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

Percentage Accurate: 99.3% → 99.8%

Time: 13.6s

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: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 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* 99.7%

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

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 99.7%

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

   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. Add Preprocessing

Alternative 2: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+46}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-138}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+46)
   (* a 120.0)
   (if (<= (* a 120.0) 2e-138)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 2e+27)
       (+ (* a 120.0) (* -60.0 (/ y z)))
       (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+46) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-138) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 2e+27) {
		tmp = (a * 120.0) + (-60.0 * (y / 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 * 120.0d0) <= (-4d+46)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d-138) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 2d+27) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / 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 * 120.0) <= -4e+46) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-138) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 2e+27) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+46:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e-138:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 2e+27:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+46)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e-138)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 2e+27)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / 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 * 120.0) <= -4e+46)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e-138)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 2e+27)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+46], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-138], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+27], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4e46 or 2e27 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.0%

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

      1. associate-/l* 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.3%

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

   if -4e46 < (*.f64 a #s(literal 120 binary64)) < 2.00000000000000013e-138

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

      2. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 78.7%

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

   if 2.00000000000000013e-138 < (*.f64 a #s(literal 120 binary64)) < 2e27

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   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 79.4%

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

      1. associate-*r/ 79.4%

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

      2. remove-double-neg 79.4%

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

      3. neg-mul-1 79.4%

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

      4. times-frac 79.4%

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

      5. metadata-eval 79.4%

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

      6. sub-neg 79.4%

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

      7. distribute-neg-in 79.4%

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

      8. remove-double-neg 79.4%

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

      9. +-commutative 79.4%

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

      10. sub-neg 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in t around 0 71.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+46}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-138}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4.75 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-128}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (/ y z)))))
   (if (<= z -4.75e+26)
     t_2
     (if (<= z -2.7e-100)
       t_1
       (if (<= z 1e-128)
         (+ (* a 120.0) (/ (* x -60.0) t))
         (if (<= z 5.8e-16) t_1 t_2))))))

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 * (y / z));
	double tmp;
	if (z <= -4.75e+26) {
		tmp = t_2;
	} else if (z <= -2.7e-100) {
		tmp = t_1;
	} else if (z <= 1e-128) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 5.8e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) * (y / z))
    if (z <= (-4.75d+26)) then
        tmp = t_2
    else if (z <= (-2.7d-100)) then
        tmp = t_1
    else if (z <= 1d-128) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else if (z <= 5.8d-16) then
        tmp = t_1
    else
        tmp = t_2
    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 * (y / z));
	double tmp;
	if (z <= -4.75e+26) {
		tmp = t_2;
	} else if (z <= -2.7e-100) {
		tmp = t_1;
	} else if (z <= 1e-128) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 5.8e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 * (y / z))
	tmp = 0
	if z <= -4.75e+26:
		tmp = t_2
	elif z <= -2.7e-100:
		tmp = t_1
	elif z <= 1e-128:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	elif z <= 5.8e-16:
		tmp = t_1
	else:
		tmp = t_2
	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(y / z)))
	tmp = 0.0
	if (z <= -4.75e+26)
		tmp = t_2;
	elseif (z <= -2.7e-100)
		tmp = t_1;
	elseif (z <= 1e-128)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	elseif (z <= 5.8e-16)
		tmp = t_1;
	else
		tmp = t_2;
	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 * (y / z));
	tmp = 0.0;
	if (z <= -4.75e+26)
		tmp = t_2;
	elseif (z <= -2.7e-100)
		tmp = t_1;
	elseif (z <= 1e-128)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	elseif (z <= 5.8e-16)
		tmp = t_1;
	else
		tmp = t_2;
	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[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.75e+26], t$95$2, If[LessEqual[z, -2.7e-100], t$95$1, If[LessEqual[z, 1e-128], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.75000000000000027e26 or 5.7999999999999996e-16 < z

   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 87.0%

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

      1. associate-*r/ 87.0%

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

      2. remove-double-neg 87.0%

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

      3. neg-mul-1 87.0%

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

      4. times-frac 87.0%

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

      5. metadata-eval 87.0%

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

      6. sub-neg 87.0%

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

      7. distribute-neg-in 87.0%

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

      8. remove-double-neg 87.0%

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

      9. +-commutative 87.0%

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

      10. sub-neg 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in t around 0 82.3%

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

   if -4.75000000000000027e26 < z < -2.70000000000000016e-100 or 1.00000000000000005e-128 < z < 5.7999999999999996e-16

   1. Initial program 97.8%

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

      1. associate-/l* 99.6%

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

      2. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 75.6%

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

   if -2.70000000000000016e-100 < z < 1.00000000000000005e-128

   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. clear-num 99.7%

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

      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 83.7%

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

   8. Taylor expanded in z around 0 80.3%

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

      1. associate-*r/ 80.3%

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

   10. Simplified 80.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.75 \cdot 10^{+26}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-100}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 10^{-128}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-132}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (/ y z)))))
   (if (<= z -1.7e+26)
     t_2
     (if (<= z -2e-97)
       t_1
       (if (<= z 4e-132)
         (+ (* a 120.0) (* x (/ -60.0 t)))
         (if (<= z 5.5e-16) t_1 t_2))))))

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 * (y / z));
	double tmp;
	if (z <= -1.7e+26) {
		tmp = t_2;
	} else if (z <= -2e-97) {
		tmp = t_1;
	} else if (z <= 4e-132) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if (z <= 5.5e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) * (y / z))
    if (z <= (-1.7d+26)) then
        tmp = t_2
    else if (z <= (-2d-97)) then
        tmp = t_1
    else if (z <= 4d-132) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else if (z <= 5.5d-16) then
        tmp = t_1
    else
        tmp = t_2
    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 * (y / z));
	double tmp;
	if (z <= -1.7e+26) {
		tmp = t_2;
	} else if (z <= -2e-97) {
		tmp = t_1;
	} else if (z <= 4e-132) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if (z <= 5.5e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 * (y / z))
	tmp = 0
	if z <= -1.7e+26:
		tmp = t_2
	elif z <= -2e-97:
		tmp = t_1
	elif z <= 4e-132:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	elif z <= 5.5e-16:
		tmp = t_1
	else:
		tmp = t_2
	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(y / z)))
	tmp = 0.0
	if (z <= -1.7e+26)
		tmp = t_2;
	elseif (z <= -2e-97)
		tmp = t_1;
	elseif (z <= 4e-132)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	elseif (z <= 5.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	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 * (y / z));
	tmp = 0.0;
	if (z <= -1.7e+26)
		tmp = t_2;
	elseif (z <= -2e-97)
		tmp = t_1;
	elseif (z <= 4e-132)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	elseif (z <= 5.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	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[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+26], t$95$2, If[LessEqual[z, -2e-97], t$95$1, If[LessEqual[z, 4e-132], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7000000000000001e26 or 5.49999999999999964e-16 < z

   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 87.0%

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

      1. associate-*r/ 87.0%

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

      2. remove-double-neg 87.0%

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

      3. neg-mul-1 87.0%

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

      4. times-frac 87.0%

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

      5. metadata-eval 87.0%

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

      6. sub-neg 87.0%

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

      7. distribute-neg-in 87.0%

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

      8. remove-double-neg 87.0%

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

      9. +-commutative 87.0%

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

      10. sub-neg 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in t around 0 82.3%

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

   if -1.7000000000000001e26 < z < -2.00000000000000007e-97 or 3.9999999999999999e-132 < z < 5.49999999999999964e-16

   1. Initial program 97.8%

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

      1. associate-/l* 99.6%

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

      2. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 75.6%

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

   if -2.00000000000000007e-97 < z < 3.9999999999999999e-132

   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. clear-num 99.7%

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

      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 83.7%

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

      1. associate-/r/ 83.7%

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

   9. Applied egg-rr 83.7%

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

   10. Taylor expanded in z around 0 80.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-97}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-132}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-16}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+85} \lor \neg \left(y \leq 1.2 \cdot 10^{-62}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.1e+85) (not (<= y 1.2e-62)))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))
   (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.1e+85) || !(y <= 1.2e-62)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.1d+85)) .or. (.not. (y <= 1.2d-62))) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    else
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.1e+85) || !(y <= 1.2e-62)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.1e+85) or not (y <= 1.2e-62):
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	else:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.1e+85) || !(y <= 1.2e-62))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.1e+85) || ~((y <= 1.2e-62)))
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	else
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.1e+85], N[Not[LessEqual[y, 1.2e-62]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e85 or 1.19999999999999992e-62 < y

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   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 86.7%

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

      1. associate-*r/ 86.7%

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

      2. remove-double-neg 86.7%

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

      3. neg-mul-1 86.7%

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

      4. times-frac 86.7%

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

      5. metadata-eval 86.7%

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

      6. sub-neg 86.7%

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

      7. distribute-neg-in 86.7%

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

      8. remove-double-neg 86.7%

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

      9. +-commutative 86.7%

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

      10. sub-neg 86.7%

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

   7. Simplified 86.7%

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

   if -2.1000000000000001e85 < y < 1.19999999999999992e-62

   1. Initial program 99.1%

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

      1. associate-/l* 99.7%

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

   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 99.7%

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

      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 96.6%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+85} \lor \neg \left(y \leq 1.2 \cdot 10^{-62}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+85} \lor \neg \left(y \leq 1.2 \cdot 10^{-62}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.1e+85) (not (<= y 1.2e-62)))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.1e+85) || !(y <= 1.2e-62)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.1d+85)) .or. (.not. (y <= 1.2d-62))) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    else
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.1e+85) || !(y <= 1.2e-62)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.1e+85) or not (y <= 1.2e-62):
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.1e+85) || !(y <= 1.2e-62))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.1e+85) || ~((y <= 1.2e-62)))
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.1e+85], N[Not[LessEqual[y, 1.2e-62]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e85 or 1.19999999999999992e-62 < y

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   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 86.7%

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

      1. associate-*r/ 86.7%

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

      2. remove-double-neg 86.7%

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

      3. neg-mul-1 86.7%

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

      4. times-frac 86.7%

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

      5. metadata-eval 86.7%

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

      6. sub-neg 86.7%

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

      7. distribute-neg-in 86.7%

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

      8. remove-double-neg 86.7%

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

      9. +-commutative 86.7%

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

      10. sub-neg 86.7%

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

   7. Simplified 86.7%

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

   if -2.1000000000000001e85 < y < 1.19999999999999992e-62

   1. Initial program 99.1%

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

      1. associate-/l* 99.7%

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

   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 99.7%

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

      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 96.4%

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

      1. associate-*r/ 95.8%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

   9. Simplified 96.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+85} \lor \neg \left(y \leq 1.2 \cdot 10^{-62}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+223} \lor \neg \left(x \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -6.4e+223) (not (<= x 5e+114)))
   (* 60.0 (/ (- x y) (- z t)))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.4e+223) || !(x <= 5e+114)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-6.4d+223)) .or. (.not. (x <= 5d+114))) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.4e+223) || !(x <= 5e+114)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -6.4e+223) or not (x <= 5e+114):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -6.4e+223) || !(x <= 5e+114))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -6.4e+223) || ~((x <= 5e+114)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -6.4e+223], N[Not[LessEqual[x, 5e+114]], $MachinePrecision]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4000000000000003e223 or 5.0000000000000001e114 < x

   1. Initial program 98.3%

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

      1. associate-/l* 99.6%

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

      2. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 78.8%

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

   if -6.4000000000000003e223 < x < 5.0000000000000001e114

   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 88.0%

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

      1. associate-*r/ 88.0%

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

      2. remove-double-neg 88.0%

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

      3. neg-mul-1 88.0%

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

      4. times-frac 88.0%

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

      5. metadata-eval 88.0%

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

      6. sub-neg 88.0%

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

      7. distribute-neg-in 88.0%

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

      8. remove-double-neg 88.0%

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

      9. +-commutative 88.0%

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

      10. sub-neg 88.0%

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

   7. Simplified 88.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+223} \lor \neg \left(x \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+85}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-62}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.1e+85)
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))
   (if (<= y 1.5e-62)
     (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
     (+ (* a 120.0) (/ (* y -60.0) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.1e+85) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else if (y <= 1.5e-62) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + ((y * -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 <= (-2.1d+85)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    else if (y <= 1.5d-62) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    else
        tmp = (a * 120.0d0) + ((y * (-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 <= -2.1e+85) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else if (y <= 1.5e-62) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.1e+85:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	elif y <= 1.5e-62:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.1e+85)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	elseif (y <= 1.5e-62)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.1e+85)
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	elseif (y <= 1.5e-62)
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	else
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.1e+85], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-62], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1000000000000001e85

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   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 92.6%

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

      1. associate-*r/ 92.5%

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

      2. remove-double-neg 92.5%

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

      3. neg-mul-1 92.5%

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

      4. times-frac 92.6%

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

      5. metadata-eval 92.6%

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

      6. sub-neg 92.6%

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

      7. distribute-neg-in 92.6%

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

      8. remove-double-neg 92.6%

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

      9. +-commutative 92.6%

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

      10. sub-neg 92.6%

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

   7. Simplified 92.6%

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

   if -2.1000000000000001e85 < y < 1.5000000000000001e-62

   1. Initial program 99.1%

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

      1. associate-/l* 99.7%

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

   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 99.7%

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

      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 96.6%

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

   if 1.5000000000000001e-62 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 83.7%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+85}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-62}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.7 \cdot 10^{+38} \lor \neg \left(a \leq 7.4 \cdot 10^{-31}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.7e+38) (not (<= a 7.4e-31)))
   (* 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 <= -6.7e+38) || !(a <= 7.4e-31)) {
		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 <= (-6.7d+38)) .or. (.not. (a <= 7.4d-31))) 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 <= -6.7e+38) || !(a <= 7.4e-31)) {
		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 <= -6.7e+38) or not (a <= 7.4e-31):
		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 <= -6.7e+38) || !(a <= 7.4e-31))
		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 <= -6.7e+38) || ~((a <= 7.4e-31)))
		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, -6.7e+38], N[Not[LessEqual[a, 7.4e-31]], $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 < -6.70000000000000025e38 or 7.3999999999999996e-31 < a

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.7%

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

   if -6.70000000000000025e38 < a < 7.3999999999999996e-31

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

      2. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 74.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.7 \cdot 10^{+38} \lor \neg \left(a \leq 7.4 \cdot 10^{-31}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+89} \lor \neg \left(y \leq 1.1 \cdot 10^{+126}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.2e+89) (not (<= y 1.1e+126)))
   (* 60.0 (/ y (- t z)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.2e+89) || !(y <= 1.1e+126)) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.2d+89)) .or. (.not. (y <= 1.1d+126))) then
        tmp = 60.0d0 * (y / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.2e+89) || !(y <= 1.1e+126)) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.2e+89) or not (y <= 1.1e+126):
		tmp = 60.0 * (y / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.2e+89) || !(y <= 1.1e+126))
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.2e+89) || ~((y <= 1.1e+126)))
		tmp = 60.0 * (y / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.2e+89], N[Not[LessEqual[y, 1.1e+126]], $MachinePrecision]], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.19999999999999972e89 or 1.09999999999999999e126 < y

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 88.5%

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

      1. associate-*r/ 88.5%

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

      2. remove-double-neg 88.5%

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

      3. neg-mul-1 88.5%

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

      4. times-frac 88.5%

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

      5. metadata-eval 88.5%

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

      6. sub-neg 88.5%

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

      7. distribute-neg-in 88.5%

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

      8. remove-double-neg 88.5%

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

      9. +-commutative 88.5%

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

      10. sub-neg 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in y around inf 60.5%

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

   if -4.19999999999999972e89 < y < 1.09999999999999999e126

   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* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 60.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+89} \lor \neg \left(y \leq 1.1 \cdot 10^{+126}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+89}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+125}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.5e+89)
   (* 60.0 (/ y (- t z)))
   (if (<= y 1.15e+125) (* a 120.0) (/ (* 60.0 y) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.5e+89) {
		tmp = 60.0 * (y / (t - z));
	} else if (y <= 1.15e+125) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 * y) / (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-7.5d+89)) then
        tmp = 60.0d0 * (y / (t - z))
    else if (y <= 1.15d+125) then
        tmp = a * 120.0d0
    else
        tmp = (60.0d0 * y) / (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.5e+89) {
		tmp = 60.0 * (y / (t - z));
	} else if (y <= 1.15e+125) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 * y) / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.5e+89:
		tmp = 60.0 * (y / (t - z))
	elif y <= 1.15e+125:
		tmp = a * 120.0
	else:
		tmp = (60.0 * y) / (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.5e+89)
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	elseif (y <= 1.15e+125)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(60.0 * y) / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.5e+89)
		tmp = 60.0 * (y / (t - z));
	elseif (y <= 1.15e+125)
		tmp = a * 120.0;
	else
		tmp = (60.0 * y) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.5e+89], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+125], N[(a * 120.0), $MachinePrecision], N[(N[(60.0 * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.49999999999999947e89

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   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 92.1%

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

      1. associate-*r/ 91.9%

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

      2. remove-double-neg 91.9%

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

      3. neg-mul-1 91.9%

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

      4. times-frac 92.1%

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

      5. metadata-eval 92.1%

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

      6. sub-neg 92.1%

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

      7. distribute-neg-in 92.1%

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

      8. remove-double-neg 92.1%

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

      9. +-commutative 92.1%

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

      10. sub-neg 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in y around inf 65.7%

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

   if -7.49999999999999947e89 < y < 1.15000000000000006e125

   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* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 60.0%

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

   if 1.15000000000000006e125 < y

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   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 85.1%

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

      1. associate-*r/ 85.2%

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

      2. remove-double-neg 85.2%

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

      3. neg-mul-1 85.2%

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

      4. times-frac 85.1%

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

      5. metadata-eval 85.1%

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

      6. sub-neg 85.1%

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

      7. distribute-neg-in 85.1%

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

      8. remove-double-neg 85.1%

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

      9. +-commutative 85.1%

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

      10. sub-neg 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in y around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. associate-*l/ 55.7%

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

   10. Applied egg-rr 55.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+89}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+125}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-199} \lor \neg \left(a \leq 9 \cdot 10^{-141}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.2e-199) (not (<= a 9e-141))) (* a 120.0) (/ (* y -60.0) z)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.2e-199) || !(a <= 9e-141)) {
		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 <= (-8.2d-199)) .or. (.not. (a <= 9d-141))) 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 <= -8.2e-199) || !(a <= 9e-141)) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.2e-199) or not (a <= 9e-141):
		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 <= -8.2e-199) || !(a <= 9e-141))
		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 <= -8.2e-199) || ~((a <= 9e-141)))
		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, -8.2e-199], N[Not[LessEqual[a, 9e-141]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.20000000000000043e-199 or 9.0000000000000001e-141 < 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%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.8%

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

   if -8.20000000000000043e-199 < a < 9.0000000000000001e-141

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 0 57.8%

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

      1. associate-*r/ 57.8%

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

      2. remove-double-neg 57.8%

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

      3. neg-mul-1 57.8%

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

      4. times-frac 57.8%

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

      5. metadata-eval 57.8%

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

      6. sub-neg 57.8%

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

      7. distribute-neg-in 57.8%

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

      8. remove-double-neg 57.8%

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

      9. +-commutative 57.8%

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

      10. sub-neg 57.8%

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

   7. Simplified 57.8%

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

   8. Taylor expanded in y around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. associate-*l/ 48.9%

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

   10. Applied egg-rr 48.9%

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

   11. Taylor expanded in t around 0 32.4%

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

       1. associate-*r/ 32.4%

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

   13. Simplified 32.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-199} \lor \neg \left(a \leq 9 \cdot 10^{-141}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-198} \lor \neg \left(a \leq 9.5 \cdot 10^{-141}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.1e-198) (not (<= a 9.5e-141)))
   (* a 120.0)
   (/ -60.0 (/ z y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1e-198) || !(a <= 9.5e-141)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.1d-198)) .or. (.not. (a <= 9.5d-141))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1e-198) || !(a <= 9.5e-141)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.1e-198) or not (a <= 9.5e-141):
		tmp = a * 120.0
	else:
		tmp = -60.0 / (z / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.1e-198) || !(a <= 9.5e-141))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.1e-198) || ~((a <= 9.5e-141)))
		tmp = a * 120.0;
	else
		tmp = -60.0 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.1e-198], N[Not[LessEqual[a, 9.5e-141]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1e-198 or 9.49999999999999996e-141 < 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%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.8%

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

   if -1.1e-198 < a < 9.49999999999999996e-141

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 0 57.8%

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

      1. associate-*r/ 57.8%

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

      2. remove-double-neg 57.8%

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

      3. neg-mul-1 57.8%

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

      4. times-frac 57.8%

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

      5. metadata-eval 57.8%

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

      6. sub-neg 57.8%

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

      7. distribute-neg-in 57.8%

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

      8. remove-double-neg 57.8%

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

      9. +-commutative 57.8%

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

      10. sub-neg 57.8%

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

   7. Simplified 57.8%

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

   8. Taylor expanded in y around inf 48.8%

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

   9. Taylor expanded in t around 0 32.4%

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

       1. clear-num 32.4%

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

       2. un-div-inv 32.4%

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

   11. Applied egg-rr 32.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-198} \lor \neg \left(a \leq 9.5 \cdot 10^{-141}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(a * 120.0), $MachinePrecision] + 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. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 99.4%

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

   2. associate-/l* 99.7%

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

4. Applied egg-rr 99.7%

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

5. Final simplification 99.7%

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

Alternative 15: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. Final simplification 99.7%

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

Alternative 16: 50.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.1e+90) (* y (/ -60.0 z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.1e+90) {
		tmp = y * (-60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.1d+90)) then
        tmp = y * ((-60.0d0) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.1e+90) {
		tmp = y * (-60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.1e+90:
		tmp = y * (-60.0 / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.1e+90)
		tmp = Float64(y * Float64(-60.0 / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.1e+90)
		tmp = y * (-60.0 / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.1e+90], N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.10000000000000042e90

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   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 92.1%

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

      1. associate-*r/ 91.9%

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

      2. remove-double-neg 91.9%

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

      3. neg-mul-1 91.9%

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

      4. times-frac 92.1%

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

      5. metadata-eval 92.1%

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

      6. sub-neg 92.1%

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

      7. distribute-neg-in 92.1%

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

      8. remove-double-neg 92.1%

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

      9. +-commutative 92.1%

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

      10. sub-neg 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in y around inf 65.7%

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

   9. Taylor expanded in t around 0 44.9%

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

       1. clear-num 44.9%

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

       2. un-div-inv 44.9%

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

   11. Applied egg-rr 44.9%

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

       1. associate-/r/ 44.9%

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

   13. Simplified 44.9%

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

   if -4.10000000000000042e90 < y

   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* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 54.0%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+90}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.2e+90) (* -60.0 (/ y z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2e+90) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.2d+90)) then
        tmp = (-60.0d0) * (y / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2e+90) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.2e+90:
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.2e+90)
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.2e+90)
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.2e+90], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999998e90

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   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 92.1%

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

      1. associate-*r/ 91.9%

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

      2. remove-double-neg 91.9%

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

      3. neg-mul-1 91.9%

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

      4. times-frac 92.1%

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

      5. metadata-eval 92.1%

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

      6. sub-neg 92.1%

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

      7. distribute-neg-in 92.1%

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

      8. remove-double-neg 92.1%

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

      9. +-commutative 92.1%

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

      10. sub-neg 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in y around inf 65.7%

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

   9. Taylor expanded in t around 0 44.9%

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

   if -3.19999999999999998e90 < y

   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* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 54.0%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+90}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.1% 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* 99.7%

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

   2. fma-define 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in 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 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024177 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

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