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

Percentage Accurate: 99.3% → 99.8%

Time: 13.9s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. fma-def 99.4%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 57.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-98}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))) (t_2 (* -60.0 (/ y (- z t)))))
   (if (<= a -2.3e-98)
     (* a 120.0)
     (if (<= a -9.6e-200)
       t_2
       (if (<= a -2.1e-243)
         t_1
         (if (<= a -2.6e-297)
           t_2
           (if (<= a 1.14e-178)
             t_1
             (if (<= a 1.65e-56)
               t_2
               (if (<= a 1.25e+25) t_1 (* a 120.0))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -2.3e-98) {
		tmp = a * 120.0;
	} else if (a <= -9.6e-200) {
		tmp = t_2;
	} else if (a <= -2.1e-243) {
		tmp = t_1;
	} else if (a <= -2.6e-297) {
		tmp = t_2;
	} else if (a <= 1.14e-178) {
		tmp = t_1;
	} else if (a <= 1.65e-56) {
		tmp = t_2;
	} else if (a <= 1.25e+25) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    t_2 = (-60.0d0) * (y / (z - t))
    if (a <= (-2.3d-98)) then
        tmp = a * 120.0d0
    else if (a <= (-9.6d-200)) then
        tmp = t_2
    else if (a <= (-2.1d-243)) then
        tmp = t_1
    else if (a <= (-2.6d-297)) then
        tmp = t_2
    else if (a <= 1.14d-178) then
        tmp = t_1
    else if (a <= 1.65d-56) then
        tmp = t_2
    else if (a <= 1.25d+25) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -2.3e-98) {
		tmp = a * 120.0;
	} else if (a <= -9.6e-200) {
		tmp = t_2;
	} else if (a <= -2.1e-243) {
		tmp = t_1;
	} else if (a <= -2.6e-297) {
		tmp = t_2;
	} else if (a <= 1.14e-178) {
		tmp = t_1;
	} else if (a <= 1.65e-56) {
		tmp = t_2;
	} else if (a <= 1.25e+25) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	t_2 = -60.0 * (y / (z - t))
	tmp = 0
	if a <= -2.3e-98:
		tmp = a * 120.0
	elif a <= -9.6e-200:
		tmp = t_2
	elif a <= -2.1e-243:
		tmp = t_1
	elif a <= -2.6e-297:
		tmp = t_2
	elif a <= 1.14e-178:
		tmp = t_1
	elif a <= 1.65e-56:
		tmp = t_2
	elif a <= 1.25e+25:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	t_2 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (a <= -2.3e-98)
		tmp = Float64(a * 120.0);
	elseif (a <= -9.6e-200)
		tmp = t_2;
	elseif (a <= -2.1e-243)
		tmp = t_1;
	elseif (a <= -2.6e-297)
		tmp = t_2;
	elseif (a <= 1.14e-178)
		tmp = t_1;
	elseif (a <= 1.65e-56)
		tmp = t_2;
	elseif (a <= 1.25e+25)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / (z - t));
	t_2 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (a <= -2.3e-98)
		tmp = a * 120.0;
	elseif (a <= -9.6e-200)
		tmp = t_2;
	elseif (a <= -2.1e-243)
		tmp = t_1;
	elseif (a <= -2.6e-297)
		tmp = t_2;
	elseif (a <= 1.14e-178)
		tmp = t_1;
	elseif (a <= 1.65e-56)
		tmp = t_2;
	elseif (a <= 1.25e+25)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-98], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -9.6e-200], t$95$2, If[LessEqual[a, -2.1e-243], t$95$1, If[LessEqual[a, -2.6e-297], t$95$2, If[LessEqual[a, 1.14e-178], t$95$1, If[LessEqual[a, 1.65e-56], t$95$2, If[LessEqual[a, 1.25e+25], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.30000000000000001e-98 or 1.25000000000000006e25 < a

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.4%

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

   if -2.30000000000000001e-98 < a < -9.60000000000000006e-200 or -2.1000000000000001e-243 < a < -2.6000000000000001e-297 or 1.14e-178 < a < 1.64999999999999992e-56

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 60.1%

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

   if -9.60000000000000006e-200 < a < -2.1000000000000001e-243 or -2.6000000000000001e-297 < a < 1.14e-178 or 1.64999999999999992e-56 < a < 1.25000000000000006e25

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 65.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-98}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-200}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-243}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-178}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-56}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+25}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3: 57.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.42 \cdot 10^{-92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-204}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))) (t_2 (* -60.0 (/ y (- z t)))))
   (if (<= a -1.42e-92)
     (* a 120.0)
     (if (<= a -3.6e-204)
       (/ -60.0 (/ (- z t) y))
       (if (<= a -1e-240)
         t_1
         (if (<= a -4.4e-297)
           t_2
           (if (<= a 1.08e-178)
             t_1
             (if (<= a 1e-56) t_2 (if (<= a 7.4e+25) t_1 (* a 120.0))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.42e-92) {
		tmp = a * 120.0;
	} else if (a <= -3.6e-204) {
		tmp = -60.0 / ((z - t) / y);
	} else if (a <= -1e-240) {
		tmp = t_1;
	} else if (a <= -4.4e-297) {
		tmp = t_2;
	} else if (a <= 1.08e-178) {
		tmp = t_1;
	} else if (a <= 1e-56) {
		tmp = t_2;
	} else if (a <= 7.4e+25) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    t_2 = (-60.0d0) * (y / (z - t))
    if (a <= (-1.42d-92)) then
        tmp = a * 120.0d0
    else if (a <= (-3.6d-204)) then
        tmp = (-60.0d0) / ((z - t) / y)
    else if (a <= (-1d-240)) then
        tmp = t_1
    else if (a <= (-4.4d-297)) then
        tmp = t_2
    else if (a <= 1.08d-178) then
        tmp = t_1
    else if (a <= 1d-56) then
        tmp = t_2
    else if (a <= 7.4d+25) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.42e-92) {
		tmp = a * 120.0;
	} else if (a <= -3.6e-204) {
		tmp = -60.0 / ((z - t) / y);
	} else if (a <= -1e-240) {
		tmp = t_1;
	} else if (a <= -4.4e-297) {
		tmp = t_2;
	} else if (a <= 1.08e-178) {
		tmp = t_1;
	} else if (a <= 1e-56) {
		tmp = t_2;
	} else if (a <= 7.4e+25) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	t_2 = -60.0 * (y / (z - t))
	tmp = 0
	if a <= -1.42e-92:
		tmp = a * 120.0
	elif a <= -3.6e-204:
		tmp = -60.0 / ((z - t) / y)
	elif a <= -1e-240:
		tmp = t_1
	elif a <= -4.4e-297:
		tmp = t_2
	elif a <= 1.08e-178:
		tmp = t_1
	elif a <= 1e-56:
		tmp = t_2
	elif a <= 7.4e+25:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	t_2 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (a <= -1.42e-92)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.6e-204)
		tmp = Float64(-60.0 / Float64(Float64(z - t) / y));
	elseif (a <= -1e-240)
		tmp = t_1;
	elseif (a <= -4.4e-297)
		tmp = t_2;
	elseif (a <= 1.08e-178)
		tmp = t_1;
	elseif (a <= 1e-56)
		tmp = t_2;
	elseif (a <= 7.4e+25)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / (z - t));
	t_2 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (a <= -1.42e-92)
		tmp = a * 120.0;
	elseif (a <= -3.6e-204)
		tmp = -60.0 / ((z - t) / y);
	elseif (a <= -1e-240)
		tmp = t_1;
	elseif (a <= -4.4e-297)
		tmp = t_2;
	elseif (a <= 1.08e-178)
		tmp = t_1;
	elseif (a <= 1e-56)
		tmp = t_2;
	elseif (a <= 7.4e+25)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.42e-92], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.6e-204], N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-240], t$95$1, If[LessEqual[a, -4.4e-297], t$95$2, If[LessEqual[a, 1.08e-178], t$95$1, If[LessEqual[a, 1e-56], t$95$2, If[LessEqual[a, 7.4e+25], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.42e-92 or 7.3999999999999998e25 < a

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.4%

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

   if -1.42e-92 < a < -3.59999999999999965e-204

   1. Initial program 99.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 58.9%

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

      1. clear-num 58.9%

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

      2. un-div-inv 59.0%

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

   8. Applied egg-rr 59.0%

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

   if -3.59999999999999965e-204 < a < -9.9999999999999997e-241 or -4.3999999999999997e-297 < a < 1.07999999999999995e-178 or 1e-56 < a < 7.3999999999999998e25

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 65.6%

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

   if -9.9999999999999997e-241 < a < -4.3999999999999997e-297 or 1.07999999999999995e-178 < a < 1e-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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 61.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{-92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-204}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-240}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-178}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 10^{-56}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+25}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 57.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{-98}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-202}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-58}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= a -1.9e-98)
     (* a 120.0)
     (if (<= a -4e-202)
       (/ -60.0 (/ (- z t) y))
       (if (<= a -1.3e-240)
         t_1
         (if (<= a -2.9e-297)
           (* -60.0 (/ y (- z t)))
           (if (<= a 1e-178)
             t_1
             (if (<= a 2.7e-58)
               (/ (* y -60.0) (- z t))
               (if (<= a 1.05e+25) t_1 (* a 120.0))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -1.9e-98) {
		tmp = a * 120.0;
	} else if (a <= -4e-202) {
		tmp = -60.0 / ((z - t) / y);
	} else if (a <= -1.3e-240) {
		tmp = t_1;
	} else if (a <= -2.9e-297) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1e-178) {
		tmp = t_1;
	} else if (a <= 2.7e-58) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 1.05e+25) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    if (a <= (-1.9d-98)) then
        tmp = a * 120.0d0
    else if (a <= (-4d-202)) then
        tmp = (-60.0d0) / ((z - t) / y)
    else if (a <= (-1.3d-240)) then
        tmp = t_1
    else if (a <= (-2.9d-297)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 1d-178) then
        tmp = t_1
    else if (a <= 2.7d-58) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (a <= 1.05d+25) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -1.9e-98) {
		tmp = a * 120.0;
	} else if (a <= -4e-202) {
		tmp = -60.0 / ((z - t) / y);
	} else if (a <= -1.3e-240) {
		tmp = t_1;
	} else if (a <= -2.9e-297) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1e-178) {
		tmp = t_1;
	} else if (a <= 2.7e-58) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 1.05e+25) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	tmp = 0
	if a <= -1.9e-98:
		tmp = a * 120.0
	elif a <= -4e-202:
		tmp = -60.0 / ((z - t) / y)
	elif a <= -1.3e-240:
		tmp = t_1
	elif a <= -2.9e-297:
		tmp = -60.0 * (y / (z - t))
	elif a <= 1e-178:
		tmp = t_1
	elif a <= 2.7e-58:
		tmp = (y * -60.0) / (z - t)
	elif a <= 1.05e+25:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (a <= -1.9e-98)
		tmp = Float64(a * 120.0);
	elseif (a <= -4e-202)
		tmp = Float64(-60.0 / Float64(Float64(z - t) / y));
	elseif (a <= -1.3e-240)
		tmp = t_1;
	elseif (a <= -2.9e-297)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 1e-178)
		tmp = t_1;
	elseif (a <= 2.7e-58)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (a <= 1.05e+25)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / (z - t));
	tmp = 0.0;
	if (a <= -1.9e-98)
		tmp = a * 120.0;
	elseif (a <= -4e-202)
		tmp = -60.0 / ((z - t) / y);
	elseif (a <= -1.3e-240)
		tmp = t_1;
	elseif (a <= -2.9e-297)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 1e-178)
		tmp = t_1;
	elseif (a <= 2.7e-58)
		tmp = (y * -60.0) / (z - t);
	elseif (a <= 1.05e+25)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e-98], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4e-202], N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e-240], t$95$1, If[LessEqual[a, -2.9e-297], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-178], t$95$1, If[LessEqual[a, 2.7e-58], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+25], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.9000000000000002e-98 or 1.05e25 < a

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.4%

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

   if -1.9000000000000002e-98 < a < -4.0000000000000001e-202

   1. Initial program 99.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 58.9%

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

      1. clear-num 58.9%

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

      2. un-div-inv 59.0%

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

   8. Applied egg-rr 59.0%

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

   if -4.0000000000000001e-202 < a < -1.29999999999999996e-240 or -2.89999999999999989e-297 < a < 9.9999999999999995e-179 or 2.6999999999999999e-58 < a < 1.05e25

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 65.6%

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

   if -1.29999999999999996e-240 < a < -2.89999999999999989e-297

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 70.6%

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

   if 9.9999999999999995e-179 < a < 2.6999999999999999e-58

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 55.4%

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

      1. associate-*r/ 55.5%

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

   8. Simplified 55.5%

      \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-98}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-202}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-240}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 10^{-178}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-58}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+25}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 57.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot x}{z - t}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{-96}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-199}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-56}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 x) (- z t))))
   (if (<= a -5.4e-96)
     (* a 120.0)
     (if (<= a -6.5e-199)
       (/ -60.0 (/ (- z t) y))
       (if (<= a -1.9e-240)
         t_1
         (if (<= a -2.65e-297)
           (* -60.0 (/ y (- z t)))
           (if (<= a 1.02e-178)
             t_1
             (if (<= a 7.2e-56)
               (/ (* y -60.0) (- z t))
               (if (<= a 1.05e+25) t_1 (* a 120.0))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * x) / (z - t);
	double tmp;
	if (a <= -5.4e-96) {
		tmp = a * 120.0;
	} else if (a <= -6.5e-199) {
		tmp = -60.0 / ((z - t) / y);
	} else if (a <= -1.9e-240) {
		tmp = t_1;
	} else if (a <= -2.65e-297) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1.02e-178) {
		tmp = t_1;
	} else if (a <= 7.2e-56) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 1.05e+25) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * x) / (z - t)
    if (a <= (-5.4d-96)) then
        tmp = a * 120.0d0
    else if (a <= (-6.5d-199)) then
        tmp = (-60.0d0) / ((z - t) / y)
    else if (a <= (-1.9d-240)) then
        tmp = t_1
    else if (a <= (-2.65d-297)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 1.02d-178) then
        tmp = t_1
    else if (a <= 7.2d-56) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (a <= 1.05d+25) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * x) / (z - t);
	double tmp;
	if (a <= -5.4e-96) {
		tmp = a * 120.0;
	} else if (a <= -6.5e-199) {
		tmp = -60.0 / ((z - t) / y);
	} else if (a <= -1.9e-240) {
		tmp = t_1;
	} else if (a <= -2.65e-297) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1.02e-178) {
		tmp = t_1;
	} else if (a <= 7.2e-56) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 1.05e+25) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * x) / (z - t)
	tmp = 0
	if a <= -5.4e-96:
		tmp = a * 120.0
	elif a <= -6.5e-199:
		tmp = -60.0 / ((z - t) / y)
	elif a <= -1.9e-240:
		tmp = t_1
	elif a <= -2.65e-297:
		tmp = -60.0 * (y / (z - t))
	elif a <= 1.02e-178:
		tmp = t_1
	elif a <= 7.2e-56:
		tmp = (y * -60.0) / (z - t)
	elif a <= 1.05e+25:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * x) / Float64(z - t))
	tmp = 0.0
	if (a <= -5.4e-96)
		tmp = Float64(a * 120.0);
	elseif (a <= -6.5e-199)
		tmp = Float64(-60.0 / Float64(Float64(z - t) / y));
	elseif (a <= -1.9e-240)
		tmp = t_1;
	elseif (a <= -2.65e-297)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 1.02e-178)
		tmp = t_1;
	elseif (a <= 7.2e-56)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (a <= 1.05e+25)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * x) / (z - t);
	tmp = 0.0;
	if (a <= -5.4e-96)
		tmp = a * 120.0;
	elseif (a <= -6.5e-199)
		tmp = -60.0 / ((z - t) / y);
	elseif (a <= -1.9e-240)
		tmp = t_1;
	elseif (a <= -2.65e-297)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 1.02e-178)
		tmp = t_1;
	elseif (a <= 7.2e-56)
		tmp = (y * -60.0) / (z - t);
	elseif (a <= 1.05e+25)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e-96], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6.5e-199], N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9e-240], t$95$1, If[LessEqual[a, -2.65e-297], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-178], t$95$1, If[LessEqual[a, 7.2e-56], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+25], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.3999999999999999e-96 or 1.05e25 < a

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.4%

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

   if -5.3999999999999999e-96 < a < -6.50000000000000017e-199

   1. Initial program 99.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 58.9%

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

      1. clear-num 58.9%

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

      2. un-div-inv 59.0%

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

   8. Applied egg-rr 59.0%

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

   if -6.50000000000000017e-199 < a < -1.89999999999999994e-240 or -2.6500000000000001e-297 < a < 1.02000000000000006e-178 or 7.19999999999999956e-56 < a < 1.05e25

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 94.3%

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

      1. associate-*r/ 94.4%

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

   8. Simplified 94.4%

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

   9. Taylor expanded in x around inf 65.6%

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

       1. *-commutative 65.6%

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

   11. Simplified 65.6%

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

   if -1.89999999999999994e-240 < a < -2.6500000000000001e-297

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 70.6%

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

   if 1.02000000000000006e-178 < a < 7.19999999999999956e-56

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 55.4%

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

      1. associate-*r/ 55.5%

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

   8. Simplified 55.5%

      \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-96}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-199}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-240}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-178}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-56}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+25}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 88.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -30 \lor \neg \left(y \leq 280000 \lor \neg \left(y \leq 2.05 \cdot 10^{+123}\right) \land y \leq 6.5 \cdot 10^{+171}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -30.0)
         (not
          (or (<= y 280000.0) (and (not (<= y 2.05e+123)) (<= y 6.5e+171)))))
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -30.0) || !((y <= 280000.0) || (!(y <= 2.05e+123) && (y <= 6.5e+171)))) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 / ((z - t) / x)) + (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 <= (-30.0d0)) .or. (.not. (y <= 280000.0d0) .or. (.not. (y <= 2.05d+123)) .and. (y <= 6.5d+171))) then
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    else
        tmp = (60.0d0 / ((z - t) / x)) + (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 <= -30.0) || !((y <= 280000.0) || (!(y <= 2.05e+123) && (y <= 6.5e+171)))) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -30.0) or not ((y <= 280000.0) or (not (y <= 2.05e+123) and (y <= 6.5e+171))):
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	else:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -30.0) || !((y <= 280000.0) || (!(y <= 2.05e+123) && (y <= 6.5e+171))))
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -30.0) || ~(((y <= 280000.0) || (~((y <= 2.05e+123)) && (y <= 6.5e+171)))))
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	else
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -30.0], N[Not[Or[LessEqual[y, 280000.0], And[N[Not[LessEqual[y, 2.05e+123]], $MachinePrecision], LessEqual[y, 6.5e+171]]]], $MachinePrecision]], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -30 or 2.8e5 < y < 2.04999999999999995e123 or 6.5e171 < y

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 90.0%

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

      1. associate-*r/ 90.0%

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

      2. associate-/l* 90.0%

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

   6. Simplified 90.0%

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

   if -30 < y < 2.8e5 or 2.04999999999999995e123 < y < 6.5e171

   1. Initial program 99.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 95.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -30 \lor \neg \left(y \leq 280000 \lor \neg \left(y \leq 2.05 \cdot 10^{+123}\right) \land y \leq 6.5 \cdot 10^{+171}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \]

Alternative 7: 88.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{if}\;y \leq -3 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 280000:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+122} \lor \neg \left(y \leq 6.5 \cdot 10^{+171}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))))
   (if (<= y -3e-5)
     t_1
     (if (<= y 280000.0)
       (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
       (if (or (<= y 7.6e+122) (not (<= y 6.5e+171)))
         t_1
         (+ (/ 60.0 (/ (- z t) x)) (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / ((z - t) / y)) + (a * 120.0);
	double tmp;
	if (y <= -3e-5) {
		tmp = t_1;
	} else if (y <= 280000.0) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if ((y <= 7.6e+122) || !(y <= 6.5e+171)) {
		tmp = t_1;
	} else {
		tmp = (60.0 / ((z - t) / x)) + (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) / ((z - t) / y)) + (a * 120.0d0)
    if (y <= (-3d-5)) then
        tmp = t_1
    else if (y <= 280000.0d0) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else if ((y <= 7.6d+122) .or. (.not. (y <= 6.5d+171))) then
        tmp = t_1
    else
        tmp = (60.0d0 / ((z - t) / x)) + (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 / ((z - t) / y)) + (a * 120.0);
	double tmp;
	if (y <= -3e-5) {
		tmp = t_1;
	} else if (y <= 280000.0) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if ((y <= 7.6e+122) || !(y <= 6.5e+171)) {
		tmp = t_1;
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 / ((z - t) / y)) + (a * 120.0)
	tmp = 0
	if y <= -3e-5:
		tmp = t_1
	elif y <= 280000.0:
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	elif (y <= 7.6e+122) or not (y <= 6.5e+171):
		tmp = t_1
	else:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0))
	tmp = 0.0
	if (y <= -3e-5)
		tmp = t_1;
	elseif (y <= 280000.0)
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	elseif ((y <= 7.6e+122) || !(y <= 6.5e+171))
		tmp = t_1;
	else
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 / ((z - t) / y)) + (a * 120.0);
	tmp = 0.0;
	if (y <= -3e-5)
		tmp = t_1;
	elseif (y <= 280000.0)
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	elseif ((y <= 7.6e+122) || ~((y <= 6.5e+171)))
		tmp = t_1;
	else
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e-5], t$95$1, If[LessEqual[y, 280000.0], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7.6e+122], N[Not[LessEqual[y, 6.5e+171]], $MachinePrecision]], t$95$1, N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.00000000000000008e-5 or 2.8e5 < y < 7.5999999999999996e122 or 6.5e171 < y

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 90.0%

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

      1. associate-*r/ 90.0%

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

      2. associate-/l* 90.0%

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

   6. Simplified 90.0%

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

   if -3.00000000000000008e-5 < y < 2.8e5

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 97.2%

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

      1. *-commutative 97.2%

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

      2. associate-*l/ 96.4%

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

      3. associate-/l* 97.2%

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

   6. Simplified 97.2%

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

   if 7.5999999999999996e122 < y < 6.5e171

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 86.7%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-5}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 280000:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+122} \lor \neg \left(y \leq 6.5 \cdot 10^{+171}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \]

Alternative 8: 88.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31.5:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+122} \lor \neg \left(y \leq 1.35 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -31.5)
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))
   (if (<= y 160000.0)
     (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
     (if (or (<= y 2.45e+122) (not (<= y 1.35e+172)))
       (+ (/ (* y -60.0) (- z t)) (* a 120.0))
       (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -31.5) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (y <= 160000.0) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if ((y <= 2.45e+122) || !(y <= 1.35e+172)) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (60.0 / ((z - t) / x)) + (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 <= (-31.5d0)) then
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    else if (y <= 160000.0d0) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else if ((y <= 2.45d+122) .or. (.not. (y <= 1.35d+172))) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = (60.0d0 / ((z - t) / x)) + (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 <= -31.5) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (y <= 160000.0) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if ((y <= 2.45e+122) || !(y <= 1.35e+172)) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -31.5:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	elif y <= 160000.0:
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	elif (y <= 2.45e+122) or not (y <= 1.35e+172):
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -31.5)
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	elseif (y <= 160000.0)
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	elseif ((y <= 2.45e+122) || !(y <= 1.35e+172))
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -31.5)
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	elseif (y <= 160000.0)
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	elseif ((y <= 2.45e+122) || ~((y <= 1.35e+172)))
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -31.5], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 160000.0], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.45e+122], N[Not[LessEqual[y, 1.35e+172]], $MachinePrecision]], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -31.5

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 89.1%

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

      1. associate-*r/ 89.1%

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

      2. associate-/l* 89.1%

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

   6. Simplified 89.1%

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

   if -31.5 < y < 1.6e5

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 97.2%

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

      1. *-commutative 97.2%

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

      2. associate-*l/ 96.4%

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

      3. associate-/l* 97.2%

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

   6. Simplified 97.2%

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

   if 1.6e5 < y < 2.4499999999999999e122 or 1.35e172 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 91.1%

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

   if 2.4499999999999999e122 < y < 1.35e172

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 86.7%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31.5:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+122} \lor \neg \left(y \leq 1.35 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \]

Alternative 9: 81.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-90} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-90) (not (<= (* a 120.0) 2e+20)))
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))
   (* (/ 60.0 (- z t)) (- x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-90) || !((a * 120.0) <= 2e+20)) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2d-90)) .or. (.not. ((a * 120.0d0) <= 2d+20))) then
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    else
        tmp = (60.0d0 / (z - t)) * (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-90) || !((a * 120.0) <= 2e+20)) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-90) or not ((a * 120.0) <= 2e+20):
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	else:
		tmp = (60.0 / (z - t)) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-90) || !(Float64(a * 120.0) <= 2e+20))
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-90) || ~(((a * 120.0) <= 2e+20)))
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	else
		tmp = (60.0 / (z - t)) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-90], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+20]], $MachinePrecision]], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -1.99999999999999999e-90 or 2e20 < (*.f64 a 120)

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 90.1%

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

      1. associate-*r/ 90.1%

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

      2. associate-/l* 90.1%

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

   6. Simplified 90.1%

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

   if -1.99999999999999999e-90 < (*.f64 a 120) < 2e20

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 88.1%

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

      1. associate-*r/ 88.1%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

   8. Simplified 88.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-90} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 10: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+43)
   (* a 120.0)
   (if (<= (* a 120.0) 2e+27) (* (/ 60.0 (- z t)) (- x y)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+43) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e+27) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d+43)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d+27) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+43) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e+27) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+43:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e+27:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+43)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e+27)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+43)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e+27)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+43], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+27], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -2.00000000000000003e43 or 2e27 < (*.f64 a 120)

   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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 83.0%

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

   if -2.00000000000000003e43 < (*.f64 a 120) < 2e27

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 82.6%

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

      1. associate-*r/ 82.7%

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

      2. associate-*l/ 82.7%

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

      3. *-commutative 82.7%

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

   8. Simplified 82.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -6.4 \cdot 10^{-98}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-145}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-42}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 155000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x z))))
   (if (<= a -6.4e-98)
     (* a 120.0)
     (if (<= a -5.5e-283)
       t_1
       (if (<= a 4.2e-145)
         (* -60.0 (/ x t))
         (if (<= a 4.7e-42)
           (* -60.0 (/ y z))
           (if (<= a 155000.0) t_1 (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / z);
	double tmp;
	if (a <= -6.4e-98) {
		tmp = a * 120.0;
	} else if (a <= -5.5e-283) {
		tmp = t_1;
	} else if (a <= 4.2e-145) {
		tmp = -60.0 * (x / t);
	} else if (a <= 4.7e-42) {
		tmp = -60.0 * (y / z);
	} else if (a <= 155000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (x / z)
    if (a <= (-6.4d-98)) then
        tmp = a * 120.0d0
    else if (a <= (-5.5d-283)) then
        tmp = t_1
    else if (a <= 4.2d-145) then
        tmp = (-60.0d0) * (x / t)
    else if (a <= 4.7d-42) then
        tmp = (-60.0d0) * (y / z)
    else if (a <= 155000.0d0) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / z);
	double tmp;
	if (a <= -6.4e-98) {
		tmp = a * 120.0;
	} else if (a <= -5.5e-283) {
		tmp = t_1;
	} else if (a <= 4.2e-145) {
		tmp = -60.0 * (x / t);
	} else if (a <= 4.7e-42) {
		tmp = -60.0 * (y / z);
	} else if (a <= 155000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / z)
	tmp = 0
	if a <= -6.4e-98:
		tmp = a * 120.0
	elif a <= -5.5e-283:
		tmp = t_1
	elif a <= 4.2e-145:
		tmp = -60.0 * (x / t)
	elif a <= 4.7e-42:
		tmp = -60.0 * (y / z)
	elif a <= 155000.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / z))
	tmp = 0.0
	if (a <= -6.4e-98)
		tmp = Float64(a * 120.0);
	elseif (a <= -5.5e-283)
		tmp = t_1;
	elseif (a <= 4.2e-145)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (a <= 4.7e-42)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (a <= 155000.0)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / z);
	tmp = 0.0;
	if (a <= -6.4e-98)
		tmp = a * 120.0;
	elseif (a <= -5.5e-283)
		tmp = t_1;
	elseif (a <= 4.2e-145)
		tmp = -60.0 * (x / t);
	elseif (a <= 4.7e-42)
		tmp = -60.0 * (y / z);
	elseif (a <= 155000.0)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.4e-98], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -5.5e-283], t$95$1, If[LessEqual[a, 4.2e-145], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e-42], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 155000.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.4000000000000001e-98 or 155000 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.0%

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

   if -6.4000000000000001e-98 < a < -5.49999999999999953e-283 or 4.7000000000000001e-42 < a < 155000

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 90.4%

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

      1. associate-*r/ 90.3%

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

      2. associate-*l/ 90.4%

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

      3. *-commutative 90.4%

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

   8. Simplified 90.4%

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

   9. Taylor expanded in z around inf 50.5%

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

   10. Taylor expanded in x around inf 30.7%

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

   if -5.49999999999999953e-283 < a < 4.19999999999999982e-145

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 61.9%

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

   5. Taylor expanded in z around 0 48.2%

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

   6. Taylor expanded in a around 0 40.1%

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

   if 4.19999999999999982e-145 < a < 4.7000000000000001e-42

   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* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 57.8%

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

   7. Taylor expanded in z around inf 38.6%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-98}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-283}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-145}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-42}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 155000:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-285}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-178}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 0.00034:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e-100)
   (* a 120.0)
   (if (<= a -4.1e-285)
     (* 60.0 (/ x z))
     (if (<= a 1.46e-178)
       (* -60.0 (/ x t))
       (if (<= a 0.00034) (* 60.0 (/ y t)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e-100) {
		tmp = a * 120.0;
	} else if (a <= -4.1e-285) {
		tmp = 60.0 * (x / z);
	} else if (a <= 1.46e-178) {
		tmp = -60.0 * (x / t);
	} else if (a <= 0.00034) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2d-100)) then
        tmp = a * 120.0d0
    else if (a <= (-4.1d-285)) then
        tmp = 60.0d0 * (x / z)
    else if (a <= 1.46d-178) then
        tmp = (-60.0d0) * (x / t)
    else if (a <= 0.00034d0) then
        tmp = 60.0d0 * (y / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e-100) {
		tmp = a * 120.0;
	} else if (a <= -4.1e-285) {
		tmp = 60.0 * (x / z);
	} else if (a <= 1.46e-178) {
		tmp = -60.0 * (x / t);
	} else if (a <= 0.00034) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e-100:
		tmp = a * 120.0
	elif a <= -4.1e-285:
		tmp = 60.0 * (x / z)
	elif a <= 1.46e-178:
		tmp = -60.0 * (x / t)
	elif a <= 0.00034:
		tmp = 60.0 * (y / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e-100)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.1e-285)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (a <= 1.46e-178)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (a <= 0.00034)
		tmp = Float64(60.0 * Float64(y / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e-100)
		tmp = a * 120.0;
	elseif (a <= -4.1e-285)
		tmp = 60.0 * (x / z);
	elseif (a <= 1.46e-178)
		tmp = -60.0 * (x / t);
	elseif (a <= 0.00034)
		tmp = 60.0 * (y / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e-100], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.1e-285], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.46e-178], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.00034], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2e-100 or 3.4e-4 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 75.5%

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

   if -2e-100 < a < -4.1e-285

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 89.4%

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

      1. associate-*r/ 89.3%

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

      2. associate-*l/ 89.4%

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

      3. *-commutative 89.4%

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

   8. Simplified 89.4%

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

   9. Taylor expanded in z around inf 51.5%

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

   10. Taylor expanded in x around inf 29.5%

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

   if -4.1e-285 < a < 1.46e-178

   1. Initial program 99.7%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 61.6%

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

   5. Taylor expanded in z around 0 45.0%

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

   6. Taylor expanded in a around 0 42.7%

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

   if 1.46e-178 < a < 3.4e-4

   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* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 52.5%

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

   7. Taylor expanded in z around 0 34.1%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-285}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-178}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 0.00034:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+28}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e+32)
   (* a 120.0)
   (if (<= a 3.4e+28) (* 60.0 (/ (- x y) (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e+32) {
		tmp = a * 120.0;
	} else if (a <= 3.4e+28) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.45d+32)) then
        tmp = a * 120.0d0
    else if (a <= 3.4d+28) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e+32) {
		tmp = a * 120.0;
	} else if (a <= 3.4e+28) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e+32:
		tmp = a * 120.0
	elif a <= 3.4e+28:
		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 (a <= -1.45e+32)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.4e+28)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.45e+32)
		tmp = a * 120.0;
	elseif (a <= 3.4e+28)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e+32], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.4e+28], 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 a < -1.45000000000000001e32 or 3.4e28 < 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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 83.0%

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

   if -1.45000000000000001e32 < a < 3.4e28

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 82.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+28}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 15: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (- x y) (* (- z t) 0.016666666666666666)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x - y) / ((z - t) * 0.016666666666666666)) + (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) / ((z - t) * 0.016666666666666666d0)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x - y) / ((z - t) * 0.016666666666666666)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((x - y) / ((z - t) * 0.016666666666666666)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x - y) / ((z - t) * 0.016666666666666666)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

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%

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

3. Simplified 99.8%

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

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

   1. *-commutative 99.8%

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

   2. clear-num 99.7%

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

   3. un-div-inv 99.8%

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

   4. div-inv 99.8%

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

   5. metadata-eval 99.8%

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

7. Applied egg-rr 99.8%

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

8. Final simplification 99.8%

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

Alternative 16: 52.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-101}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-202}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-149}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-101)
   (* a 120.0)
   (if (<= a -4.2e-202)
     (* -60.0 (/ y z))
     (if (<= a 9.2e-149) (* -60.0 (/ x t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-101) {
		tmp = a * 120.0;
	} else if (a <= -4.2e-202) {
		tmp = -60.0 * (y / z);
	} else if (a <= 9.2e-149) {
		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 (a <= (-1.2d-101)) then
        tmp = a * 120.0d0
    else if (a <= (-4.2d-202)) then
        tmp = (-60.0d0) * (y / z)
    else if (a <= 9.2d-149) 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 (a <= -1.2e-101) {
		tmp = a * 120.0;
	} else if (a <= -4.2e-202) {
		tmp = -60.0 * (y / z);
	} else if (a <= 9.2e-149) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-101:
		tmp = a * 120.0
	elif a <= -4.2e-202:
		tmp = -60.0 * (y / z)
	elif a <= 9.2e-149:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-101)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.2e-202)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (a <= 9.2e-149)
		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 (a <= -1.2e-101)
		tmp = a * 120.0;
	elseif (a <= -4.2e-202)
		tmp = -60.0 * (y / z);
	elseif (a <= 9.2e-149)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-101], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.2e-202], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e-149], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2e-101 or 9.1999999999999999e-149 < a

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 67.2%

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

   if -1.2e-101 < a < -4.1999999999999997e-202

   1. Initial program 99.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 58.9%

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

   7. Taylor expanded in z around inf 31.9%

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

   if -4.1999999999999997e-202 < a < 9.1999999999999999e-149

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 64.1%

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

   5. Taylor expanded in z around 0 42.7%

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

   6. Taylor expanded in a around 0 35.5%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-101}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-202}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-149}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17: 58.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 170000:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e-93)
   (* a 120.0)
   (if (<= a 170000.0) (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e-93) {
		tmp = a * 120.0;
	} else if (a <= 170000.0) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.3d-93)) then
        tmp = a * 120.0d0
    else if (a <= 170000.0d0) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e-93) {
		tmp = a * 120.0;
	} else if (a <= 170000.0) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e-93:
		tmp = a * 120.0
	elif a <= 170000.0:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e-93)
		tmp = Float64(a * 120.0);
	elseif (a <= 170000.0)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e-93)
		tmp = a * 120.0;
	elseif (a <= 170000.0)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e-93], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 170000.0], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2999999999999998e-93 or 1.7e5 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.0%

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

   if -2.2999999999999998e-93 < a < 1.7e5

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 48.1%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 170000:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18: 52.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-102}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-149}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e-102)
   (* a 120.0)
   (if (<= a 3.35e-149) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e-102) {
		tmp = a * 120.0;
	} else if (a <= 3.35e-149) {
		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 (a <= (-1.45d-102)) then
        tmp = a * 120.0d0
    else if (a <= 3.35d-149) 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 (a <= -1.45e-102) {
		tmp = a * 120.0;
	} else if (a <= 3.35e-149) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e-102:
		tmp = a * 120.0
	elif a <= 3.35e-149:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e-102)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.35e-149)
		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 (a <= -1.45e-102)
		tmp = a * 120.0;
	elseif (a <= 3.35e-149)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e-102], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.35e-149], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.44999999999999993e-102 or 3.3499999999999998e-149 < a

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 67.2%

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

   if -1.44999999999999993e-102 < a < 3.3499999999999998e-149

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 57.3%

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

   5. Taylor expanded in z around 0 36.0%

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

   6. Taylor expanded in a around 0 29.8%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-102}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-149}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19: 50.8% 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 99.4%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in z around inf 47.7%

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

5. Final simplification 47.7%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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