <= 1.8e+27:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	else:
		tmp = (a * 120.0) + (y * (60.0 / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.1e+30)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	elseif (y <= 1.8e+27)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(60.0 / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.1e+30)
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	elseif (y <= 1.8e+27)
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	else
		tmp = (a * 120.0) + (y * (60.0 / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.1e+30], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+27], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1e30

   1. Initial program 98.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 90.4%

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

      1. associate-*r/ 88.6%

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

      2. remove-double-neg 88.6%

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

      3. neg-mul-1 88.6%

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

      4. times-frac 90.4%

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

      5. metadata-eval 90.4%

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

      6. neg-sub0 90.4%

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

      7. sub-neg 90.4%

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

      8. +-commutative 90.4%

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

      9. associate--r+ 90.4%

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

      10. neg-sub0 90.4%

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

      11. remove-double-neg 90.4%

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

   7. Simplified 90.4%

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

   if -2.1e30 < y < 1.79999999999999991e27

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      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 96.3%

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

   if 1.79999999999999991e27 < y

   1. Initial program 95.1%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 88.6%

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

      1. associate-*r/ 85.5%

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

      2. remove-double-neg 85.5%

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

      3. neg-mul-1 85.5%

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

      4. times-frac 88.6%

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

      5. metadata-eval 88.6%

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

      6. neg-sub0 88.6%

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

      7. sub-neg 88.6%

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

      8. +-commutative 88.6%

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

      9. associate--r+ 88.6%

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

      10. neg-sub0 88.6%

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

      11. remove-double-neg 88.6%

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

   7. Simplified 88.6%

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

      1. clear-num 88.6%

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

      2. un-div-inv 88.6%

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

   9. Applied egg-rr 88.6%

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

       1. associate-/r/ 88.7%

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

   11. Applied egg-rr 88.7%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+110} \lor \neg \left(y \leq 7.4 \cdot 10^{+86}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.7e+110) (not (<= y 7.4e+86)))
   (* 60.0 (/ y (- t z)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.7e+110) || !(y <= 7.4e+86)) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.7d+110)) .or. (.not. (y <= 7.4d+86))) then
        tmp = 60.0d0 * (y / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.7e+110) || !(y <= 7.4e+86)) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.7e+110) or not (y <= 7.4e+86):
		tmp = 60.0 * (y / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.7e+110) || !(y <= 7.4e+86))
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.7e+110) || ~((y <= 7.4e+86)))
		tmp = 60.0 * (y / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.7e+110], N[Not[LessEqual[y, 7.4e+86]], $MachinePrecision]], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000012e110 or 7.39999999999999983e86 < y

   1. Initial program 95.4%

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

      1. associate-/l* 99.8%

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

      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 73.1%

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

   6. Taylor expanded in x around 0 64.3%

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

      1. associate-*r/ 87.6%

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

      2. remove-double-neg 87.6%

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

      3. neg-mul-1 87.6%

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

      4. times-frac 90.9%

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

      5. metadata-eval 90.9%

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

      6. neg-sub0 90.9%

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

      7. sub-neg 90.9%

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

      8. +-commutative 90.9%

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

      9. associate--r+ 90.9%

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

      10. neg-sub0 90.9%

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

      11. remove-double-neg 90.9%

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

   8. Simplified 64.3%

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

   if -3.70000000000000012e110 < y < 7.39999999999999983e86

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

      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 62.4%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+110} \lor \neg \left(y \leq 7.4 \cdot 10^{+86}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+142} \lor \neg \left(x \leq 2.9 \cdot 10^{+164}\right):\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.2e+142) (not (<= x 2.9e+164)))
   (* x (/ -60.0 t))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.2e+142) || !(x <= 2.9e+164)) {
		tmp = x * (-60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.2d+142)) .or. (.not. (x <= 2.9d+164))) then
        tmp = x * ((-60.0d0) / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.2e+142) || !(x <= 2.9e+164)) {
		tmp = x * (-60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.2e+142) or not (x <= 2.9e+164):
		tmp = x * (-60.0 / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.2e+142) || !(x <= 2.9e+164))
		tmp = Float64(x * Float64(-60.0 / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.2e+142) || ~((x <= 2.9e+164)))
		tmp = x * (-60.0 / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.2e+142], N[Not[LessEqual[x, 2.9e+164]], $MachinePrecision]], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999987e142 or 2.8999999999999999e164 < x

   1. Initial program 93.4%

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

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

   6. Taylor expanded in x around inf 69.6%

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

   7. Taylor expanded in z around 0 44.0%

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

   if -2.19999999999999987e142 < x < 2.8999999999999999e164

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

      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 60.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+142} \lor \neg \left(x \leq 2.9 \cdot 10^{+164}\right):\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+143} \lor \neg \left(x \leq 1.9 \cdot 10^{+165}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.55e+143) (not (<= x 1.9e+165)))
   (* -60.0 (/ x t))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.55e+143) || !(x <= 1.9e+165)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.55d+143)) .or. (.not. (x <= 1.9d+165))) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.55e+143) || !(x <= 1.9e+165)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.55e+143) or not (x <= 1.9e+165):
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.55e+143) || !(x <= 1.9e+165))
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.55e+143) || ~((x <= 1.9e+165)))
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.55e+143], N[Not[LessEqual[x, 1.9e+165]], $MachinePrecision]], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.54999999999999995e143 or 1.89999999999999995e165 < x

   1. Initial program 93.4%

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

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

   6. Taylor expanded in x around inf 69.6%

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

   7. Taylor expanded in z around 0 43.9%

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

   if -1.54999999999999995e143 < x < 1.89999999999999995e165

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

      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 60.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+143} \lor \neg \left(x \leq 1.9 \cdot 10^{+165}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

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

Alternative 14: 50.0% 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 98.0%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 50.7%

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

6. Final simplification 50.7%

   \[\leadsto a \cdot 120 \]
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 2024144 
(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)))