Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 91.3% → 96.1%

Time: 9.6s

Alternatives: 12

Speedup: 0.6×

• 29.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+299}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{y}{a \cdot z} - \frac{\frac{t}{x}}{a}\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+285}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - t \cdot \frac{z}{x}}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 -5e+299)
     (* x (* z (- (/ y (* a z)) (/ (/ t x) a))))
     (if (<= t_1 1e+285) (/ t_1 a) (* x (/ (- y (* t (/ z x))) a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -5e+299) {
		tmp = x * (z * ((y / (a * z)) - ((t / x) / a)));
	} else if (t_1 <= 1e+285) {
		tmp = t_1 / a;
	} else {
		tmp = x * ((y - (t * (z / x))) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= (-5d+299)) then
        tmp = x * (z * ((y / (a * z)) - ((t / x) / a)))
    else if (t_1 <= 1d+285) then
        tmp = t_1 / a
    else
        tmp = x * ((y - (t * (z / x))) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -5e+299) {
		tmp = x * (z * ((y / (a * z)) - ((t / x) / a)));
	} else if (t_1 <= 1e+285) {
		tmp = t_1 / a;
	} else {
		tmp = x * ((y - (t * (z / x))) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -5e+299:
		tmp = x * (z * ((y / (a * z)) - ((t / x) / a)))
	elif t_1 <= 1e+285:
		tmp = t_1 / a
	else:
		tmp = x * ((y - (t * (z / x))) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -5e+299)
		tmp = Float64(x * Float64(z * Float64(Float64(y / Float64(a * z)) - Float64(Float64(t / x) / a))));
	elseif (t_1 <= 1e+285)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(x * Float64(Float64(y - Float64(t * Float64(z / x))) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -5e+299)
		tmp = x * (z * ((y / (a * z)) - ((t / x) / a)));
	elseif (t_1 <= 1e+285)
		tmp = t_1 / a;
	else
		tmp = x * ((y - (t * (z / x))) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+299], N[(x * N[(z * N[(N[(y / N[(a * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t / x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+285], N[(t$95$1 / a), $MachinePrecision], N[(x * N[(N[(y - N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000003e299

   1. Initial program 67.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

      3. associate-/l* 67.6%

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

   5. Simplified 67.6%

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

      1. associate-/l* 96.6%

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

      2. *-commutative 96.6%

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

   7. Applied egg-rr 96.6%

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

   8. Taylor expanded in z around inf 92.9%

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

      1. +-commutative 92.9%

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

      2. mul-1-neg 92.9%

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

      3. unsub-neg 92.9%

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

      4. *-commutative 92.9%

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

      5. *-commutative 92.9%

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

      6. associate-/r* 96.3%

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

   10. Simplified 96.3%

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

   if -5.0000000000000003e299 < (-.f64 (*.f64 x y) (*.f64 z t)) < 9.9999999999999998e284

   1. Initial program 99.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 9.9999999999999998e284 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 74.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

      3. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

      1. associate-/l* 93.6%

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

      2. *-commutative 93.6%

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

   7. Applied egg-rr 93.6%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+299}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{y}{a \cdot z} - \frac{\frac{t}{x}}{a}\right)\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 10^{+285}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - t \cdot \frac{z}{x}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+80}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt{a}} \cdot \frac{y}{\sqrt{a}} - t \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 2.9e+80)
   (/ (fma x y (* z (- t))) a)
   (- (* (/ x (sqrt a)) (/ y (sqrt a))) (* t (/ z a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.9e+80) {
		tmp = fma(x, y, (z * -t)) / a;
	} else {
		tmp = ((x / sqrt(a)) * (y / sqrt(a))) - (t * (z / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 2.9e+80)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a);
	else
		tmp = Float64(Float64(Float64(x / sqrt(a)) * Float64(y / sqrt(a))) - Float64(t * Float64(z / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 2.9e+80], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(x / N[Sqrt[a], $MachinePrecision]), $MachinePrecision] * N[(y / N[Sqrt[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.89999999999999986e80

   1. Initial program 94.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

      1. div-sub 91.5%

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

      2. *-commutative 91.5%

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

      3. div-sub 94.8%

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

      4. *-commutative 94.8%

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

      5. fma-neg 95.3%

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

      6. distribute-rgt-neg-out 95.3%

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

   3. Simplified 95.3%

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

   if 2.89999999999999986e80 < a

   1. Initial program 75.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 75.7%

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

      2. *-un-lft-identity 75.7%

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

      3. add-sqr-sqrt 75.5%

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

      4. times-frac 75.5%

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

      5. fma-neg 75.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\sqrt{a}}, \frac{x \cdot y}{\sqrt{a}}, -\frac{z \cdot t}{a}\right)} \]

      6. associate-/l* 83.3%

         \[\leadsto \mathsf{fma}\left(\frac{1}{\sqrt{a}}, \frac{x \cdot y}{\sqrt{a}}, -\color{blue}{z \cdot \frac{t}{a}}\right) \]

   4. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\sqrt{a}}, \frac{x \cdot y}{\sqrt{a}}, -z \cdot \frac{t}{a}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 75.5%

         \[\leadsto \mathsf{fma}\left(\frac{1}{\sqrt{a}}, \frac{x \cdot y}{\sqrt{a}}, -\color{blue}{\frac{z \cdot t}{a}}\right) \]

      2. *-commutative 75.5%

         \[\leadsto \mathsf{fma}\left(\frac{1}{\sqrt{a}}, \frac{x \cdot y}{\sqrt{a}}, -\frac{\color{blue}{t \cdot z}}{a}\right) \]

      3. fma-neg 75.5%

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

      4. associate-*l/ 75.5%

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

      5. *-lft-identity 75.5%

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

      6. associate-/l* 84.4%

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

      7. associate-*l/ 88.7%

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

      8. associate-/l* 97.5%

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

   6. Simplified 97.5%

      \[\leadsto \color{blue}{\frac{x}{\sqrt{a}} \cdot \frac{y}{\sqrt{a}} - t \cdot \frac{z}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+285}\right):\\ \;\;\;\;x \cdot \frac{y - t \cdot \frac{z}{x}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+285)))
     (* x (/ (- y (* t (/ z x))) a))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+285)) {
		tmp = x * ((y - (t * (z / x))) / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+285)) {
		tmp = x * ((y - (t * (z / x))) / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+285):
		tmp = x * ((y - (t * (z / x))) / a)
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+285))
		tmp = Float64(x * Float64(Float64(y - Float64(t * Float64(z / x))) / a));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+285)))
		tmp = x * ((y - (t * (z / x))) / a);
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+285]], $MachinePrecision]], N[(x * N[(N[(y - N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 9.9999999999999998e284 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 69.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

      3. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

      1. associate-/l* 94.5%

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

      2. *-commutative 94.5%

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

   7. Applied egg-rr 94.5%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 9.9999999999999998e284

   1. Initial program 99.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+285}\right):\\ \;\;\;\;x \cdot \frac{y - t \cdot \frac{z}{x}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{1}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-41)
   (/ x (* a (/ 1.0 y)))
   (if (<= (* x y) 1e-30) (/ (* z (- t)) a) (/ y (/ a x)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (1.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = (z * -t) / a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * y) <= (-2d-41)) then
        tmp = x / (a * (1.0d0 / y))
    else if ((x * y) <= 1d-30) then
        tmp = (z * -t) / a
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (1.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = (z * -t) / a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-41:
		tmp = x / (a * (1.0 / y))
	elif (x * y) <= 1e-30:
		tmp = (z * -t) / a
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-41)
		tmp = Float64(x / Float64(a * Float64(1.0 / y)));
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-41)
		tmp = x / (a * (1.0 / y));
	elseif ((x * y) <= 1e-30)
		tmp = (z * -t) / a;
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-41], N[(x / N[(a * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000001e-41

   1. Initial program 87.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.0%

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

      1. associate-*r/ 74.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]

   5. Simplified 74.4%

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

      1. clear-num 74.4%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      2. un-div-inv 75.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Applied egg-rr 75.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
   8. Step-by-step derivation

      1. clear-num 74.3%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\frac{y}{a}}}} \]

      2. associate-/r/ 75.0%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{y} \cdot a}} \]

   9. Applied egg-rr 75.0%

      \[\leadsto \frac{x}{\color{blue}{\frac{1}{y} \cdot a}} \]

   if -2.00000000000000001e-41 < (*.f64 x y) < 1e-30

   1. Initial program 98.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. *-commutative 84.5%

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

      3. distribute-rgt-neg-in 84.5%

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

   5. Simplified 84.5%

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

   if 1e-30 < (*.f64 x y)

   1. Initial program 86.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.7%

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

      1. clear-num 67.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot y}}} \]

      2. associate-/r* 69.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

      3. associate-/r/ 69.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}} \cdot y} \]

      4. clear-num 69.0%

         \[\leadsto \color{blue}{\frac{x}{a}} \cdot y \]

   5. Applied egg-rr 69.0%

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

      1. *-commutative 69.0%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

      2. clear-num 69.0%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      3. un-div-inv 69.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   7. Applied egg-rr 69.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{1}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-41)
   (/ x (/ a y))
   (if (<= (* x y) 1e-30) (/ (* z (- t)) a) (/ y (/ a x)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e-30) {
		tmp = (z * -t) / a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * y) <= (-2d-41)) then
        tmp = x / (a / y)
    else if ((x * y) <= 1d-30) then
        tmp = (z * -t) / a
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e-30) {
		tmp = (z * -t) / a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-41:
		tmp = x / (a / y)
	elif (x * y) <= 1e-30:
		tmp = (z * -t) / a
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-41)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-41)
		tmp = x / (a / y);
	elseif ((x * y) <= 1e-30)
		tmp = (z * -t) / a;
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-41], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000001e-41

   1. Initial program 87.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.0%

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

      1. associate-*r/ 74.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]

   5. Simplified 74.4%

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

      1. clear-num 74.4%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      2. un-div-inv 75.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Applied egg-rr 75.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -2.00000000000000001e-41 < (*.f64 x y) < 1e-30

   1. Initial program 98.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. *-commutative 84.5%

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

      3. distribute-rgt-neg-in 84.5%

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

   5. Simplified 84.5%

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

   if 1e-30 < (*.f64 x y)

   1. Initial program 86.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.7%

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

      1. clear-num 67.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot y}}} \]

      2. associate-/r* 69.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

      3. associate-/r/ 69.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}} \cdot y} \]

      4. clear-num 69.0%

         \[\leadsto \color{blue}{\frac{x}{a}} \cdot y \]

   5. Applied egg-rr 69.0%

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

      1. *-commutative 69.0%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

      2. clear-num 69.0%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      3. un-div-inv 69.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   7. Applied egg-rr 69.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -20000000.0)
   (/ x (/ a y))
   (if (<= (* x y) 1e-30) (* (- z) (/ t a)) (/ y (/ a x)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000.0) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e-30) {
		tmp = -z * (t / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * y) <= (-20000000.0d0)) then
        tmp = x / (a / y)
    else if ((x * y) <= 1d-30) then
        tmp = -z * (t / a)
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000.0) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e-30) {
		tmp = -z * (t / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -20000000.0:
		tmp = x / (a / y)
	elif (x * y) <= 1e-30:
		tmp = -z * (t / a)
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -20000000.0)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(Float64(-z) * Float64(t / a));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -20000000.0)
		tmp = x / (a / y);
	elseif ((x * y) <= 1e-30)
		tmp = -z * (t / a);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -20000000.0], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e7

   1. Initial program 87.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.5%

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

      1. associate-*r/ 76.2%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]

   5. Simplified 76.2%

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

      1. clear-num 76.2%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      2. un-div-inv 76.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -2e7 < (*.f64 x y) < 1e-30

   1. Initial program 97.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 82.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 82.0%

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

      2. associate-*r/ 78.5%

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

      3. neg-mul-1 78.5%

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

      4. distribute-rgt-neg-in 78.5%

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

      5. distribute-frac-neg 78.5%

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

   5. Simplified 78.5%

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

   if 1e-30 < (*.f64 x y)

   1. Initial program 86.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.7%

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

      1. clear-num 67.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot y}}} \]

      2. associate-/r* 69.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

      3. associate-/r/ 69.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}} \cdot y} \]

      4. clear-num 69.0%

         \[\leadsto \color{blue}{\frac{x}{a}} \cdot y \]

   5. Applied egg-rr 69.0%

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

      1. *-commutative 69.0%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

      2. clear-num 69.0%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      3. un-div-inv 69.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   7. Applied egg-rr 69.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0001:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -0.0001)
   (/ x (/ a y))
   (if (<= (* x y) 1e-30) (* t (/ (- z) a)) (/ y (/ a x)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -0.0001) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e-30) {
		tmp = t * (-z / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * y) <= (-0.0001d0)) then
        tmp = x / (a / y)
    else if ((x * y) <= 1d-30) then
        tmp = t * (-z / a)
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -0.0001) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e-30) {
		tmp = t * (-z / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -0.0001:
		tmp = x / (a / y)
	elif (x * y) <= 1e-30:
		tmp = t * (-z / a)
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -0.0001)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(t * Float64(Float64(-z) / a));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -0.0001)
		tmp = x / (a / y);
	elseif ((x * y) <= 1e-30)
		tmp = t * (-z / a);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -0.0001], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000005e-4

   1. Initial program 88.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 69.9%

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

      1. associate-*r/ 75.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]

   5. Simplified 75.4%

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

      1. clear-num 75.4%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      2. un-div-inv 76.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Applied egg-rr 76.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -1.00000000000000005e-4 < (*.f64 x y) < 1e-30

   1. Initial program 97.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 82.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. mul-1-neg 82.6%

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

      2. associate-/l* 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

      4. distribute-neg-frac2 78.3%

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

   5. Simplified 78.3%

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

   if 1e-30 < (*.f64 x y)

   1. Initial program 86.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.7%

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

      1. clear-num 67.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot y}}} \]

      2. associate-/r* 69.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

      3. associate-/r/ 69.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}} \cdot y} \]

      4. clear-num 69.0%

         \[\leadsto \color{blue}{\frac{x}{a}} \cdot y \]

   5. Applied egg-rr 69.0%

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

      1. *-commutative 69.0%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

      2. clear-num 69.0%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      3. un-div-inv 69.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   7. Applied egg-rr 69.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0001:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+180) (* y (/ x a)) (/ (- (* x y) (* z t)) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+180) {
		tmp = y * (x / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * y) <= (-5d+180)) then
        tmp = y * (x / a)
    else
        tmp = ((x * y) - (z * t)) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+180) {
		tmp = y * (x / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+180:
		tmp = y * (x / a)
	else:
		tmp = ((x * y) - (z * t)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+180)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+180)
		tmp = y * (x / a);
	else
		tmp = ((x * y) - (z * t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+180], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.9999999999999996e180

   1. Initial program 73.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.2%

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

      1. clear-num 77.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot y}}} \]

      2. associate-/r* 99.7%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

      3. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}} \cdot y} \]

      4. clear-num 99.9%

         \[\leadsto \color{blue}{\frac{x}{a}} \cdot y \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]

   if -4.9999999999999996e180 < (*.f64 x y)

   1. Initial program 93.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 5.5e-62) (/ (* x y) a) (* y (/ x a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 5.5e-62) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 5.5d-62) then
        tmp = (x * y) / a
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 5.5e-62) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if a <= 5.5e-62:
		tmp = (x * y) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 5.5e-62)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 5.5e-62)
		tmp = (x * y) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 5.5e-62], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.50000000000000022e-62

   1. Initial program 95.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 52.3%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]

   if 5.50000000000000022e-62 < a

   1. Initial program 83.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 47.3%

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

      1. clear-num 45.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot y}}} \]

      2. associate-/r* 53.2%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

      3. associate-/r/ 54.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}} \cdot y} \]

      4. clear-num 55.7%

         \[\leadsto \color{blue}{\frac{x}{a}} \cdot y \]

   5. Applied egg-rr 55.7%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.5e+164) (* x (/ y a)) (* y (/ x a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.5e+164) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3.5d+164)) then
        tmp = x * (y / a)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.5e+164) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.5e+164:
		tmp = x * (y / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.5e+164)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.5e+164)
		tmp = x * (y / a);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.5e+164], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4999999999999998e164

   1. Initial program 89.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.5%

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

      1. associate-*r/ 87.9%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]

   5. Simplified 87.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]

   if -3.4999999999999998e164 < x

   1. Initial program 91.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 45.7%

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

      1. clear-num 45.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot y}}} \]

      2. associate-/r* 44.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

      3. associate-/r/ 45.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}} \cdot y} \]

      4. clear-num 45.5%

         \[\leadsto \color{blue}{\frac{x}{a}} \cdot y \]

   5. Applied egg-rr 45.5%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \frac{y}{\frac{a}{x}} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (/ y (/ a x)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return y / (a / x);
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = y / (a / x)
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return y / (a / x);
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return y / (a / x)

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(y / Float64(a / x))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = y / (a / x);
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.6%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 50.9%

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

   1. clear-num 50.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot y}}} \]

   2. associate-/r* 50.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{a}{x}}{y}}} \]

   3. associate-/r/ 51.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}} \cdot y} \]

   4. clear-num 51.5%

      \[\leadsto \color{blue}{\frac{x}{a}} \cdot y \]

5. Applied egg-rr 51.5%

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

   1. *-commutative 51.5%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

   2. clear-num 51.2%

      \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

   3. un-div-inv 51.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

7. Applied egg-rr 51.3%

   \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
8. Add Preprocessing

Alternative 12: 52.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ x \cdot \frac{y}{a} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* x (/ y a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return x * (y / a);
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x * (y / a)
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return x * (y / a);
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return x * (y / a)

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(x * Float64(y / a))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = x * (y / a);
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.6%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 50.9%

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

   1. associate-*r/ 51.8%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]

5. Simplified 51.8%

   \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
6. Add Preprocessing

Developer Target 1: 91.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -246868496869954800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6309831121978371/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z)))))

  (/ (- (* x y) (* z t)) a))