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

Percentage Accurate: 99.4% → 99.8%

Time: 14.1s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. clear-num 99.8%

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

   2. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 56.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t - z}\\ t_2 := 60 \cdot \frac{y}{t - z}\\ \mathbf{if}\;a \leq -4 \cdot 10^{-75}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x (- t z)))) (t_2 (* 60.0 (/ y (- t z)))))
   (if (<= a -4e-75)
     (* a 120.0)
     (if (<= a -2.75e-210)
       t_2
       (if (<= a -2e-219)
         t_1
         (if (<= a 7.8e-274)
           t_2
           (if (<= a 1.15e-222) t_1 (if (<= a 3e+20) t_2 (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / (t - z));
	double t_2 = 60.0 * (y / (t - z));
	double tmp;
	if (a <= -4e-75) {
		tmp = a * 120.0;
	} else if (a <= -2.75e-210) {
		tmp = t_2;
	} else if (a <= -2e-219) {
		tmp = t_1;
	} else if (a <= 7.8e-274) {
		tmp = t_2;
	} else if (a <= 1.15e-222) {
		tmp = t_1;
	} else if (a <= 3e+20) {
		tmp = t_2;
	} 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 / (t - z))
    t_2 = 60.0d0 * (y / (t - z))
    if (a <= (-4d-75)) then
        tmp = a * 120.0d0
    else if (a <= (-2.75d-210)) then
        tmp = t_2
    else if (a <= (-2d-219)) then
        tmp = t_1
    else if (a <= 7.8d-274) then
        tmp = t_2
    else if (a <= 1.15d-222) then
        tmp = t_1
    else if (a <= 3d+20) then
        tmp = t_2
    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 / (t - z));
	double t_2 = 60.0 * (y / (t - z));
	double tmp;
	if (a <= -4e-75) {
		tmp = a * 120.0;
	} else if (a <= -2.75e-210) {
		tmp = t_2;
	} else if (a <= -2e-219) {
		tmp = t_1;
	} else if (a <= 7.8e-274) {
		tmp = t_2;
	} else if (a <= 1.15e-222) {
		tmp = t_1;
	} else if (a <= 3e+20) {
		tmp = t_2;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / (t - z))
	t_2 = 60.0 * (y / (t - z))
	tmp = 0
	if a <= -4e-75:
		tmp = a * 120.0
	elif a <= -2.75e-210:
		tmp = t_2
	elif a <= -2e-219:
		tmp = t_1
	elif a <= 7.8e-274:
		tmp = t_2
	elif a <= 1.15e-222:
		tmp = t_1
	elif a <= 3e+20:
		tmp = t_2
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / Float64(t - z)))
	t_2 = Float64(60.0 * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (a <= -4e-75)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.75e-210)
		tmp = t_2;
	elseif (a <= -2e-219)
		tmp = t_1;
	elseif (a <= 7.8e-274)
		tmp = t_2;
	elseif (a <= 1.15e-222)
		tmp = t_1;
	elseif (a <= 3e+20)
		tmp = t_2;
	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 / (t - z));
	t_2 = 60.0 * (y / (t - z));
	tmp = 0.0;
	if (a <= -4e-75)
		tmp = a * 120.0;
	elseif (a <= -2.75e-210)
		tmp = t_2;
	elseif (a <= -2e-219)
		tmp = t_1;
	elseif (a <= 7.8e-274)
		tmp = t_2;
	elseif (a <= 1.15e-222)
		tmp = t_1;
	elseif (a <= 3e+20)
		tmp = t_2;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e-75], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.75e-210], t$95$2, If[LessEqual[a, -2e-219], t$95$1, If[LessEqual[a, 7.8e-274], t$95$2, If[LessEqual[a, 1.15e-222], t$95$1, If[LessEqual[a, 3e+20], t$95$2, N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9999999999999998e-75 or 3e20 < 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* 99.9%

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

   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 inf 72.3%

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

   if -3.9999999999999998e-75 < a < -2.75000000000000012e-210 or -2.0000000000000001e-219 < a < 7.79999999999999971e-274 or 1.1500000000000001e-222 < a < 3e20

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 55.5%

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

   if -2.75000000000000012e-210 < a < -2.0000000000000001e-219 or 7.79999999999999971e-274 < a < 1.1500000000000001e-222

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 88.4%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-75}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-210}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-219}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-274}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-222}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+20}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t - z}\\ t_2 := 60 \cdot \frac{y}{t - z}\\ \mathbf{if}\;a \leq -2.65 \cdot 10^{-73}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-275}:\\ \;\;\;\;\frac{60 \cdot y}{t - z}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x (- t z)))) (t_2 (* 60.0 (/ y (- t z)))))
   (if (<= a -2.65e-73)
     (* a 120.0)
     (if (<= a -2.7e-210)
       t_2
       (if (<= a -2.1e-219)
         t_1
         (if (<= a 1.1e-275)
           (/ (* 60.0 y) (- t z))
           (if (<= a 4.8e-225) t_1 (if (<= a 4.5e+20) t_2 (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / (t - z));
	double t_2 = 60.0 * (y / (t - z));
	double tmp;
	if (a <= -2.65e-73) {
		tmp = a * 120.0;
	} else if (a <= -2.7e-210) {
		tmp = t_2;
	} else if (a <= -2.1e-219) {
		tmp = t_1;
	} else if (a <= 1.1e-275) {
		tmp = (60.0 * y) / (t - z);
	} else if (a <= 4.8e-225) {
		tmp = t_1;
	} else if (a <= 4.5e+20) {
		tmp = t_2;
	} 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 / (t - z))
    t_2 = 60.0d0 * (y / (t - z))
    if (a <= (-2.65d-73)) then
        tmp = a * 120.0d0
    else if (a <= (-2.7d-210)) then
        tmp = t_2
    else if (a <= (-2.1d-219)) then
        tmp = t_1
    else if (a <= 1.1d-275) then
        tmp = (60.0d0 * y) / (t - z)
    else if (a <= 4.8d-225) then
        tmp = t_1
    else if (a <= 4.5d+20) then
        tmp = t_2
    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 / (t - z));
	double t_2 = 60.0 * (y / (t - z));
	double tmp;
	if (a <= -2.65e-73) {
		tmp = a * 120.0;
	} else if (a <= -2.7e-210) {
		tmp = t_2;
	} else if (a <= -2.1e-219) {
		tmp = t_1;
	} else if (a <= 1.1e-275) {
		tmp = (60.0 * y) / (t - z);
	} else if (a <= 4.8e-225) {
		tmp = t_1;
	} else if (a <= 4.5e+20) {
		tmp = t_2;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / (t - z))
	t_2 = 60.0 * (y / (t - z))
	tmp = 0
	if a <= -2.65e-73:
		tmp = a * 120.0
	elif a <= -2.7e-210:
		tmp = t_2
	elif a <= -2.1e-219:
		tmp = t_1
	elif a <= 1.1e-275:
		tmp = (60.0 * y) / (t - z)
	elif a <= 4.8e-225:
		tmp = t_1
	elif a <= 4.5e+20:
		tmp = t_2
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / Float64(t - z)))
	t_2 = Float64(60.0 * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (a <= -2.65e-73)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.7e-210)
		tmp = t_2;
	elseif (a <= -2.1e-219)
		tmp = t_1;
	elseif (a <= 1.1e-275)
		tmp = Float64(Float64(60.0 * y) / Float64(t - z));
	elseif (a <= 4.8e-225)
		tmp = t_1;
	elseif (a <= 4.5e+20)
		tmp = t_2;
	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 / (t - z));
	t_2 = 60.0 * (y / (t - z));
	tmp = 0.0;
	if (a <= -2.65e-73)
		tmp = a * 120.0;
	elseif (a <= -2.7e-210)
		tmp = t_2;
	elseif (a <= -2.1e-219)
		tmp = t_1;
	elseif (a <= 1.1e-275)
		tmp = (60.0 * y) / (t - z);
	elseif (a <= 4.8e-225)
		tmp = t_1;
	elseif (a <= 4.5e+20)
		tmp = t_2;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.65e-73], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.7e-210], t$95$2, If[LessEqual[a, -2.1e-219], t$95$1, If[LessEqual[a, 1.1e-275], N[(N[(60.0 * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-225], t$95$1, If[LessEqual[a, 4.5e+20], t$95$2, N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.64999999999999986e-73 or 4.5e20 < 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* 99.9%

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

   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 inf 72.3%

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

   if -2.64999999999999986e-73 < a < -2.69999999999999992e-210 or 4.79999999999999992e-225 < a < 4.5e20

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 55.0%

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

   if -2.69999999999999992e-210 < a < -2.1e-219 or 1.09999999999999994e-275 < a < 4.79999999999999992e-225

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 88.4%

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

   if -2.1e-219 < a < 1.09999999999999994e-275

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 56.9%

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

      1. associate-*r/ 56.9%

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

   7. Simplified 56.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{-73}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-210}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-219}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-275}:\\ \;\;\;\;\frac{60 \cdot y}{t - z}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-225}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+20}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-222}:\\ \;\;\;\;\frac{x - y}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+21} \lor \neg \left(a \leq 1.02 \cdot 10^{+131}\right) \land a \leq 3.6 \cdot 10^{+135}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e-78)
   (* a 120.0)
   (if (<= a 1.5e-222)
     (/ (- x y) (* z 0.016666666666666666))
     (if (or (<= a 1.4e+21) (and (not (<= a 1.02e+131)) (<= a 3.6e+135)))
       (* 60.0 (/ y (- t z)))
       (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-78) {
		tmp = a * 120.0;
	} else if (a <= 1.5e-222) {
		tmp = (x - y) / (z * 0.016666666666666666);
	} else if ((a <= 1.4e+21) || (!(a <= 1.02e+131) && (a <= 3.6e+135))) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.8d-78)) then
        tmp = a * 120.0d0
    else if (a <= 1.5d-222) then
        tmp = (x - y) / (z * 0.016666666666666666d0)
    else if ((a <= 1.4d+21) .or. (.not. (a <= 1.02d+131)) .and. (a <= 3.6d+135)) then
        tmp = 60.0d0 * (y / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-78) {
		tmp = a * 120.0;
	} else if (a <= 1.5e-222) {
		tmp = (x - y) / (z * 0.016666666666666666);
	} else if ((a <= 1.4e+21) || (!(a <= 1.02e+131) && (a <= 3.6e+135))) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e-78:
		tmp = a * 120.0
	elif a <= 1.5e-222:
		tmp = (x - y) / (z * 0.016666666666666666)
	elif (a <= 1.4e+21) or (not (a <= 1.02e+131) and (a <= 3.6e+135)):
		tmp = 60.0 * (y / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e-78)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.5e-222)
		tmp = Float64(Float64(x - y) / Float64(z * 0.016666666666666666));
	elseif ((a <= 1.4e+21) || (!(a <= 1.02e+131) && (a <= 3.6e+135)))
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e-78)
		tmp = a * 120.0;
	elseif (a <= 1.5e-222)
		tmp = (x - y) / (z * 0.016666666666666666);
	elseif ((a <= 1.4e+21) || (~((a <= 1.02e+131)) && (a <= 3.6e+135)))
		tmp = 60.0 * (y / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e-78], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.5e-222], N[(N[(x - y), $MachinePrecision] / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.4e+21], And[N[Not[LessEqual[a, 1.02e+131]], $MachinePrecision], LessEqual[a, 3.6e+135]]], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.79999999999999999e-78 or 1.4e21 < a < 1.0199999999999999e131 or 3.5999999999999998e135 < 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* 99.9%

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

   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 inf 74.2%

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

   if -4.79999999999999999e-78 < a < 1.50000000000000015e-222

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. metadata-eval 86.0%

         \[\leadsto \frac{x - y}{t - z} \cdot \color{blue}{\frac{1}{-0.016666666666666666}} \]

      3. times-frac 85.9%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{\left(t - z\right) \cdot -0.016666666666666666}} \]

      4. *-rgt-identity 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in t around 0 53.7%

      \[\leadsto \frac{x - y}{\color{blue}{0.016666666666666666 \cdot z}} \]
   9. Step-by-step derivation

      1. *-commutative 53.7%

         \[\leadsto \frac{x - y}{\color{blue}{z \cdot 0.016666666666666666}} \]

   10. Simplified 53.7%

       \[\leadsto \frac{x - y}{\color{blue}{z \cdot 0.016666666666666666}} \]

   if 1.50000000000000015e-222 < a < 1.4e21 or 1.0199999999999999e131 < a < 3.5999999999999998e135

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 56.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-222}:\\ \;\;\;\;\frac{x - y}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+21} \lor \neg \left(a \leq 1.02 \cdot 10^{+131}\right) \land a \leq 3.6 \cdot 10^{+135}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+171} \lor \neg \left(x \leq 2.3 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -8.2e+171) (not (<= x 2.3e+83)))
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))
   (+ (* 60.0 (/ y (- t z))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8.2e+171) || !(x <= 2.3e+83)) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-8.2d+171)) .or. (.not. (x <= 2.3d+83))) then
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    else
        tmp = (60.0d0 * (y / (t - z))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8.2e+171) || !(x <= 2.3e+83)) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -8.2e+171) or not (x <= 2.3e+83):
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	else:
		tmp = (60.0 * (y / (t - z))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -8.2e+171) || !(x <= 2.3e+83))
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 * Float64(y / Float64(t - z))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -8.2e+171) || ~((x <= 2.3e+83)))
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	else
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -8.2e+171], N[Not[LessEqual[x, 2.3e+83]], $MachinePrecision]], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999992e171 or 2.29999999999999995e83 < x

   1. Initial program 98.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 92.6%

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

   if -8.1999999999999992e171 < x < 2.29999999999999995e83

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 91.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+171} \lor \neg \left(x \leq 2.3 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+197}:\\ \;\;\;\;\frac{x - y}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+24}:\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6e+197)
   (/ (- x y) (* (- t z) -0.016666666666666666))
   (if (<= x 4.2e+24)
     (+ (* 60.0 (/ y (- t z))) (* a 120.0))
     (* -60.0 (/ (- x y) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6e+197) {
		tmp = (x - y) / ((t - z) * -0.016666666666666666);
	} else if (x <= 4.2e+24) {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	} else {
		tmp = -60.0 * ((x - y) / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6d+197)) then
        tmp = (x - y) / ((t - z) * (-0.016666666666666666d0))
    else if (x <= 4.2d+24) then
        tmp = (60.0d0 * (y / (t - z))) + (a * 120.0d0)
    else
        tmp = (-60.0d0) * ((x - y) / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6e+197) {
		tmp = (x - y) / ((t - z) * -0.016666666666666666);
	} else if (x <= 4.2e+24) {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	} else {
		tmp = -60.0 * ((x - y) / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6e+197:
		tmp = (x - y) / ((t - z) * -0.016666666666666666)
	elif x <= 4.2e+24:
		tmp = (60.0 * (y / (t - z))) + (a * 120.0)
	else:
		tmp = -60.0 * ((x - y) / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6e+197)
		tmp = Float64(Float64(x - y) / Float64(Float64(t - z) * -0.016666666666666666));
	elseif (x <= 4.2e+24)
		tmp = Float64(Float64(60.0 * Float64(y / Float64(t - z))) + Float64(a * 120.0));
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6e+197)
		tmp = (x - y) / ((t - z) * -0.016666666666666666);
	elseif (x <= 4.2e+24)
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	else
		tmp = -60.0 * ((x - y) / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6e+197], N[(N[(x - y), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] * -0.016666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+24], N[(N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0000000000000004e197

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 83.4%

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

      1. *-commutative 83.4%

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

      2. metadata-eval 83.4%

         \[\leadsto \frac{x - y}{t - z} \cdot \color{blue}{\frac{1}{-0.016666666666666666}} \]

      3. times-frac 83.4%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{\left(t - z\right) \cdot -0.016666666666666666}} \]

      4. *-rgt-identity 83.4%

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

   7. Simplified 83.4%

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

   if -6.0000000000000004e197 < x < 4.2000000000000003e24

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.2%

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

   if 4.2000000000000003e24 < x

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 67.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+197}:\\ \;\;\;\;\frac{x - y}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+24}:\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+171}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+82}:\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.2e+171)
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))
   (if (<= x 3.05e+82)
     (+ (* 60.0 (/ y (- t z))) (* a 120.0))
     (+ (* a 120.0) (/ (* 60.0 x) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.2e+171) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else if (x <= 3.05e+82) {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	} 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 (x <= (-8.2d+171)) then
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    else if (x <= 3.05d+82) then
        tmp = (60.0d0 * (y / (t - z))) + (a * 120.0d0)
    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 (x <= -8.2e+171) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else if (x <= 3.05e+82) {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.2e+171:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	elif x <= 3.05e+82:
		tmp = (60.0 * (y / (t - z))) + (a * 120.0)
	else:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.2e+171)
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	elseif (x <= 3.05e+82)
		tmp = Float64(Float64(60.0 * Float64(y / Float64(t - z))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8.2e+171)
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	elseif (x <= 3.05e+82)
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	else
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.2e+171], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.05e+82], N[(N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.1999999999999992e171

   1. Initial program 96.5%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 99.8%

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

   if -8.1999999999999992e171 < x < 3.0499999999999999e82

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 91.5%

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

   if 3.0499999999999999e82 < x

   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 x around inf 87.1%

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

      1. associate-*r/ 87.1%

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

   7. Simplified 87.1%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+171}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+82}:\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-42} \lor \neg \left(a \leq 6.8 \cdot 10^{+66}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.2e-42) (not (<= a 6.8e+66)))
   (* a 120.0)
   (* -60.0 (/ (- x y) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.2e-42) || !(a <= 6.8e+66)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.2d-42)) .or. (.not. (a <= 6.8d+66))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - y) / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.2e-42) || !(a <= 6.8e+66)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.2e-42) or not (a <= 6.8e+66):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.2e-42) || !(a <= 6.8e+66))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.2e-42) || ~((a <= 6.8e+66)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.2e-42], N[Not[LessEqual[a, 6.8e+66]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.20000000000000013e-42 or 6.8000000000000006e66 < 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* 99.9%

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

   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 inf 79.8%

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

   if -4.20000000000000013e-42 < a < 6.8000000000000006e66

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 77.4%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-42} \lor \neg \left(a \leq 6.8 \cdot 10^{+66}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+199} \lor \neg \left(x \leq 3.8 \cdot 10^{+32}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.15e+199) (not (<= x 3.8e+32)))
   (* -60.0 (/ x (- t z)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.15e+199) || !(x <= 3.8e+32)) {
		tmp = -60.0 * (x / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-3.15d+199)) .or. (.not. (x <= 3.8d+32))) then
        tmp = (-60.0d0) * (x / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.15e+199) || !(x <= 3.8e+32)) {
		tmp = -60.0 * (x / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.15e+199) or not (x <= 3.8e+32):
		tmp = -60.0 * (x / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.15e+199) || !(x <= 3.8e+32))
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3.15e+199) || ~((x <= 3.8e+32)))
		tmp = -60.0 * (x / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.15e+199], N[Not[LessEqual[x, 3.8e+32]], $MachinePrecision]], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.15e199 or 3.8000000000000003e32 < x

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 58.6%

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

   if -3.15e199 < x < 3.8000000000000003e32

   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 59.3%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+199} \lor \neg \left(x \leq 3.8 \cdot 10^{+32}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-146} \lor \neg \left(a \leq 7.8 \cdot 10^{-148}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.5e-146) (not (<= a 7.8e-148)))
   (* a 120.0)
   (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e-146) || !(a <= 7.8e-148)) {
		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 <= (-5.5d-146)) .or. (.not. (a <= 7.8d-148))) 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 <= -5.5e-146) || !(a <= 7.8e-148)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.5e-146) or not (a <= 7.8e-148):
		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 <= -5.5e-146) || !(a <= 7.8e-148))
		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 <= -5.5e-146) || ~((a <= 7.8e-148)))
		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, -5.5e-146], N[Not[LessEqual[a, 7.8e-148]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.49999999999999998e-146 or 7.79999999999999988e-148 < 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 63.2%

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

   if -5.49999999999999998e-146 < a < 7.79999999999999988e-148

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 53.3%

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

      1. associate-*r/ 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in t around 0 29.4%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-146} \lor \neg \left(a \leq 7.8 \cdot 10^{-148}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-146} \lor \neg \left(a \leq 2.95 \cdot 10^{-149}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.5e-146) (not (<= a 2.95e-149)))
   (* a 120.0)
   (/ (* y -60.0) z)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e-146) || !(a <= 2.95e-149)) {
		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 <= (-5.5d-146)) .or. (.not. (a <= 2.95d-149))) 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 <= -5.5e-146) || !(a <= 2.95e-149)) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.5e-146) or not (a <= 2.95e-149):
		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 <= -5.5e-146) || !(a <= 2.95e-149))
		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 <= -5.5e-146) || ~((a <= 2.95e-149)))
		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, -5.5e-146], N[Not[LessEqual[a, 2.95e-149]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.49999999999999998e-146 or 2.9500000000000001e-149 < 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 63.2%

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

   if -5.49999999999999998e-146 < a < 2.9500000000000001e-149

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 53.3%

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

      1. associate-*r/ 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in t around 0 29.4%

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

      1. associate-*r/ 29.5%

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

   10. Simplified 29.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-146} \lor \neg \left(a \leq 2.95 \cdot 10^{-149}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 13: 52.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+198}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.1e+198) (* -60.0 (/ x t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e+198) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.1d+198)) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e+198) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.1e+198:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.1e+198)
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.1e+198)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.1e+198], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e198

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 83.4%

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

      1. *-commutative 83.4%

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

      2. metadata-eval 83.4%

         \[\leadsto \frac{x - y}{t - z} \cdot \color{blue}{\frac{1}{-0.016666666666666666}} \]

      3. times-frac 83.4%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{\left(t - z\right) \cdot -0.016666666666666666}} \]

      4. *-rgt-identity 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in t around inf 45.9%

      \[\leadsto \frac{x - y}{\color{blue}{-0.016666666666666666 \cdot t}} \]
   9. Step-by-step derivation

      1. *-commutative 45.9%

         \[\leadsto \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}} \]

   10. Simplified 45.9%

       \[\leadsto \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}} \]

   11. Taylor expanded in x around inf 45.9%

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

   if -1.1e198 < x

   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 53.4%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+198}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.5% 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 50.0%

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

6. Final simplification 50.0%

   \[\leadsto a \cdot 120 \]
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 2024089 
(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)))