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

Percentage Accurate: 99.4% → 99.8%

Time: 22.6s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-define 99.8%

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

   3. associate-*r/ 99.5%

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

   4. *-commutative 99.5%

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

   5. associate-/l* 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+128}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -8 \cdot 10^{+54}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t))))
        (t_2 (+ (* a 120.0) (* -60.0 (/ x t)))))
   (if (<= (* a 120.0) -2e+128)
     (+ (* a 120.0) (* 60.0 (/ y t)))
     (if (<= (* a 120.0) -8e+54)
       (+ (* a 120.0) (/ (* y -60.0) z))
       (if (<= (* a 120.0) -1e-59)
         t_2
         (if (<= (* a 120.0) 5e-33)
           t_1
           (if (<= (* a 120.0) 2e-13)
             t_2
             (if (<= (* a 120.0) 2e+28) t_1 (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -2e+128) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= -8e+54) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else if ((a * 120.0) <= -1e-59) {
		tmp = t_2;
	} else if ((a * 120.0) <= 5e-33) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-13) {
		tmp = t_2;
	} else if ((a * 120.0) <= 2e+28) {
		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 - y) / (z - t))
    t_2 = (a * 120.0d0) + ((-60.0d0) * (x / t))
    if ((a * 120.0d0) <= (-2d+128)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= (-8d+54)) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / z)
    else if ((a * 120.0d0) <= (-1d-59)) then
        tmp = t_2
    else if ((a * 120.0d0) <= 5d-33) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-13) then
        tmp = t_2
    else if ((a * 120.0d0) <= 2d+28) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -2e+128) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= -8e+54) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else if ((a * 120.0) <= -1e-59) {
		tmp = t_2;
	} else if ((a * 120.0) <= 5e-33) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-13) {
		tmp = t_2;
	} else if ((a * 120.0) <= 2e+28) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	t_2 = (a * 120.0) + (-60.0 * (x / t))
	tmp = 0
	if (a * 120.0) <= -2e+128:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= -8e+54:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	elif (a * 120.0) <= -1e-59:
		tmp = t_2
	elif (a * 120.0) <= 5e-33:
		tmp = t_1
	elif (a * 120.0) <= 2e-13:
		tmp = t_2
	elif (a * 120.0) <= 2e+28:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+128)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= -8e+54)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	elseif (Float64(a * 120.0) <= -1e-59)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= 5e-33)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-13)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= 2e+28)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	t_2 = (a * 120.0) + (-60.0 * (x / t));
	tmp = 0.0;
	if ((a * 120.0) <= -2e+128)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= -8e+54)
		tmp = (a * 120.0) + ((y * -60.0) / z);
	elseif ((a * 120.0) <= -1e-59)
		tmp = t_2;
	elseif ((a * 120.0) <= 5e-33)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-13)
		tmp = t_2;
	elseif ((a * 120.0) <= 2e+28)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+128], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -8e+54], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-59], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-33], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-13], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+28], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -2.0000000000000002e128

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.3%

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

   6. Taylor expanded in x around 0 97.0%

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

   if -2.0000000000000002e128 < (*.f64 a 120) < -8.0000000000000006e54

   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* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.8%

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

      1. associate-*r/ 23.2%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in x around 0 92.9%

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

   if -8.0000000000000006e54 < (*.f64 a 120) < -1e-59 or 5.00000000000000028e-33 < (*.f64 a 120) < 2.0000000000000001e-13

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 93.1%

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

   6. Taylor expanded in z around 0 79.8%

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

   if -1e-59 < (*.f64 a 120) < 5.00000000000000028e-33 or 2.0000000000000001e-13 < (*.f64 a 120) < 1.99999999999999992e28

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 98.8%

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

      4. *-commutative 98.8%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 82.6%

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

   if 1.99999999999999992e28 < (*.f64 a 120)

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 86.0%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+128}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -8 \cdot 10^{+54}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-59}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-33}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-13}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(120 + 60 \cdot \frac{y}{a \cdot t}\right)\\ \mathbf{elif}\;a \cdot 120 \leq -8 \cdot 10^{+54}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t))))
        (t_2 (+ (* a 120.0) (* -60.0 (/ x t)))))
   (if (<= (* a 120.0) -2e+128)
     (* a (+ 120.0 (* 60.0 (/ y (* a t)))))
     (if (<= (* a 120.0) -8e+54)
       (+ (* a 120.0) (/ (* y -60.0) z))
       (if (<= (* a 120.0) -1e-59)
         t_2
         (if (<= (* a 120.0) 5e-33)
           t_1
           (if (<= (* a 120.0) 2e-13)
             t_2
             (if (<= (* a 120.0) 2e+28) t_1 (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -2e+128) {
		tmp = a * (120.0 + (60.0 * (y / (a * t))));
	} else if ((a * 120.0) <= -8e+54) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else if ((a * 120.0) <= -1e-59) {
		tmp = t_2;
	} else if ((a * 120.0) <= 5e-33) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-13) {
		tmp = t_2;
	} else if ((a * 120.0) <= 2e+28) {
		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 - y) / (z - t))
    t_2 = (a * 120.0d0) + ((-60.0d0) * (x / t))
    if ((a * 120.0d0) <= (-2d+128)) then
        tmp = a * (120.0d0 + (60.0d0 * (y / (a * t))))
    else if ((a * 120.0d0) <= (-8d+54)) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / z)
    else if ((a * 120.0d0) <= (-1d-59)) then
        tmp = t_2
    else if ((a * 120.0d0) <= 5d-33) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-13) then
        tmp = t_2
    else if ((a * 120.0d0) <= 2d+28) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -2e+128) {
		tmp = a * (120.0 + (60.0 * (y / (a * t))));
	} else if ((a * 120.0) <= -8e+54) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else if ((a * 120.0) <= -1e-59) {
		tmp = t_2;
	} else if ((a * 120.0) <= 5e-33) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-13) {
		tmp = t_2;
	} else if ((a * 120.0) <= 2e+28) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	t_2 = (a * 120.0) + (-60.0 * (x / t))
	tmp = 0
	if (a * 120.0) <= -2e+128:
		tmp = a * (120.0 + (60.0 * (y / (a * t))))
	elif (a * 120.0) <= -8e+54:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	elif (a * 120.0) <= -1e-59:
		tmp = t_2
	elif (a * 120.0) <= 5e-33:
		tmp = t_1
	elif (a * 120.0) <= 2e-13:
		tmp = t_2
	elif (a * 120.0) <= 2e+28:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+128)
		tmp = Float64(a * Float64(120.0 + Float64(60.0 * Float64(y / Float64(a * t)))));
	elseif (Float64(a * 120.0) <= -8e+54)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	elseif (Float64(a * 120.0) <= -1e-59)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= 5e-33)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-13)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= 2e+28)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	t_2 = (a * 120.0) + (-60.0 * (x / t));
	tmp = 0.0;
	if ((a * 120.0) <= -2e+128)
		tmp = a * (120.0 + (60.0 * (y / (a * t))));
	elseif ((a * 120.0) <= -8e+54)
		tmp = (a * 120.0) + ((y * -60.0) / z);
	elseif ((a * 120.0) <= -1e-59)
		tmp = t_2;
	elseif ((a * 120.0) <= 5e-33)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-13)
		tmp = t_2;
	elseif ((a * 120.0) <= 2e+28)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+128], N[(a * N[(120.0 + N[(60.0 * N[(y / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -8e+54], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-59], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-33], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-13], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+28], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -2.0000000000000002e128

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. times-frac 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 82.4%

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

      1. *-commutative 82.4%

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

   10. Simplified 82.4%

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

   11. Taylor expanded in x around 0 97.1%

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

       1. *-commutative 97.1%

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

   13. Simplified 97.1%

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

   if -2.0000000000000002e128 < (*.f64 a 120) < -8.0000000000000006e54

   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* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.8%

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

      1. associate-*r/ 23.2%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in x around 0 92.9%

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

   if -8.0000000000000006e54 < (*.f64 a 120) < -1e-59 or 5.00000000000000028e-33 < (*.f64 a 120) < 2.0000000000000001e-13

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 93.1%

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

   6. Taylor expanded in z around 0 79.8%

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

   if -1e-59 < (*.f64 a 120) < 5.00000000000000028e-33 or 2.0000000000000001e-13 < (*.f64 a 120) < 1.99999999999999992e28

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 98.8%

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

      4. *-commutative 98.8%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 82.6%

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

   if 1.99999999999999992e28 < (*.f64 a 120)

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 86.0%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(120 + 60 \cdot \frac{y}{a \cdot t}\right)\\ \mathbf{elif}\;a \cdot 120 \leq -8 \cdot 10^{+54}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-59}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-33}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-13}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-13}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -1e-58)
     (* a 120.0)
     (if (<= (* a 120.0) 5e-33)
       t_1
       (if (<= (* a 120.0) 2e-13)
         (+ (* a 120.0) (* -60.0 (/ x t)))
         (if (<= (* a 120.0) 2e+28) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -1e-58) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-33) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-13) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 2e+28) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-1d-58)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d-33) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-13) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else if ((a * 120.0d0) <= 2d+28) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -1e-58) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-33) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-13) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 2e+28) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -1e-58:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e-33:
		tmp = t_1
	elif (a * 120.0) <= 2e-13:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	elif (a * 120.0) <= 2e+28:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-58)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e-33)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-13)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 2e+28)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -1e-58)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e-33)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-13)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	elseif ((a * 120.0) <= 2e+28)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-58], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-33], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-13], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+28], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -1e-58 or 1.99999999999999992e28 < (*.f64 a 120)

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 83.7%

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

   if -1e-58 < (*.f64 a 120) < 5.00000000000000028e-33 or 2.0000000000000001e-13 < (*.f64 a 120) < 1.99999999999999992e28

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 98.8%

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

      4. *-commutative 98.8%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 82.5%

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

   if 5.00000000000000028e-33 < (*.f64 a 120) < 2.0000000000000001e-13

   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* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

   6. Taylor expanded in z around 0 99.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-33}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-13}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-221}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-295}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-52}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.2e-120)
   (* a 120.0)
   (if (<= a -6e-221)
     (* -60.0 (/ (- x y) t))
     (if (<= a -2.5e-295)
       (/ (* (- x y) 60.0) z)
       (if (<= a 6.2e-52) (* -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 <= -7.2e-120) {
		tmp = a * 120.0;
	} else if (a <= -6e-221) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= -2.5e-295) {
		tmp = ((x - y) * 60.0) / z;
	} else if (a <= 6.2e-52) {
		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 <= (-7.2d-120)) then
        tmp = a * 120.0d0
    else if (a <= (-6d-221)) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= (-2.5d-295)) then
        tmp = ((x - y) * 60.0d0) / z
    else if (a <= 6.2d-52) 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 <= -7.2e-120) {
		tmp = a * 120.0;
	} else if (a <= -6e-221) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= -2.5e-295) {
		tmp = ((x - y) * 60.0) / z;
	} else if (a <= 6.2e-52) {
		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 <= -7.2e-120:
		tmp = a * 120.0
	elif a <= -6e-221:
		tmp = -60.0 * ((x - y) / t)
	elif a <= -2.5e-295:
		tmp = ((x - y) * 60.0) / z
	elif a <= 6.2e-52:
		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 <= -7.2e-120)
		tmp = Float64(a * 120.0);
	elseif (a <= -6e-221)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= -2.5e-295)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / z);
	elseif (a <= 6.2e-52)
		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 <= -7.2e-120)
		tmp = a * 120.0;
	elseif (a <= -6e-221)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= -2.5e-295)
		tmp = ((x - y) * 60.0) / z;
	elseif (a <= 6.2e-52)
		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, -7.2e-120], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6e-221], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5e-295], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 6.2e-52], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.2000000000000005e-120 or 6.1999999999999998e-52 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 76.6%

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

   if -7.2000000000000005e-120 < a < -6.0000000000000003e-221

   1. Initial program 94.9%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. fma-define 99.5%

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

      3. associate-*r/ 94.9%

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

      4. *-commutative 94.9%

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

      5. associate-/l* 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 88.3%

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

   8. Taylor expanded in z around 0 66.1%

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

   if -6.0000000000000003e-221 < a < -2.50000000000000004e-295

   1. Initial program 99.5%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. associate-*r/ 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-/l* 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 84.1%

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

   8. Taylor expanded in z around inf 76.3%

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

      1. associate-*r/ 76.1%

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

   10. Simplified 76.1%

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

   if -2.50000000000000004e-295 < a < 6.1999999999999998e-52

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. associate-*r/ 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 87.1%

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

   8. Taylor expanded in x around 0 57.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-221}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-295}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-52}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \frac{60}{-t}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-294}:\\ \;\;\;\;\frac{x \cdot 60}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-168}:\\ \;\;\;\;-60 \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e-120)
   (* a 120.0)
   (if (<= a -1.04e-218)
     (* x (/ 60.0 (- t)))
     (if (<= a -5e-294)
       (/ (* x 60.0) z)
       (if (<= a 2.3e-168) (* -60.0 (/ y (- t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-120) {
		tmp = a * 120.0;
	} else if (a <= -1.04e-218) {
		tmp = x * (60.0 / -t);
	} else if (a <= -5e-294) {
		tmp = (x * 60.0) / z;
	} else if (a <= 2.3e-168) {
		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 <= (-8.5d-120)) then
        tmp = a * 120.0d0
    else if (a <= (-1.04d-218)) then
        tmp = x * (60.0d0 / -t)
    else if (a <= (-5d-294)) then
        tmp = (x * 60.0d0) / z
    else if (a <= 2.3d-168) 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 <= -8.5e-120) {
		tmp = a * 120.0;
	} else if (a <= -1.04e-218) {
		tmp = x * (60.0 / -t);
	} else if (a <= -5e-294) {
		tmp = (x * 60.0) / z;
	} else if (a <= 2.3e-168) {
		tmp = -60.0 * (y / -t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e-120:
		tmp = a * 120.0
	elif a <= -1.04e-218:
		tmp = x * (60.0 / -t)
	elif a <= -5e-294:
		tmp = (x * 60.0) / z
	elif a <= 2.3e-168:
		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 <= -8.5e-120)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.04e-218)
		tmp = Float64(x * Float64(60.0 / Float64(-t)));
	elseif (a <= -5e-294)
		tmp = Float64(Float64(x * 60.0) / z);
	elseif (a <= 2.3e-168)
		tmp = Float64(-60.0 * Float64(y / Float64(-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 <= -8.5e-120)
		tmp = a * 120.0;
	elseif (a <= -1.04e-218)
		tmp = x * (60.0 / -t);
	elseif (a <= -5e-294)
		tmp = (x * 60.0) / z;
	elseif (a <= 2.3e-168)
		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, -8.5e-120], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.04e-218], N[(x * N[(60.0 / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-294], N[(N[(x * 60.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.3e-168], N[(-60.0 * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.50000000000000059e-120 or 2.29999999999999986e-168 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.3%

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

   if -8.50000000000000059e-120 < a < -1.04000000000000001e-218

   1. Initial program 94.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 59.0%

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

   6. Taylor expanded in x around -inf 58.9%

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

      1. associate-*r* 58.9%

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

      2. neg-mul-1 58.9%

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

      3. *-commutative 58.9%

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

      4. associate-*r/ 58.8%

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

      5. metadata-eval 58.8%

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

   8. Simplified 58.8%

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

   9. Taylor expanded in z around 0 51.1%

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

   10. Taylor expanded in a around 0 39.0%

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

   if -1.04000000000000001e-218 < a < -5.0000000000000003e-294

   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* 99.5%

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

   3. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. fma-define 99.5%

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

      3. associate-*r/ 99.4%

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

      4. *-commutative 99.4%

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

      5. associate-/l* 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 85.2%

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

   8. Taylor expanded in z around inf 70.5%

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

      1. associate-*r/ 70.3%

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

   10. Simplified 70.3%

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

   11. Taylor expanded in x around inf 41.6%

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

   if -5.0000000000000003e-294 < a < 2.29999999999999986e-168

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 91.6%

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

   8. Taylor expanded in x around 0 61.4%

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

   9. Taylor expanded in z around 0 41.4%

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

       1. associate-*r/ 41.4%

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

       2. neg-mul-1 41.4%

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

   11. Simplified 41.4%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \frac{60}{-t}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-294}:\\ \;\;\;\;\frac{x \cdot 60}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-168}:\\ \;\;\;\;-60 \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-117} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-33}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-117) (not (<= (* a 120.0) 5e-33)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (* 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) <= -2e-117) || !((a * 120.0) <= 5e-33)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2d-117)) .or. (.not. ((a * 120.0d0) <= 5d-33))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-117) || !((a * 120.0) <= 5e-33)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-117) or not ((a * 120.0) <= 5e-33):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	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) <= -2e-117) || !(Float64(a * 120.0) <= 5e-33))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-117) || ~(((a * 120.0) <= 5e-33)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	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], -2e-117], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-33]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -2.00000000000000006e-117 or 5.00000000000000028e-33 < (*.f64 a 120)

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 89.9%

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

   if -2.00000000000000006e-117 < (*.f64 a 120) < 5.00000000000000028e-33

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 98.6%

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

      4. *-commutative 98.6%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 85.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-117} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-33}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-46} \lor \neg \left(z \leq 6 \cdot 10^{-41}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e-46) (not (<= z 6e-41)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (+ (* a 120.0) (* -60.0 (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-46) || !(z <= 6e-41)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (-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 ((z <= (-1.2d-46)) .or. (.not. (z <= 6d-41))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = (a * 120.0d0) + ((-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 ((z <= -1.2e-46) || !(z <= 6e-41)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e-46) or not (z <= 6e-41):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e-46) || !(z <= 6e-41))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + 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 ((z <= -1.2e-46) || ~((z <= 6e-41)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e-46], N[Not[LessEqual[z, 6e-41]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000007e-46 or 5.99999999999999978e-41 < z

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 87.6%

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

   if -1.20000000000000007e-46 < z < 5.99999999999999978e-41

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 93.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-46} \lor \neg \left(z \leq 6 \cdot 10^{-41}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-15} \lor \neg \left(y \leq 9.2 \cdot 10^{+111}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.8e-15) (not (<= y 9.2e+111)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (+ (* a 120.0) (* 60.0 (/ x (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e-15) || !(y <= 9.2e+111)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.8d-15)) .or. (.not. (y <= 9.2d+111))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e-15) || !(y <= 9.2e+111)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.8e-15) or not (y <= 9.2e+111):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.8e-15) || !(y <= 9.2e+111))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.8e-15) || ~((y <= 9.2e+111)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.8e-15], N[Not[LessEqual[y, 9.2e+111]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8000000000000001e-15 or 9.20000000000000008e111 < y

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 91.1%

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

   if -1.8000000000000001e-15 < y < 9.20000000000000008e111

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 93.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-15} \lor \neg \left(y \leq 9.2 \cdot 10^{+111}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-15} \lor \neg \left(y \leq 3 \cdot 10^{+111}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.8e-15) (not (<= y 3e+111)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (+ (* a 120.0) (/ (* x 60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e-15) || !(y <= 3e+111)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.8d-15)) .or. (.not. (y <= 3d+111))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = (a * 120.0d0) + ((x * 60.0d0) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e-15) || !(y <= 3e+111)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.8e-15) or not (y <= 3e+111):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = (a * 120.0) + ((x * 60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.8e-15) || !(y <= 3e+111))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * 60.0) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.8e-15) || ~((y <= 3e+111)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.8e-15], N[Not[LessEqual[y, 3e+111]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8000000000000001e-15 or 3e111 < y

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 91.1%

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

   if -1.8000000000000001e-15 < y < 3e111

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 93.9%

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

      1. associate-*r/ 93.9%

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

   7. Simplified 93.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-15} \lor \neg \left(y \leq 3 \cdot 10^{+111}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-61} \lor \neg \left(a \leq 1.05 \cdot 10^{+27}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.3e-61) (not (<= a 1.05e+27)))
   (* 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 <= -5.3e-61) || !(a <= 1.05e+27)) {
		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 <= (-5.3d-61)) .or. (.not. (a <= 1.05d+27))) 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 <= -5.3e-61) || !(a <= 1.05e+27)) {
		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 <= -5.3e-61) or not (a <= 1.05e+27):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.3e-61) || !(a <= 1.05e+27))
		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 <= -5.3e-61) || ~((a <= 1.05e+27)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.3e-61], N[Not[LessEqual[a, 1.05e+27]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.3e-61 or 1.04999999999999997e27 < a

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 83.7%

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

   if -5.3e-61 < a < 1.04999999999999997e27

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 98.9%

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

      4. *-commutative 98.9%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 79.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-61} \lor \neg \left(a \leq 1.05 \cdot 10^{+27}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-121} \lor \neg \left(a \leq 1.1 \cdot 10^{-51}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.6e-121) (not (<= a 1.1e-51)))
   (* 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 <= -7.6e-121) || !(a <= 1.1e-51)) {
		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 <= (-7.6d-121)) .or. (.not. (a <= 1.1d-51))) 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 <= -7.6e-121) || !(a <= 1.1e-51)) {
		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 <= -7.6e-121) or not (a <= 1.1e-51):
		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 <= -7.6e-121) || !(a <= 1.1e-51))
		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 <= -7.6e-121) || ~((a <= 1.1e-51)))
		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, -7.6e-121], N[Not[LessEqual[a, 1.1e-51]], $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 < -7.6000000000000002e-121 or 1.1e-51 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 76.2%

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

   if -7.6000000000000002e-121 < a < 1.1e-51

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 98.5%

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

      4. *-commutative 98.5%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 87.2%

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

   8. Taylor expanded in x around 0 52.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-121} \lor \neg \left(a \leq 1.1 \cdot 10^{-51}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-120} \lor \neg \left(a \leq 5.9 \cdot 10^{-34}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.2e-120) (not (<= a 5.9e-34)))
   (* 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 <= -7.2e-120) || !(a <= 5.9e-34)) {
		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 <= (-7.2d-120)) .or. (.not. (a <= 5.9d-34))) 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 <= -7.2e-120) || !(a <= 5.9e-34)) {
		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 <= -7.2e-120) or not (a <= 5.9e-34):
		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 <= -7.2e-120) || !(a <= 5.9e-34))
		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 <= -7.2e-120) || ~((a <= 5.9e-34)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.2e-120], N[Not[LessEqual[a, 5.9e-34]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.2000000000000005e-120 or 5.9000000000000002e-34 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 78.0%

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

   if -7.2000000000000005e-120 < a < 5.9000000000000002e-34

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 98.6%

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

      4. *-commutative 98.6%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 85.6%

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

   8. Taylor expanded in z around 0 50.8%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-120} \lor \neg \left(a \leq 5.9 \cdot 10^{-34}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-122} \lor \neg \left(a \leq 1.5 \cdot 10^{-165}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8e-122) (not (<= a 1.5e-165)))
   (* a 120.0)
   (* -60.0 (/ y (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8e-122) || !(a <= 1.5e-165)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (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 <= (-8d-122)) .or. (.not. (a <= 1.5d-165))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (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 <= -8e-122) || !(a <= 1.5e-165)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8e-122) or not (a <= 1.5e-165):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / -t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8e-122) || !(a <= 1.5e-165))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8e-122) || ~((a <= 1.5e-165)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8e-122], N[Not[LessEqual[a, 1.5e-165]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.00000000000000047e-122 or 1.49999999999999989e-165 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -8.00000000000000047e-122 < a < 1.49999999999999989e-165

   1. Initial program 98.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 98.2%

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

      4. *-commutative 98.2%

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

      5. associate-/l* 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 89.6%

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

   8. Taylor expanded in x around 0 53.2%

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

   9. Taylor expanded in z around 0 34.0%

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

       1. associate-*r/ 34.0%

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

       2. neg-mul-1 34.0%

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

   11. Simplified 34.0%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-122} \lor \neg \left(a \leq 1.5 \cdot 10^{-165}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-251} \lor \neg \left(a \leq 6.1 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.7e-251) (not (<= a 6.1e-52))) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e-251) || !(a <= 6.1e-52)) {
		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 ((a <= (-1.7d-251)) .or. (.not. (a <= 6.1d-52))) 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 ((a <= -1.7e-251) || !(a <= 6.1e-52)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.7e-251) or not (a <= 6.1e-52):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.7e-251) || !(a <= 6.1e-52))
		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 ((a <= -1.7e-251) || ~((a <= 6.1e-52)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.7e-251], N[Not[LessEqual[a, 6.1e-52]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.70000000000000008e-251 or 6.0999999999999999e-52 < 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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 69.0%

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

   if -1.70000000000000008e-251 < a < 6.0999999999999999e-52

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. associate-*r/ 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 88.5%

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

   8. Taylor expanded in x around 0 57.0%

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

   9. Taylor expanded in z around inf 33.3%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-251} \lor \neg \left(a \leq 6.1 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-121} \lor \neg \left(a \leq 6 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.2e-121) (not (<= a 6e-52))) (* a 120.0) (/ (* y -60.0) z)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.2e-121) || !(a <= 6e-52)) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.2d-121)) .or. (.not. (a <= 6d-52))) then
        tmp = a * 120.0d0
    else
        tmp = (y * (-60.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.2e-121) || !(a <= 6e-52)) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.2e-121) or not (a <= 6e-52):
		tmp = a * 120.0
	else:
		tmp = (y * -60.0) / z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.2e-121) || !(a <= 6e-52))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(y * -60.0) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.2e-121) || ~((a <= 6e-52)))
		tmp = a * 120.0;
	else
		tmp = (y * -60.0) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.2e-121], N[Not[LessEqual[a, 6e-52]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.20000000000000002e-121 or 6e-52 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 76.2%

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

   if -1.20000000000000002e-121 < a < 6e-52

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 98.5%

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

      4. *-commutative 98.5%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 87.2%

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

   8. Taylor expanded in x around 0 52.4%

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

   9. Taylor expanded in z around inf 28.7%

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

       1. associate-*r/ 28.8%

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

       2. *-commutative 28.8%

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

   11. Simplified 28.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-121} \lor \neg \left(a \leq 6 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 99.8% accurate, 1.0× speedup

Math

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

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(60.0 * Float64(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[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $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%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 18: 50.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 57.1%

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

6. Final simplification 57.1%

   \[\leadsto a \cdot 120 \]
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 2024055 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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