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

Percentage Accurate: 91.6% → 96.0%

Time: 12.5s

Alternatives: 9

Speedup: 0.6×

• 28.4% 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: 91.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+263}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-z\right) \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(\frac{\frac{x}{t}}{z}, y, -1\right)}{a} \cdot z\right) \cdot t\\ \end{array} \end{array} \]

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 -1e+187)
     (fma (/ y a) x (* (- t) (/ z a)))
     (if (<= t_1 4e+263)
       (/ (fma y x (* (- z) t)) a)
       (* (* (/ (fma (/ (/ x t) z) y -1.0) a) z) t)))))

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 <= -1e+187) {
		tmp = fma((y / a), x, (-t * (z / a)));
	} else if (t_1 <= 4e+263) {
		tmp = fma(y, x, (-z * t)) / a;
	} else {
		tmp = ((fma(((x / t) / z), y, -1.0) / a) * z) * t;
	}
	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 <= -1e+187)
		tmp = fma(Float64(y / a), x, Float64(Float64(-t) * Float64(z / a)));
	elseif (t_1 <= 4e+263)
		tmp = Float64(fma(y, x, Float64(Float64(-z) * t)) / a);
	else
		tmp = Float64(Float64(Float64(fma(Float64(Float64(x / t) / z), y, -1.0) / a) * z) * t);
	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, -1e+187], N[(N[(y / a), $MachinePrecision] * x + N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+263], N[(N[(y * x + N[((-z) * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(N[(N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision] * y + -1.0), $MachinePrecision] / a), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -9.99999999999999907e186

   1. Initial program 84.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. lift-*.f64 N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 93.1

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

   4. Applied rewrites 93.1%

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

   if -9.99999999999999907e186 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.00000000000000006e263

   1. Initial program 98.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 98.5

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

   4. Applied rewrites 98.5%

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

   if 4.00000000000000006e263 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lft-identity N/A

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

      2. metadata-eval N/A

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

      3. associate-*r* N/A

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

      4. distribute-lft-out-- N/A

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

      5. distribute-lft-out-- N/A

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

      6. associate-*r* N/A

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in t around inf

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. remove-double-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. distribute-lft-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. distribute-lft-neg-in N/A

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

      13. *-commutative N/A

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

      14. distribute-lft-neg-in N/A

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

      15. lower-*.f64 N/A

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

   8. Applied rewrites 84.5%

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

   9. Taylor expanded in z around -inf

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

   11. Applied rewrites 94.7%

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

Alternative 2: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+254}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-z\right) \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \end{array} \]

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 (<= (* x y) (- INFINITY))
   (* (/ y a) x)
   (if (<= (* x y) 5e+254) (/ (fma y x (* (- z) t)) 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 ((x * y) <= -((double) INFINITY)) {
		tmp = (y / a) * x;
	} else if ((x * y) <= 5e+254) {
		tmp = fma(y, x, (-z * t)) / 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 (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(Float64(y / a) * x);
	elseif (Float64(x * y) <= 5e+254)
		tmp = Float64(fma(y, x, Float64(Float64(-z) * t)) / a);
	else
		tmp = Float64(Float64(x / a) * y);
	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_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+254], N[(N[(y * x + N[((-z) * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 49.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 99.6

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

   5. Applied rewrites 99.6%

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

   7. Applied rewrites 100.0%

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

   if -inf.0 < (*.f64 x y) < 4.99999999999999994e254

   1. Initial program 96.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   if 4.99999999999999994e254 < (*.f64 x y)

   1. Initial program 75.2%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 96.3

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

   5. Applied rewrites 96.3%

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

Alternative 3: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+254}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \end{array} \]

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 (<= (* x y) (- INFINITY))
   (* (/ y a) x)
   (if (<= (* x y) 5e+254) (/ (- (* x y) (* z t)) 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 ((x * y) <= -((double) INFINITY)) {
		tmp = (y / a) * x;
	} else if ((x * y) <= 5e+254) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (x / a) * y;
	}
	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 tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = (y / a) * x;
	} else if ((x * y) <= 5e+254) {
		tmp = ((x * y) - (z * t)) / 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 (x * y) <= -math.inf:
		tmp = (y / a) * x
	elif (x * y) <= 5e+254:
		tmp = ((x * y) - (z * t)) / 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 (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(Float64(y / a) * x);
	elseif (Float64(x * y) <= 5e+254)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(x / 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 ((x * y) <= -Inf)
		tmp = (y / a) * x;
	elseif ((x * y) <= 5e+254)
		tmp = ((x * y) - (z * t)) / 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[N[(x * y), $MachinePrecision], (-Infinity)], N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+254], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 49.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 99.6

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

   5. Applied rewrites 99.6%

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

   7. Applied rewrites 100.0%

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

   if -inf.0 < (*.f64 x y) < 4.99999999999999994e254

   1. Initial program 96.2%

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

   if 4.99999999999999994e254 < (*.f64 x y)

   1. Initial program 75.2%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 96.3

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

   5. Applied rewrites 96.3%

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

Alternative 4: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-z\right) \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, \left(-t\right) \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

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
 (if (<= a 3.4e+46)
   (/ (fma y x (* (- z) t)) a)
   (fma (/ y a) x (* (- 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 (a <= 3.4e+46) {
		tmp = fma(y, x, (-z * t)) / a;
	} else {
		tmp = fma((y / a), x, (-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 (a <= 3.4e+46)
		tmp = Float64(fma(y, x, Float64(Float64(-z) * t)) / a);
	else
		tmp = fma(Float64(y / a), x, Float64(Float64(-t) * Float64(z / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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, 3.4e+46], N[(N[(y * x + N[((-z) * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * x + N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.3999999999999998e46

   1. Initial program 94.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 95.1

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

   4. Applied rewrites 95.1%

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

   if 3.3999999999999998e46 < a

   1. Initial program 79.8%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. lift-*.f64 N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 90.9

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

   4. Applied rewrites 90.9%

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

Alternative 5: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+52}:\\ \;\;\;\;\frac{\left(-z\right) \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \end{array} \]

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 (<= (* x y) -2e+18)
   (* (/ y a) x)
   (if (<= (* x y) 5e+52) (/ (* (- z) t) 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 ((x * y) <= -2e+18) {
		tmp = (y / a) * x;
	} else if ((x * y) <= 5e+52) {
		tmp = (-z * t) / 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 ((x * y) <= (-2d+18)) then
        tmp = (y / a) * x
    else if ((x * y) <= 5d+52) then
        tmp = (-z * t) / 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 ((x * y) <= -2e+18) {
		tmp = (y / a) * x;
	} else if ((x * y) <= 5e+52) {
		tmp = (-z * t) / 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 (x * y) <= -2e+18:
		tmp = (y / a) * x
	elif (x * y) <= 5e+52:
		tmp = (-z * t) / 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 (Float64(x * y) <= -2e+18)
		tmp = Float64(Float64(y / a) * x);
	elseif (Float64(x * y) <= 5e+52)
		tmp = Float64(Float64(Float64(-z) * t) / a);
	else
		tmp = Float64(Float64(x / 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 ((x * y) <= -2e+18)
		tmp = (y / a) * x;
	elseif ((x * y) <= 5e+52)
		tmp = (-z * t) / 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[N[(x * y), $MachinePrecision], -2e+18], N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+52], N[(N[((-z) * t), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e18

   1. Initial program 86.0%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 73.6

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

   5. Applied rewrites 73.6%

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

   7. Applied rewrites 68.5%

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

   if -2e18 < (*.f64 x y) < 5e52

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 78.5

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

   5. Applied rewrites 78.5%

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

   if 5e52 < (*.f64 x y)

   1. Initial program 87.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 83.4

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

   5. Applied rewrites 83.4%

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

Alternative 6: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+59}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \end{array} \]

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 (<= (* x y) -2e+146)
   (* (/ y a) x)
   (if (<= (* x y) 4e+59) (* (/ (- z) a) t) (* (/ 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 ((x * y) <= -2e+146) {
		tmp = (y / a) * x;
	} else if ((x * y) <= 4e+59) {
		tmp = (-z / a) * t;
	} 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 ((x * y) <= (-2d+146)) then
        tmp = (y / a) * x
    else if ((x * y) <= 4d+59) then
        tmp = (-z / a) * t
    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 ((x * y) <= -2e+146) {
		tmp = (y / a) * x;
	} else if ((x * y) <= 4e+59) {
		tmp = (-z / a) * t;
	} 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 (x * y) <= -2e+146:
		tmp = (y / a) * x
	elif (x * y) <= 4e+59:
		tmp = (-z / a) * t
	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 (Float64(x * y) <= -2e+146)
		tmp = Float64(Float64(y / a) * x);
	elseif (Float64(x * y) <= 4e+59)
		tmp = Float64(Float64(Float64(-z) / a) * t);
	else
		tmp = Float64(Float64(x / 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 ((x * y) <= -2e+146)
		tmp = (y / a) * x;
	elseif ((x * y) <= 4e+59)
		tmp = (-z / a) * t;
	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[N[(x * y), $MachinePrecision], -2e+146], N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+59], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999987e146

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 87.3

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

   5. Applied rewrites 87.3%

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

   7. Applied rewrites 84.5%

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

   if -1.99999999999999987e146 < (*.f64 x y) < 3.99999999999999989e59

   1. Initial program 95.0%

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

   4. Applied rewrites 37.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t \cdot \left(z \cdot {\left(\sqrt{-1}\right)}^{2}\right)}{a}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(z \cdot {\left(\sqrt{-1}\right)}^{2}\right) \cdot t}}{a} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{z \cdot {\left(\sqrt{-1}\right)}^{2}}{a} \cdot t} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot {\left(\sqrt{-1}\right)}^{2}}{a} \cdot t} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{{\left(\sqrt{-1}\right)}^{2} \cdot z}}{a} \cdot t \]

      5. unpow2 N/A

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

      6. rem-square-sqrt N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 69.7

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

   7. Applied rewrites 69.7%

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

   if 3.99999999999999989e59 < (*.f64 x y)

   1. Initial program 88.9%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 85.9

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

   5. Applied rewrites 85.9%

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

Alternative 7: 51.8% accurate, 1.5× speedup

Math

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

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 a) x))

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 / a) * x;
}

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 / a) * x
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 / a) * x;
}

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 / a) * x

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(Float64(y / a) * x)
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 / a) * x;
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[(N[(y / a), $MachinePrecision] * x), $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

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 53.0

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

5. Applied rewrites 53.0%

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

7. Applied rewrites 51.6%

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

Alternative 8: 52.0% accurate, 1.5× speedup

Math

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

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

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 / a) * y
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 / a) * y;
}

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 / a) * y

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(Float64(x / a) * y)
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 / a) * y;
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[(N[(x / a), $MachinePrecision] * y), $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

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 53.0

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

5. Applied rewrites 53.0%

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

Alternative 9: 8.8% accurate, 1.5× speedup

Math

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

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 (* z (/ t 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 z * (t / 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 = z * (t / 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 z * (t / 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 z * (t / 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(z * Float64(t / 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 = z * (t / 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[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.6%

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

4. Applied rewrites 26.1%

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

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{t \cdot \left(z \cdot {\left(\sqrt{-1}\right)}^{2}\right)}{a}} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{\color{blue}{\left(z \cdot {\left(\sqrt{-1}\right)}^{2}\right) \cdot t}}{a} \]

   2. associate-*l/ N/A

      \[\leadsto \color{blue}{\frac{z \cdot {\left(\sqrt{-1}\right)}^{2}}{a} \cdot t} \]

   3. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{z \cdot {\left(\sqrt{-1}\right)}^{2}}{a} \cdot t} \]

   4. *-commutative N/A

      \[\leadsto \frac{\color{blue}{{\left(\sqrt{-1}\right)}^{2} \cdot z}}{a} \cdot t \]

   5. unpow2 N/A

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

   6. rem-square-sqrt N/A

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

   7. lower-/.f64 N/A

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

   8. mul-1-neg N/A

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

   9. lower-neg.f64 51.4

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

7. Applied rewrites 51.4%

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

9. Applied rewrites 10.8%

   \[\leadsto z \cdot \color{blue}{\frac{t}{a}} \]
10. Add Preprocessing

Developer Target 1: 92.0% accurate, 0.5× 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 2024339 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

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

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