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

Percentage Accurate: 91.4% → 97.4%

Time: 9.8s

Alternatives: 10

Speedup: 0.4×

• 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: 97.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (- INFINITY))
     (- (/ x (/ a y)) (* t (/ z a)))
     (if (<= t_1 2e+263)
       (/ (fma (- z) t (* x y)) a)
       (fma -1.0 (/ t (/ a z)) (* y (/ x a)))))))

C

assert(x < y && y < z && z < t && t < a);
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)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else if (t_1 <= 2e+263) {
		tmp = fma(-z, t, (x * y)) / a;
	} else {
		tmp = fma(-1.0, (t / (a / z)), (y * (x / a)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(t * Float64(z / a)));
	elseif (t_1 <= 2e+263)
		tmp = Float64(fma(Float64(-z), t, Float64(x * y)) / a);
	else
		tmp = fma(-1.0, Float64(t / Float64(a / z)), Float64(y * Float64(x / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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, (-Infinity)], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+263], N[(N[((-z) * t + N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(-1.0 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 71.6%

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

      1. div-sub 71.6%

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

      2. associate-/l* 82.7%

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

      3. associate-/l* 96.8%

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

   4. Applied egg-rr 96.8%

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

      1. associate-/r/ 93.8%

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

   6. Applied egg-rr 93.8%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.00000000000000003e263

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. distribute-lft-neg-in 99.2%

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

      4. fma-def 99.2%

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

   4. Applied egg-rr 99.2%

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

   if 2.00000000000000003e263 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 77.7%

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

   3. Taylor expanded in x around 0 75.1%

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

      1. associate-/l* 77.4%

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

      2. fma-def 77.4%

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

      3. associate-/l* 94.5%

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

      4. associate-/r/ 97.2%

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

   5. Simplified 97.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{x}{a} \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+284}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 5e+284)))
     (- (/ x (/ a y)) (* t (/ z a)))
     (/ (fma (- z) t (* x y)) a))))

C

assert(x < y && y < z && z < t && t < a);
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 <= 5e+284)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else {
		tmp = fma(-z, t, (x * y)) / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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 <= 5e+284))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(t * Float64(z / a)));
	else
		tmp = Float64(fma(Float64(-z), t, Float64(x * y)) / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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, 5e+284]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-z) * t + N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 4.9999999999999999e284 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 73.4%

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

      1. div-sub 71.9%

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

      2. associate-/l* 78.7%

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

      3. associate-/l* 95.4%

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

   4. Applied egg-rr 95.4%

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

      1. associate-/r/ 93.9%

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

   6. Applied egg-rr 93.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999999e284

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. distribute-lft-neg-in 99.2%

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

      4. fma-def 99.2%

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

   4. Applied egg-rr 99.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-z, t, x \cdot y\right)}}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+284}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+284}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 5e+284)))
     (- (/ x (/ a y)) (* t (/ z a)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
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 <= 5e+284)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
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 <= 5e+284)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[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 <= 5e+284):
		tmp = (x / (a / y)) - (t * (z / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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 <= 5e+284))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(t * Float64(z / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= 5e+284)))
		tmp = (x / (a / y)) - (t * (z / 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.
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, 5e+284]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $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 4.9999999999999999e284 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 73.4%

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

      1. div-sub 71.9%

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

      2. associate-/l* 78.7%

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

      3. associate-/l* 95.4%

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

   4. Applied egg-rr 95.4%

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

      1. associate-/r/ 93.9%

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

   6. Applied egg-rr 93.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999999e284

   1. Initial program 99.2%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+284}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+274}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -5e+274)
   (* (- z) (/ t a))
   (if (<= (* z t) 5e+294) (/ (- (* x y) (* z t)) a) (* t (/ (- z) a)))))

C

assert(x < y && y < z && z < t && t < a);
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) <= -5e+274) {
		tmp = -z * (t / a);
	} else if ((z * t) <= 5e+294) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t * (-z / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-5d+274)) then
        tmp = -z * (t / a)
    else if ((z * t) <= 5d+294) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t * (-z / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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) <= -5e+274) {
		tmp = -z * (t / a);
	} else if ((z * t) <= 5e+294) {
		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])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -5e+274:
		tmp = -z * (t / a)
	elif (z * t) <= 5e+294:
		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])
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) <= -5e+274)
		tmp = Float64(Float64(-z) * Float64(t / a));
	elseif (Float64(z * t) <= 5e+294)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(t * Float64(Float64(-z) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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) <= -5e+274)
		tmp = -z * (t / a);
	elseif ((z * t) <= 5e+294)
		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.
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], -5e+274], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+294], 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) < -4.9999999999999998e274

   1. Initial program 63.4%

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

   3. Taylor expanded in x around 0 63.4%

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

      1. associate-*r/ 63.4%

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

      2. associate-*r* 63.4%

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

      3. neg-mul-1 63.4%

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

   5. Simplified 63.4%

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

      1. associate-/l* 94.4%

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

      2. distribute-frac-neg 94.4%

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

      3. mul-1-neg 94.4%

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

      4. associate-/r/ 94.7%

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

      5. associate-*r* 94.7%

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

   7. Applied egg-rr 94.7%

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

   if -4.9999999999999998e274 < (*.f64 z t) < 4.9999999999999999e294

   1. Initial program 96.2%

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

   if 4.9999999999999999e294 < (*.f64 z t)

   1. Initial program 81.2%

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

   3. Taylor expanded in x around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*l/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+274}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+58} \lor \neg \left(z \leq 3.6 \cdot 10^{-64}\right):\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= z -8.2e+58) (not (<= z 3.6e-64)))
   (* t (/ (- z) a))
   (* y (/ x a))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -8.2e+58) || !(z <= 3.6e-64)) {
		tmp = t * (-z / 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.
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 <= (-8.2d+58)) .or. (.not. (z <= 3.6d-64))) then
        tmp = t * (-z / a)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -8.2e+58) || !(z <= 3.6e-64)) {
		tmp = t * (-z / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.2e+58) or not (z <= 3.6e-64):
		tmp = t * (-z / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e+58) || !(z <= 3.6e-64))
		tmp = Float64(t * Float64(Float64(-z) / 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])){:}
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 <= -8.2e+58) || ~((z <= 3.6e-64)))
		tmp = t * (-z / 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.
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[z, -8.2e+58], N[Not[LessEqual[z, 3.6e-64]], $MachinePrecision]], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e58 or 3.5999999999999998e-64 < z

   1. Initial program 87.3%

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

   3. Taylor expanded in x around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*l/ 73.9%

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

      4. distribute-rgt-neg-in 73.9%

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

   5. Simplified 73.9%

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

   if -8.2e58 < z < 3.5999999999999998e-64

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 71.3%

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

      1. associate-*l/ 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+58} \lor \neg \left(z \leq 3.6 \cdot 10^{-64}\right):\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+52} \lor \neg \left(z \leq 3.6 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= z -6.5e+52) (not (<= z 3.6e-124)))
   (/ (- z) (/ a t))
   (/ (* x y) a)))

C

assert(x < y && y < z && z < t && t < a);
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 <= -6.5e+52) || !(z <= 3.6e-124)) {
		tmp = -z / (a / t);
	} 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.
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 <= (-6.5d+52)) .or. (.not. (z <= 3.6d-124))) then
        tmp = -z / (a / t)
    else
        tmp = (x * y) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -6.5e+52) || !(z <= 3.6e-124)) {
		tmp = -z / (a / t);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+52) or not (z <= 3.6e-124):
		tmp = -z / (a / t)
	else:
		tmp = (x * y) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+52) || !(z <= 3.6e-124))
		tmp = Float64(Float64(-z) / Float64(a / t));
	else
		tmp = Float64(Float64(x * y) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= -6.5e+52) || ~((z <= 3.6e-124)))
		tmp = -z / (a / t);
	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.
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[z, -6.5e+52], N[Not[LessEqual[z, 3.6e-124]], $MachinePrecision]], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999996e52 or 3.6000000000000001e-124 < z

   1. Initial program 88.4%

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

   3. Taylor expanded in x around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. *-commutative 63.5%

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

      3. associate-*l/ 68.2%

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

      4. distribute-rgt-neg-in 68.2%

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

   5. Simplified 68.2%

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

      1. distribute-rgt-neg-out 68.2%

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

      2. associate-/r/ 67.7%

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

      3. distribute-neg-frac 67.7%

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

   7. Applied egg-rr 67.7%

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

   if -6.49999999999999996e52 < z < 3.6000000000000001e-124

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 73.8%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+52} \lor \neg \left(z \leq 3.6 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -4.5e+58)
   (/ t (/ (- a) z))
   (if (<= z 4.1e-64) (* y (/ x a)) (* t (/ (- z) a)))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -4.5e+58) {
		tmp = t / (-a / z);
	} else if (z <= 4.1e-64) {
		tmp = y * (x / a);
	} else {
		tmp = t * (-z / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= (-4.5d+58)) then
        tmp = t / (-a / z)
    else if (z <= 4.1d-64) then
        tmp = y * (x / a)
    else
        tmp = t * (-z / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -4.5e+58) {
		tmp = t / (-a / z);
	} else if (z <= 4.1e-64) {
		tmp = y * (x / a);
	} else {
		tmp = t * (-z / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+58:
		tmp = t / (-a / z)
	elif z <= 4.1e-64:
		tmp = y * (x / a)
	else:
		tmp = t * (-z / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+58)
		tmp = Float64(t / Float64(Float64(-a) / z));
	elseif (z <= 4.1e-64)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(t * Float64(Float64(-z) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= -4.5e+58)
		tmp = t / (-a / z);
	elseif (z <= 4.1e-64)
		tmp = y * (x / 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.
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, -4.5e+58], N[(t / N[((-a) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-64], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4999999999999998e58

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. associate-*r* 83.8%

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

      3. neg-mul-1 83.8%

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

   5. Simplified 83.8%

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

      1. associate-/l* 84.8%

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

      2. distribute-frac-neg 84.8%

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

      3. mul-1-neg 84.8%

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

      4. associate-/r/ 90.5%

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

      5. associate-*r* 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. add-sqr-sqrt 41.8%

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

      2. sqrt-unprod 39.9%

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

      3. mul-1-neg 39.9%

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

      4. mul-1-neg 39.9%

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

      5. sqr-neg 39.9%

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

      6. sqrt-unprod 0.5%

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

      7. add-sqr-sqrt 0.6%

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

      8. frac-2neg 0.6%

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

      9. associate-*l/ 0.6%

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

      10. distribute-lft-neg-in 0.6%

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

      11. distribute-rgt-neg-out 0.6%

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

      12. add-sqr-sqrt 0.6%

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

      13. sqrt-unprod 0.6%

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

      14. sqr-neg 0.6%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 83.8%

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

   9. Applied egg-rr 83.8%

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

       1. associate-/l* 84.8%

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

   11. Simplified 84.8%

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

   if -4.4999999999999998e58 < z < 4.1e-64

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 71.3%

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

      1. associate-*l/ 70.4%

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

   5. Simplified 70.4%

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

   if 4.1e-64 < z

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0 59.3%

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

      1. mul-1-neg 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-*l/ 68.8%

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

      4. distribute-rgt-neg-in 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= t 5.2e-82) (/ (* x y) a) (/ x (/ a y))))

C

assert(x < y && y < z && z < t && t < a);
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 <= 5.2e-82) {
		tmp = (x * y) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= 5.2d-82) then
        tmp = (x * y) / a
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= 5.2e-82) {
		tmp = (x * y) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 5.2e-82:
		tmp = (x * y) / a
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 5.2e-82)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= 5.2e-82)
		tmp = (x * y) / a;
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[t, 5.2e-82], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.2e-82

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf 62.2%

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

   if 5.2e-82 < t

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 32.2%

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

      1. associate-*r/ 35.9%

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

   5. Simplified 35.9%

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

      1. associate-*r/ 32.2%

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

      2. associate-/l* 35.9%

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

   7. Applied egg-rr 35.9%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.7% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 92.5%

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

3. Taylor expanded in x around inf 50.4%

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

   1. associate-*r/ 49.6%

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

5. Simplified 49.6%

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

6. Final simplification 49.6%

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

Alternative 10: 52.2% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 92.5%

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

3. Taylor expanded in x around inf 50.4%

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

   1. associate-*l/ 49.7%

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

5. Simplified 49.7%

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

6. Final simplification 49.7%

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

Developer target: 92.1% 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 2024021 
(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))