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

Percentage Accurate: 91.4% → 94.4%

Time: 10.2s

Alternatives: 11

Speedup: 0.6×

• 28.6% 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: 91.4% 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: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+165}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

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 (<= (* z t) (- INFINITY))
   (/ (- t) (/ a z))
   (if (<= (* z t) 2e+165) (/ (- (* x y) (* z t)) 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 ((z * t) <= -((double) INFINITY)) {
		tmp = -t / (a / z);
	} else if ((z * t) <= 2e+165) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = -t * (z / 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 tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = -t / (a / z);
	} else if ((z * t) <= 2e+165) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = -t * (z / 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 (z * t) <= -math.inf:
		tmp = -t / (a / z)
	elif (z * t) <= 2e+165:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = -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 (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(-t) / Float64(a / z));
	elseif (Float64(z * t) <= 2e+165)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(-t) * Float64(z / 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 ((z * t) <= -Inf)
		tmp = -t / (a / z);
	elseif ((z * t) <= 2e+165)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = -t * (z / 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[(z * t), $MachinePrecision], (-Infinity)], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+165], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -inf.0

   1. Initial program 60.6%

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

   3. Taylor expanded in x around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. associate-/l* 94.0%

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

   5. Simplified 94.0%

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

   if -inf.0 < (*.f64 z t) < 1.9999999999999998e165

   1. Initial program 95.5%

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

   if 1.9999999999999998e165 < (*.f64 z t)

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*l/ 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(-t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+165}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+147}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

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 7.8e+147)
   (/ (fma x y (* z (- t))) a)
   (- (/ x (/ a y)) (/ z (/ a t)))))

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 <= 7.8e+147) {
		tmp = fma(x, y, (z * -t)) / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	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 <= 7.8e+147)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	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, 7.8e+147], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 7.80000000000000033e147

   1. Initial program 95.3%

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

      1. div-sub 92.5%

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

      2. *-commutative 92.5%

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

      3. div-sub 95.3%

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

      4. fma-neg 95.8%

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

      5. *-commutative 95.8%

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

      6. distribute-rgt-neg-out 95.8%

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

   3. Simplified 95.8%

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

   if 7.80000000000000033e147 < a

   1. Initial program 72.6%

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

      1. div-sub 72.6%

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

      2. associate-/l* 73.1%

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

      3. associate-/l* 78.3%

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

   4. Applied egg-rr 78.3%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+147}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{a} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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)) a)))
   (if (<= t_1 (- INFINITY)) (- (* y (/ x a)) (/ z (/ a t))) t_1)))

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)) / a;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y * (x / a)) - (z / (a / t));
	} else {
		tmp = t_1;
	}
	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)) / a;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * (x / a)) - (z / (a / t));
	} else {
		tmp = t_1;
	}
	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)) / a
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y * (x / a)) - (z / (a / t))
	else:
		tmp = t_1
	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(Float64(x * y) - Float64(z * t)) / a)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y * Float64(x / a)) - Float64(z / Float64(a / t)));
	else
		tmp = t_1;
	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)) / a;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y * (x / a)) - (z / (a / t));
	else
		tmp = t_1;
	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[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < -inf.0

   1. Initial program 77.7%

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

      1. div-sub 68.9%

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

      2. associate-/l* 74.4%

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

      3. associate-/l* 88.2%

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

   4. Applied egg-rr 88.2%

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

      1. associate-/r/ 88.1%

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

   6. Applied egg-rr 88.1%

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

   if -inf.0 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 93.7%

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

4. Final simplification 92.9%

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

Alternative 4: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-74}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

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 (<= (* z t) -4e-74)
   (/ (- z) (/ a t))
   (if (<= (* z t) 4e-26) (/ (* x y) a) (* 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 ((z * t) <= -4e-74) {
		tmp = -z / (a / t);
	} else if ((z * t) <= 4e-26) {
		tmp = (x * y) / a;
	} else {
		tmp = 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 ((z * t) <= (-4d-74)) then
        tmp = -z / (a / t)
    else if ((z * t) <= 4d-26) then
        tmp = (x * y) / a
    else
        tmp = 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 ((z * t) <= -4e-74) {
		tmp = -z / (a / t);
	} else if ((z * t) <= 4e-26) {
		tmp = (x * y) / a;
	} else {
		tmp = 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 (z * t) <= -4e-74:
		tmp = -z / (a / t)
	elif (z * t) <= 4e-26:
		tmp = (x * y) / a
	else:
		tmp = 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(z * t) <= -4e-74)
		tmp = Float64(Float64(-z) / Float64(a / t));
	elseif (Float64(z * t) <= 4e-26)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(z * Float64(Float64(-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 ((z * t) <= -4e-74)
		tmp = -z / (a / t);
	elseif ((z * t) <= 4e-26)
		tmp = (x * y) / a;
	else
		tmp = 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[(z * t), $MachinePrecision], -4e-74], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e-26], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -3.99999999999999983e-74

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-*l/ 65.8%

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

      4. distribute-rgt-neg-in 65.8%

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

   5. Simplified 65.8%

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

      1. distribute-rgt-neg-out 65.8%

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

      2. associate-/r/ 69.8%

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

      3. distribute-neg-frac 69.8%

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

   7. Applied egg-rr 69.8%

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

   if -3.99999999999999983e-74 < (*.f64 z t) < 4.0000000000000002e-26

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 82.9%

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

   if 4.0000000000000002e-26 < (*.f64 z t)

   1. Initial program 90.1%

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

      1. div-sub 87.2%

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

      2. associate-/l* 84.5%

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

      3. associate-/l* 83.7%

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

   4. Applied egg-rr 83.7%

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

   5. Taylor expanded in x around 0 78.2%

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

      1. associate-*l/ 79.9%

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

      2. associate-*l* 79.9%

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

      3. neg-mul-1 79.9%

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

      4. *-commutative 79.9%

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

   7. Simplified 79.9%

      \[\leadsto \color{blue}{z \cdot \left(-\frac{t}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-74}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193} \lor \neg \left(t \leq 9.6 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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 (or (<= t -1.2e-193) (not (<= t 9.6e+24)))
   (/ (- t) (/ a z))
   (/ (* 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) {
	double tmp;
	if ((t <= -1.2e-193) || !(t <= 9.6e+24)) {
		tmp = -t / (a / z);
	} else {
		tmp = (x * y) / 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 ((t <= (-1.2d-193)) .or. (.not. (t <= 9.6d+24))) then
        tmp = -t / (a / z)
    else
        tmp = (x * y) / 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 ((t <= -1.2e-193) || !(t <= 9.6e+24)) {
		tmp = -t / (a / z);
	} else {
		tmp = (x * y) / 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 (t <= -1.2e-193) or not (t <= 9.6e+24):
		tmp = -t / (a / z)
	else:
		tmp = (x * y) / 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 ((t <= -1.2e-193) || !(t <= 9.6e+24))
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(Float64(x * y) / 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 ((t <= -1.2e-193) || ~((t <= 9.6e+24)))
		tmp = -t / (a / z);
	else
		tmp = (x * y) / 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[Or[LessEqual[t, -1.2e-193], N[Not[LessEqual[t, 9.6e+24]], $MachinePrecision]], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e-193 or 9.6000000000000003e24 < t

   1. Initial program 88.5%

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

   3. Taylor expanded in x around 0 66.9%

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

      1. mul-1-neg 66.9%

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

      2. associate-/l* 67.1%

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

   5. Simplified 67.1%

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

   if -1.2e-193 < t < 9.6000000000000003e24

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 73.2%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193} \lor \neg \left(t \leq 9.6 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193} \lor \neg \left(t \leq 2.4 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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 (or (<= t -1.2e-193) (not (<= t 2.4e+54)))
   (* z (/ (- t) a))
   (/ (* 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) {
	double tmp;
	if ((t <= -1.2e-193) || !(t <= 2.4e+54)) {
		tmp = z * (-t / a);
	} else {
		tmp = (x * y) / 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 ((t <= (-1.2d-193)) .or. (.not. (t <= 2.4d+54))) then
        tmp = z * (-t / a)
    else
        tmp = (x * y) / 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 ((t <= -1.2e-193) || !(t <= 2.4e+54)) {
		tmp = z * (-t / a);
	} else {
		tmp = (x * y) / 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 (t <= -1.2e-193) or not (t <= 2.4e+54):
		tmp = z * (-t / a)
	else:
		tmp = (x * y) / 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 ((t <= -1.2e-193) || !(t <= 2.4e+54))
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = Float64(Float64(x * y) / 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 ((t <= -1.2e-193) || ~((t <= 2.4e+54)))
		tmp = z * (-t / a);
	else
		tmp = (x * y) / 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[Or[LessEqual[t, -1.2e-193], N[Not[LessEqual[t, 2.4e+54]], $MachinePrecision]], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e-193 or 2.39999999999999998e54 < t

   1. Initial program 88.2%

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

      1. div-sub 85.0%

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

      2. associate-/l* 83.2%

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

      3. associate-/l* 82.8%

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

   4. Applied egg-rr 82.8%

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

   5. Taylor expanded in x around 0 66.7%

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

      1. associate-*l/ 68.1%

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

      2. associate-*l* 68.1%

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

      3. neg-mul-1 68.1%

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

      4. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   if -1.2e-193 < t < 2.39999999999999998e54

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 71.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193} \lor \neg \left(t \leq 2.4 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{+149}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

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 3e+149) (/ (- (* x y) (* z t)) a) (- (/ x (/ a y)) (/ z (/ a t)))))

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 <= 3e+149) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	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 <= 3d+149) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = (x / (a / y)) - (z / (a / t))
    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 <= 3e+149) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	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 <= 3e+149:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = (x / (a / y)) - (z / (a / t))
	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 <= 3e+149)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	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 <= 3e+149)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = (x / (a / y)) - (z / (a / t));
	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, 3e+149], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.00000000000000003e149

   1. Initial program 95.3%

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

   if 3.00000000000000003e149 < a

   1. Initial program 72.6%

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

      1. div-sub 72.6%

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

      2. associate-/l* 73.1%

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

      3. associate-/l* 78.3%

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

   4. Applied egg-rr 78.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{+149}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 4.8 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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 4.8e-85) (* y (/ x a)) (* 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) {
	double tmp;
	if (a <= 4.8e-85) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / 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 <= 4.8d-85) then
        tmp = y * (x / a)
    else
        tmp = x * (y / 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 <= 4.8e-85) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / 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 <= 4.8e-85:
		tmp = y * (x / a)
	else:
		tmp = x * (y / 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 <= 4.8e-85)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(x * Float64(y / 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 <= 4.8e-85)
		tmp = y * (x / a);
	else
		tmp = x * (y / 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, 4.8e-85], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.8000000000000001e-85

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 51.9%

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

      1. associate-*l/ 50.2%

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

   5. Simplified 50.2%

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

   if 4.8000000000000001e-85 < a

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf 40.7%

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

      1. associate-*l/ 47.0%

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

   5. Simplified 47.0%

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

      1. associate-/r/ 42.0%

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

   7. Applied egg-rr 42.0%

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

      1. clear-num 41.9%

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

      2. associate-/r/ 41.9%

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

      3. clear-num 42.7%

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

   9. Applied egg-rr 42.7%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.8 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2.6 \cdot 10^{-85}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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 2.6e-85) (/ y (/ a x)) (* 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) {
	double tmp;
	if (a <= 2.6e-85) {
		tmp = y / (a / x);
	} else {
		tmp = x * (y / 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 <= 2.6d-85) then
        tmp = y / (a / x)
    else
        tmp = x * (y / 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 <= 2.6e-85) {
		tmp = y / (a / x);
	} else {
		tmp = x * (y / 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 <= 2.6e-85:
		tmp = y / (a / x)
	else:
		tmp = x * (y / 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 <= 2.6e-85)
		tmp = Float64(y / Float64(a / x));
	else
		tmp = Float64(x * Float64(y / 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 <= 2.6e-85)
		tmp = y / (a / x);
	else
		tmp = x * (y / 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, 2.6e-85], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.60000000000000011e-85

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 51.9%

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

      1. associate-*l/ 50.2%

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

   5. Simplified 50.2%

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

      1. *-commutative 50.2%

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

      2. clear-num 50.2%

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

      3. un-div-inv 50.2%

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

   7. Applied egg-rr 50.2%

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

   if 2.60000000000000011e-85 < a

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf 40.7%

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

      1. associate-*l/ 47.0%

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

   5. Simplified 47.0%

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

      1. associate-/r/ 42.0%

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

   7. Applied egg-rr 42.0%

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

      1. clear-num 41.9%

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

      2. associate-/r/ 41.9%

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

      3. clear-num 42.7%

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

   9. Applied egg-rr 42.7%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.6 \cdot 10^{-85}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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 (<= z -8.5e-46) (/ y (/ a x)) (/ (* 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) {
	double tmp;
	if (z <= -8.5e-46) {
		tmp = y / (a / x);
	} else {
		tmp = (x * y) / 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 (z <= (-8.5d-46)) then
        tmp = y / (a / x)
    else
        tmp = (x * y) / 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 (z <= -8.5e-46) {
		tmp = y / (a / x);
	} else {
		tmp = (x * y) / 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 z <= -8.5e-46:
		tmp = y / (a / x)
	else:
		tmp = (x * y) / 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 (z <= -8.5e-46)
		tmp = Float64(y / Float64(a / x));
	else
		tmp = Float64(Float64(x * y) / 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 (z <= -8.5e-46)
		tmp = y / (a / x);
	else
		tmp = (x * y) / 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[z, -8.5e-46], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000001e-46

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf 38.4%

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

      1. associate-*l/ 38.4%

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

   5. Simplified 38.4%

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

      1. *-commutative 38.4%

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

      2. clear-num 38.4%

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

      3. un-div-inv 38.4%

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

   7. Applied egg-rr 38.4%

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

   if -8.5000000000000001e-46 < z

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 52.0%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.1% accurate, 1.8× speedup

Math

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

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 (* 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) {
	return y * (x / 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 = y * (x / 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 y * (x / a);
}

Python

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

Julia

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

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = y * (x / 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[(y * N[(x / 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 48.0%

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

   1. associate-*l/ 49.1%

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

5. Simplified 49.1%

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

6. Final simplification 49.1%

   \[\leadsto y \cdot \frac{x}{a} \]
7. Add Preprocessing

Developer target: 91.9% 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 2024026 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

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