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

Percentage Accurate: 99.2% → 99.8%

Time: 16.9s

Alternatives: 16

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: 99.2% 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 99.0%

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

   1. +-commutative 99.0%

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

   2. fma-def 99.0%

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

   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. Add Preprocessing

5. Final simplification 99.8%

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

Alternative 2: 57.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -1 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.7 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-92}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-12}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))))
   (if (<= a -1e+40)
     (* a 120.0)
     (if (<= a -8.7e+26)
       t_1
       (if (<= a -6e-63)
         (* a 120.0)
         (if (<= a -3.7e-92)
           (* -60.0 (/ y (- z t)))
           (if (<= a -8.5e-153)
             (* a 120.0)
             (if (<= a -5e-183)
               t_1
               (if (<= a 1.2e-12) (* -60.0 (/ (- x y) t)) (* a 120.0))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -1e+40) {
		tmp = a * 120.0;
	} else if (a <= -8.7e+26) {
		tmp = t_1;
	} else if (a <= -6e-63) {
		tmp = a * 120.0;
	} else if (a <= -3.7e-92) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= -8.5e-153) {
		tmp = a * 120.0;
	} else if (a <= -5e-183) {
		tmp = t_1;
	} else if (a <= 1.2e-12) {
		tmp = -60.0 * ((x - 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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    if (a <= (-1d+40)) then
        tmp = a * 120.0d0
    else if (a <= (-8.7d+26)) then
        tmp = t_1
    else if (a <= (-6d-63)) then
        tmp = a * 120.0d0
    else if (a <= (-3.7d-92)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= (-8.5d-153)) then
        tmp = a * 120.0d0
    else if (a <= (-5d-183)) then
        tmp = t_1
    else if (a <= 1.2d-12) then
        tmp = (-60.0d0) * ((x - 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 t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -1e+40) {
		tmp = a * 120.0;
	} else if (a <= -8.7e+26) {
		tmp = t_1;
	} else if (a <= -6e-63) {
		tmp = a * 120.0;
	} else if (a <= -3.7e-92) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= -8.5e-153) {
		tmp = a * 120.0;
	} else if (a <= -5e-183) {
		tmp = t_1;
	} else if (a <= 1.2e-12) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	tmp = 0
	if a <= -1e+40:
		tmp = a * 120.0
	elif a <= -8.7e+26:
		tmp = t_1
	elif a <= -6e-63:
		tmp = a * 120.0
	elif a <= -3.7e-92:
		tmp = -60.0 * (y / (z - t))
	elif a <= -8.5e-153:
		tmp = a * 120.0
	elif a <= -5e-183:
		tmp = t_1
	elif a <= 1.2e-12:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (a <= -1e+40)
		tmp = Float64(a * 120.0);
	elseif (a <= -8.7e+26)
		tmp = t_1;
	elseif (a <= -6e-63)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.7e-92)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= -8.5e-153)
		tmp = Float64(a * 120.0);
	elseif (a <= -5e-183)
		tmp = t_1;
	elseif (a <= 1.2e-12)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	tmp = 0.0;
	if (a <= -1e+40)
		tmp = a * 120.0;
	elseif (a <= -8.7e+26)
		tmp = t_1;
	elseif (a <= -6e-63)
		tmp = a * 120.0;
	elseif (a <= -3.7e-92)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= -8.5e-153)
		tmp = a * 120.0;
	elseif (a <= -5e-183)
		tmp = t_1;
	elseif (a <= 1.2e-12)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+40], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -8.7e+26], t$95$1, If[LessEqual[a, -6e-63], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.7e-92], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-153], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -5e-183], t$95$1, If[LessEqual[a, 1.2e-12], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.00000000000000003e40 or -8.70000000000000064e26 < a < -5.99999999999999959e-63 or -3.69999999999999977e-92 < a < -8.4999999999999996e-153 or 1.19999999999999994e-12 < a

   1. Initial program 98.5%

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

   5. Taylor expanded in z around inf 72.7%

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

   if -1.00000000000000003e40 < a < -8.70000000000000064e26 or -8.4999999999999996e-153 < a < -5.0000000000000002e-183

   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. Add Preprocessing

   5. Taylor expanded in a around 0 92.6%

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

   6. Taylor expanded in z around inf 85.3%

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

   if -5.99999999999999959e-63 < a < -3.69999999999999977e-92

   1. Initial program 99.6%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0 87.9%

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

   6. Taylor expanded in x around 0 75.8%

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

      1. neg-mul-1 75.8%

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

      2. distribute-neg-frac 75.8%

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

   8. Simplified 75.8%

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

   9. Taylor expanded in y around 0 75.8%

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

   if -5.0000000000000002e-183 < a < 1.19999999999999994e-12

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 81.0%

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

   6. Taylor expanded in z around 0 53.2%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.7 \cdot 10^{+26}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-92}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-183}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-12}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.76 \cdot 10^{+27}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-92}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-157}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-185}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-12}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+40)
   (* a 120.0)
   (if (<= a -1.76e+27)
     (/ (* 60.0 (- x y)) z)
     (if (<= a -4.5e-64)
       (* a 120.0)
       (if (<= a -3.3e-92)
         (* -60.0 (/ y (- z t)))
         (if (<= a -4.9e-157)
           (* a 120.0)
           (if (<= a -4.2e-185)
             (* 60.0 (/ (- x y) z))
             (if (<= a 1.2e-12) (* -60.0 (/ (- x y) t)) (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+40) {
		tmp = a * 120.0;
	} else if (a <= -1.76e+27) {
		tmp = (60.0 * (x - y)) / z;
	} else if (a <= -4.5e-64) {
		tmp = a * 120.0;
	} else if (a <= -3.3e-92) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= -4.9e-157) {
		tmp = a * 120.0;
	} else if (a <= -4.2e-185) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 1.2e-12) {
		tmp = -60.0 * ((x - 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 <= (-1d+40)) then
        tmp = a * 120.0d0
    else if (a <= (-1.76d+27)) then
        tmp = (60.0d0 * (x - y)) / z
    else if (a <= (-4.5d-64)) then
        tmp = a * 120.0d0
    else if (a <= (-3.3d-92)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= (-4.9d-157)) then
        tmp = a * 120.0d0
    else if (a <= (-4.2d-185)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (a <= 1.2d-12) then
        tmp = (-60.0d0) * ((x - 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 <= -1e+40) {
		tmp = a * 120.0;
	} else if (a <= -1.76e+27) {
		tmp = (60.0 * (x - y)) / z;
	} else if (a <= -4.5e-64) {
		tmp = a * 120.0;
	} else if (a <= -3.3e-92) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= -4.9e-157) {
		tmp = a * 120.0;
	} else if (a <= -4.2e-185) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 1.2e-12) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+40:
		tmp = a * 120.0
	elif a <= -1.76e+27:
		tmp = (60.0 * (x - y)) / z
	elif a <= -4.5e-64:
		tmp = a * 120.0
	elif a <= -3.3e-92:
		tmp = -60.0 * (y / (z - t))
	elif a <= -4.9e-157:
		tmp = a * 120.0
	elif a <= -4.2e-185:
		tmp = 60.0 * ((x - y) / z)
	elif a <= 1.2e-12:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+40)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.76e+27)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / z);
	elseif (a <= -4.5e-64)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.3e-92)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= -4.9e-157)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.2e-185)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (a <= 1.2e-12)
		tmp = Float64(-60.0 * Float64(Float64(x - 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 <= -1e+40)
		tmp = a * 120.0;
	elseif (a <= -1.76e+27)
		tmp = (60.0 * (x - y)) / z;
	elseif (a <= -4.5e-64)
		tmp = a * 120.0;
	elseif (a <= -3.3e-92)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= -4.9e-157)
		tmp = a * 120.0;
	elseif (a <= -4.2e-185)
		tmp = 60.0 * ((x - y) / z);
	elseif (a <= 1.2e-12)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+40], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.76e+27], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, -4.5e-64], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.3e-92], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.9e-157], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.2e-185], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-12], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.00000000000000003e40 or -1.76000000000000006e27 < a < -4.5000000000000001e-64 or -3.29999999999999998e-92 < a < -4.8999999999999998e-157 or 1.19999999999999994e-12 < a

   1. Initial program 98.5%

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

   5. Taylor expanded in z around inf 72.7%

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

   if -1.00000000000000003e40 < a < -1.76000000000000006e27

   1. Initial program 100.0%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. associate-*r/ 100.0%

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

   8. Simplified 100.0%

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

   if -4.5000000000000001e-64 < a < -3.29999999999999998e-92

   1. Initial program 99.6%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0 87.9%

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

   6. Taylor expanded in x around 0 75.8%

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

      1. neg-mul-1 75.8%

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

      2. distribute-neg-frac 75.8%

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

   8. Simplified 75.8%

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

   9. Taylor expanded in y around 0 75.8%

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

   if -4.8999999999999998e-157 < a < -4.2e-185

   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* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 86.4%

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

   6. Taylor expanded in z around inf 72.9%

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

   if -4.2e-185 < a < 1.19999999999999994e-12

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 81.0%

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

   6. Taylor expanded in z around 0 53.2%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.76 \cdot 10^{+27}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-92}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-157}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-185}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-12}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+45}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+35}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+45)
   (* a 120.0)
   (if (<= (* a 120.0) -2e+29)
     (/ (* 60.0 (- x y)) z)
     (if (<= (* a 120.0) -2e-48)
       (+ (* a 120.0) (* 60.0 (/ x z)))
       (if (<= (* a 120.0) 5e+35) (* 60.0 (/ (- x y) (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+45) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -2e+29) {
		tmp = (60.0 * (x - y)) / z;
	} else if ((a * 120.0) <= -2e-48) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 5e+35) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-4d+45)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-2d+29)) then
        tmp = (60.0d0 * (x - y)) / z
    else if ((a * 120.0d0) <= (-2d-48)) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if ((a * 120.0d0) <= 5d+35) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+45) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -2e+29) {
		tmp = (60.0 * (x - y)) / z;
	} else if ((a * 120.0) <= -2e-48) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 5e+35) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+45:
		tmp = a * 120.0
	elif (a * 120.0) <= -2e+29:
		tmp = (60.0 * (x - y)) / z
	elif (a * 120.0) <= -2e-48:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif (a * 120.0) <= 5e+35:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+45)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -2e+29)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / z);
	elseif (Float64(a * 120.0) <= -2e-48)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (Float64(a * 120.0) <= 5e+35)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e+45)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -2e+29)
		tmp = (60.0 * (x - y)) / z;
	elseif ((a * 120.0) <= -2e-48)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif ((a * 120.0) <= 5e+35)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+45], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+29], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-48], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+35], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -3.9999999999999997e45 or 5.00000000000000021e35 < (*.f64 a 120)

   1. Initial program 98.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 81.9%

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

   if -3.9999999999999997e45 < (*.f64 a 120) < -1.99999999999999983e29

   1. Initial program 100.0%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. associate-*r/ 100.0%

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

   8. Simplified 100.0%

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

   if -1.99999999999999983e29 < (*.f64 a 120) < -1.9999999999999999e-48

   1. Initial program 94.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 78.4%

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

      1. associate-*r/ 73.2%

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

      2. associate-*l/ 78.3%

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

      3. *-commutative 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in z around inf 67.9%

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

   if -1.9999999999999999e-48 < (*.f64 a 120) < 5.00000000000000021e35

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 77.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+45}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+35}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+236} \lor \neg \left(y \leq -1.65 \cdot 10^{+110} \lor \neg \left(y \leq -4.2 \cdot 10^{+54}\right) \land y \leq 2.45 \cdot 10^{+182}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9.5e+236)
         (not
          (or (<= y -1.65e+110) (and (not (<= y -4.2e+54)) (<= y 2.45e+182)))))
   (* 60.0 (/ (- x y) (- z t)))
   (+ (* (/ 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 <= -9.5e+236) || !((y <= -1.65e+110) || (!(y <= -4.2e+54) && (y <= 2.45e+182)))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} 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 <= (-9.5d+236)) .or. (.not. (y <= (-1.65d+110)) .or. (.not. (y <= (-4.2d+54))) .and. (y <= 2.45d+182))) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    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 <= -9.5e+236) || !((y <= -1.65e+110) || (!(y <= -4.2e+54) && (y <= 2.45e+182)))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9.5e+236) or not ((y <= -1.65e+110) or (not (y <= -4.2e+54) and (y <= 2.45e+182))):
		tmp = 60.0 * ((x - y) / (z - t))
	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 <= -9.5e+236) || !((y <= -1.65e+110) || (!(y <= -4.2e+54) && (y <= 2.45e+182))))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(Float64(60.0 / 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 <= -9.5e+236) || ~(((y <= -1.65e+110) || (~((y <= -4.2e+54)) && (y <= 2.45e+182)))))
		tmp = 60.0 * ((x - y) / (z - t));
	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, -9.5e+236], N[Not[Or[LessEqual[y, -1.65e+110], And[N[Not[LessEqual[y, -4.2e+54]], $MachinePrecision], LessEqual[y, 2.45e+182]]]], $MachinePrecision]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999999e236 or -1.64999999999999986e110 < y < -4.19999999999999972e54 or 2.45e182 < 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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 79.7%

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

   if -9.4999999999999999e236 < y < -1.64999999999999986e110 or -4.19999999999999972e54 < y < 2.45e182

   1. Initial program 98.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 84.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*l/ 84.5%

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

      3. *-commutative 84.5%

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

   7. Simplified 84.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+236} \lor \neg \left(y \leq -1.65 \cdot 10^{+110} \lor \neg \left(y \leq -4.2 \cdot 10^{+54}\right) \land y \leq 2.45 \cdot 10^{+182}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-64} \lor \neg \left(a \leq -2.5 \cdot 10^{-91}\right) \land \left(a \leq -1.7 \cdot 10^{-169} \lor \neg \left(a \leq 2.6 \cdot 10^{+33}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.7e-64)
         (and (not (<= a -2.5e-91))
              (or (<= a -1.7e-169) (not (<= a 2.6e+33)))))
   (* a 120.0)
   (* -60.0 (/ y (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-64) || (!(a <= -2.5e-91) && ((a <= -1.7e-169) || !(a <= 2.6e+33)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.7d-64)) .or. (.not. (a <= (-2.5d-91))) .and. (a <= (-1.7d-169)) .or. (.not. (a <= 2.6d+33))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-64) || (!(a <= -2.5e-91) && ((a <= -1.7e-169) || !(a <= 2.6e+33)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.7e-64) or (not (a <= -2.5e-91) and ((a <= -1.7e-169) or not (a <= 2.6e+33))):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.7e-64) || (!(a <= -2.5e-91) && ((a <= -1.7e-169) || !(a <= 2.6e+33))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.7e-64) || (~((a <= -2.5e-91)) && ((a <= -1.7e-169) || ~((a <= 2.6e+33)))))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.7e-64], And[N[Not[LessEqual[a, -2.5e-91]], $MachinePrecision], Or[LessEqual[a, -1.7e-169], N[Not[LessEqual[a, 2.6e+33]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.6999999999999998e-64 or -2.49999999999999999e-91 < a < -1.7e-169 or 2.5999999999999997e33 < a

   1. Initial program 98.5%

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

   5. Taylor expanded in z around inf 70.7%

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

   if -4.6999999999999998e-64 < a < -2.49999999999999999e-91 or -1.7e-169 < a < 2.5999999999999997e33

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 81.5%

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

   6. Taylor expanded in x around 0 48.9%

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

      1. neg-mul-1 48.9%

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

      2. distribute-neg-frac 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in y around 0 48.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-64} \lor \neg \left(a \leq -2.5 \cdot 10^{-91}\right) \land \left(a \leq -1.7 \cdot 10^{-169} \lor \neg \left(a \leq 2.6 \cdot 10^{+33}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-92}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-175} \lor \neg \left(a \leq 1.6 \cdot 10^{-12}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e-64)
   (* a 120.0)
   (if (<= a -3.5e-92)
     (* -60.0 (/ y (- z t)))
     (if (or (<= a -1.2e-175) (not (<= a 1.6e-12)))
       (* a 120.0)
       (* -60.0 (/ (- x y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-64) {
		tmp = a * 120.0;
	} else if (a <= -3.5e-92) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a <= -1.2e-175) || !(a <= 1.6e-12)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.5d-64)) then
        tmp = a * 120.0d0
    else if (a <= (-3.5d-92)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if ((a <= (-1.2d-175)) .or. (.not. (a <= 1.6d-12))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-64) {
		tmp = a * 120.0;
	} else if (a <= -3.5e-92) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a <= -1.2e-175) || !(a <= 1.6e-12)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e-64:
		tmp = a * 120.0
	elif a <= -3.5e-92:
		tmp = -60.0 * (y / (z - t))
	elif (a <= -1.2e-175) or not (a <= 1.6e-12):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e-64)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.5e-92)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif ((a <= -1.2e-175) || !(a <= 1.6e-12))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e-64)
		tmp = a * 120.0;
	elseif (a <= -3.5e-92)
		tmp = -60.0 * (y / (z - t));
	elseif ((a <= -1.2e-175) || ~((a <= 1.6e-12)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e-64], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.5e-92], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.2e-175], N[Not[LessEqual[a, 1.6e-12]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5000000000000001e-64 or -3.5e-92 < a < -1.2e-175 or 1.6e-12 < a

   1. Initial program 98.6%

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

   5. Taylor expanded in z around inf 68.5%

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

   if -4.5000000000000001e-64 < a < -3.5e-92

   1. Initial program 99.6%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0 87.9%

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

   6. Taylor expanded in x around 0 75.8%

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

      1. neg-mul-1 75.8%

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

      2. distribute-neg-frac 75.8%

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

   8. Simplified 75.8%

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

   9. Taylor expanded in y around 0 75.8%

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

   if -1.2e-175 < a < 1.6e-12

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 81.4%

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

   6. Taylor expanded in z around 0 52.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-92}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-175} \lor \neg \left(a \leq 1.6 \cdot 10^{-12}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ \mathbf{if}\;t \leq -3.65 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-90}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}} + a \cdot 120\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+32}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ -60.0 (/ t (- x y))) (* a 120.0))))
   (if (<= t -3.65e-10)
     t_1
     (if (<= t 3e-90)
       (+ (/ 60.0 (/ z (- x y))) (* a 120.0))
       (if (<= t 1.9e+32) (* 60.0 (/ (- x y) (- z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / (t / (x - y))) + (a * 120.0);
	double tmp;
	if (t <= -3.65e-10) {
		tmp = t_1;
	} else if (t <= 3e-90) {
		tmp = (60.0 / (z / (x - y))) + (a * 120.0);
	} else if (t <= 1.9e+32) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-60.0d0) / (t / (x - y))) + (a * 120.0d0)
    if (t <= (-3.65d-10)) then
        tmp = t_1
    else if (t <= 3d-90) then
        tmp = (60.0d0 / (z / (x - y))) + (a * 120.0d0)
    else if (t <= 1.9d+32) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / (t / (x - y))) + (a * 120.0);
	double tmp;
	if (t <= -3.65e-10) {
		tmp = t_1;
	} else if (t <= 3e-90) {
		tmp = (60.0 / (z / (x - y))) + (a * 120.0);
	} else if (t <= 1.9e+32) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 / (t / (x - y))) + (a * 120.0)
	tmp = 0
	if t <= -3.65e-10:
		tmp = t_1
	elif t <= 3e-90:
		tmp = (60.0 / (z / (x - y))) + (a * 120.0)
	elif t <= 1.9e+32:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 / Float64(t / Float64(x - y))) + Float64(a * 120.0))
	tmp = 0.0
	if (t <= -3.65e-10)
		tmp = t_1;
	elseif (t <= 3e-90)
		tmp = Float64(Float64(60.0 / Float64(z / Float64(x - y))) + Float64(a * 120.0));
	elseif (t <= 1.9e+32)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 / (t / (x - y))) + (a * 120.0);
	tmp = 0.0;
	if (t <= -3.65e-10)
		tmp = t_1;
	elseif (t <= 3e-90)
		tmp = (60.0 / (z / (x - y))) + (a * 120.0);
	elseif (t <= 1.9e+32)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.65e-10], t$95$1, If[LessEqual[t, 3e-90], N[(N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+32], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6499999999999998e-10 or 1.9000000000000002e32 < t

   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* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 89.7%

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

      1. associate-*r/ 88.9%

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

      2. associate-/l* 89.6%

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

   7. Simplified 89.6%

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

   if -3.6499999999999998e-10 < t < 3.0000000000000002e-90

   1. Initial program 98.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 87.9%

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

   if 3.0000000000000002e-90 < t < 1.9000000000000002e32

   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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 87.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{-10}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-90}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}} + a \cdot 120\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+32}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+45} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{+35}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -4e+45) (not (<= (* a 120.0) 5e+35)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -4e+45) || !((a * 120.0) <= 5e+35)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-4d+45)) .or. (.not. ((a * 120.0d0) <= 5d+35))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -4e+45) || !((a * 120.0) <= 5e+35)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -4e+45) or not ((a * 120.0) <= 5e+35):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -4e+45) || !(Float64(a * 120.0) <= 5e+35))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -4e+45) || ~(((a * 120.0) <= 5e+35)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+45], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+35]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -3.9999999999999997e45 or 5.00000000000000021e35 < (*.f64 a 120)

   1. Initial program 98.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 81.9%

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

   if -3.9999999999999997e45 < (*.f64 a 120) < 5.00000000000000021e35

   1. Initial program 99.0%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 74.3%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+45} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{+35}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+44} \lor \neg \left(x \leq 5.2 \cdot 10^{+173}\right):\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -8.2e+44) (not (<= x 5.2e+173)))
   (+ (* (/ 60.0 (- z t)) x) (* a 120.0))
   (+ (/ (* y -60.0) (- z t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8.2e+44) || !(x <= 5.2e+173)) {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-8.2d+44)) .or. (.not. (x <= 5.2d+173))) then
        tmp = ((60.0d0 / (z - t)) * x) + (a * 120.0d0)
    else
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8.2e+44) || !(x <= 5.2e+173)) {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -8.2e+44) or not (x <= 5.2e+173):
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0)
	else:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -8.2e+44) || !(x <= 5.2e+173))
		tmp = Float64(Float64(Float64(60.0 / Float64(z - t)) * x) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -8.2e+44) || ~((x <= 5.2e+173)))
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	else
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -8.2e+44], N[Not[LessEqual[x, 5.2e+173]], $MachinePrecision]], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999993e44 or 5.1999999999999997e173 < x

   1. Initial program 97.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 88.3%

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

      1. associate-*r/ 85.8%

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

      2. associate-*l/ 88.3%

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

      3. *-commutative 88.3%

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

   7. Simplified 88.3%

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

   if -8.1999999999999993e44 < x < 5.1999999999999997e173

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 92.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+44} \lor \neg \left(x \leq 5.2 \cdot 10^{+173}\right):\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-212} \lor \neg \left(a \leq 1.4 \cdot 10^{-203}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.8e-212) (not (<= a 1.4e-203)))
   (* a 120.0)
   (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.8e-212) || !(a <= 1.4e-203)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7.8d-212)) .or. (.not. (a <= 1.4d-203))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.8e-212) || !(a <= 1.4e-203)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.8e-212) or not (a <= 1.4e-203):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.8e-212) || !(a <= 1.4e-203))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.8e-212) || ~((a <= 1.4e-203)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.8e-212], N[Not[LessEqual[a, 1.4e-203]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.8e-212 or 1.40000000000000011e-203 < a

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 59.0%

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

   if -7.8e-212 < a < 1.40000000000000011e-203

   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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 93.3%

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

   6. Taylor expanded in z around 0 58.6%

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

   7. Taylor expanded in x around inf 29.1%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-212} \lor \neg \left(a \leq 1.4 \cdot 10^{-203}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+237}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 10^{+236}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.7e+237)
   (* 60.0 (/ y t))
   (if (<= y 1e+236) (* a 120.0) (* -60.0 (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.7e+237) {
		tmp = 60.0 * (y / t);
	} else if (y <= 1e+236) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.7d+237)) then
        tmp = 60.0d0 * (y / t)
    else if (y <= 1d+236) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.7e+237) {
		tmp = 60.0 * (y / t);
	} else if (y <= 1e+236) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.7e+237:
		tmp = 60.0 * (y / t)
	elif y <= 1e+236:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.7e+237)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (y <= 1e+236)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.7e+237)
		tmp = 60.0 * (y / t);
	elseif (y <= 1e+236)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.7e+237], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+236], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6999999999999999e237

   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. Add Preprocessing

   5. Taylor expanded in a around 0 86.9%

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

   6. Taylor expanded in x around 0 82.3%

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

      1. neg-mul-1 82.3%

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

      2. distribute-neg-frac 82.3%

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

   8. Simplified 82.3%

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

   9. Taylor expanded in z around 0 54.5%

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

   if -2.6999999999999999e237 < y < 1.00000000000000005e236

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 55.4%

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

   if 1.00000000000000005e236 < 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* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 87.3%

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

   6. Taylor expanded in x around 0 74.0%

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

      1. neg-mul-1 74.0%

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

      2. distribute-neg-frac 74.0%

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

   8. Simplified 74.0%

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

   9. Taylor expanded in z around inf 48.5%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+237}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 10^{+236}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+237}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+234}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{-60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.42e+237)
   (* 60.0 (/ y t))
   (if (<= y 2.3e+234) (* a 120.0) (/ y (/ z -60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.42e+237) {
		tmp = 60.0 * (y / t);
	} else if (y <= 2.3e+234) {
		tmp = a * 120.0;
	} else {
		tmp = y / (z / -60.0);
	}
	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 <= (-1.42d+237)) then
        tmp = 60.0d0 * (y / t)
    else if (y <= 2.3d+234) then
        tmp = a * 120.0d0
    else
        tmp = y / (z / (-60.0d0))
    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 <= -1.42e+237) {
		tmp = 60.0 * (y / t);
	} else if (y <= 2.3e+234) {
		tmp = a * 120.0;
	} else {
		tmp = y / (z / -60.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.42e+237:
		tmp = 60.0 * (y / t)
	elif y <= 2.3e+234:
		tmp = a * 120.0
	else:
		tmp = y / (z / -60.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.42e+237)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (y <= 2.3e+234)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y / Float64(z / -60.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.42e+237)
		tmp = 60.0 * (y / t);
	elseif (y <= 2.3e+234)
		tmp = a * 120.0;
	else
		tmp = y / (z / -60.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.42e+237], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+234], N[(a * 120.0), $MachinePrecision], N[(y / N[(z / -60.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.42000000000000004e237

   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. Add Preprocessing

   5. Taylor expanded in a around 0 86.9%

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

   6. Taylor expanded in x around 0 82.3%

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

      1. neg-mul-1 82.3%

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

      2. distribute-neg-frac 82.3%

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

   8. Simplified 82.3%

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

   9. Taylor expanded in z around 0 54.5%

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

   if -1.42000000000000004e237 < y < 2.3000000000000001e234

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 55.4%

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

   if 2.3000000000000001e234 < 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* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 87.3%

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

   6. Taylor expanded in x around 0 74.0%

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

      1. neg-mul-1 74.0%

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

      2. distribute-neg-frac 74.0%

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

   8. Simplified 74.0%

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

   9. Taylor expanded in z around inf 48.5%

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

       1. associate-*r/ 48.7%

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

       2. *-commutative 48.7%

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

       3. associate-/l* 48.6%

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

   11. Simplified 48.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+237}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+234}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{-60}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

5. Final simplification 99.7%

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

Alternative 15: 51.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.4 \cdot 10^{+232}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 8.4e+232) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 8.4e+232) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 8.4d+232) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 8.4e+232) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 8.4e+232:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 8.4e+232)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 8.4e+232)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 8.4e+232], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.39999999999999965e232

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 52.9%

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

   if 8.39999999999999965e232 < 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* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 87.3%

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

   6. Taylor expanded in x around 0 74.0%

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

      1. neg-mul-1 74.0%

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

      2. distribute-neg-frac 74.0%

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

   8. Simplified 74.0%

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

   9. Taylor expanded in z around inf 48.5%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.4 \cdot 10^{+232}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.4% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in z around inf 49.8%

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

6. Final simplification 49.8%

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

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024027 
(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)))