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

Percentage Accurate: 91.6% → 94.7%

Time: 6.8s

Alternatives: 11

Speedup: 0.6×

• 29.1% 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: 94.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+220}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{y}, \frac{z}{a}, \frac{x}{a}\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+120}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, y \cdot x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, \left(-t\right) \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 -2e+220)
     (* (fma (/ (- t) y) (/ z a) (/ x a)) y)
     (if (<= t_1 5e+120)
       (/ (fma (- z) t (* y x)) a)
       (fma (/ x a) y (* (- t) (/ z a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -2e+220) {
		tmp = fma((-t / y), (z / a), (x / a)) * y;
	} else if (t_1 <= 5e+120) {
		tmp = fma(-z, t, (y * x)) / a;
	} else {
		tmp = fma((x / a), y, (-t * (z / a)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -2e+220)
		tmp = Float64(fma(Float64(Float64(-t) / y), Float64(z / a), Float64(x / a)) * y);
	elseif (t_1 <= 5e+120)
		tmp = Float64(fma(Float64(-z), t, Float64(y * x)) / a);
	else
		tmp = fma(Float64(x / a), y, 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.
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, -2e+220], N[(N[(N[((-t) / y), $MachinePrecision] * N[(z / a), $MachinePrecision] + N[(x / a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 5e+120], N[(N[((-z) * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y + N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -2e220

   1. Initial program 83.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 83.0

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 83.0

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

   4. Applied rewrites 83.0%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 85.9

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

   7. Applied rewrites 85.9%

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

   if -2e220 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000019e120

   1. Initial program 98.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 98.9

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 98.9

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

   4. Applied rewrites 98.9%

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

   if 5.00000000000000019e120 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 87.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-/l* N/A

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

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

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

      15. lower-*.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lower-/.f64 95.9

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

   4. Applied rewrites 95.9%

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

Alternative 2: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+226} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, y \cdot x\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 -5e+226) (not (<= t_1 5e+120)))
     (fma (/ x a) y (* (- t) (/ z a)))
     (/ (fma (- z) t (* y x)) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -5e+226) || !(t_1 <= 5e+120)) {
		tmp = fma((x / a), y, (-t * (z / a)));
	} else {
		tmp = fma(-z, t, (y * x)) / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -5e+226) || !(t_1 <= 5e+120))
		tmp = fma(Float64(x / a), y, Float64(Float64(-t) * Float64(z / a)));
	else
		tmp = Float64(fma(Float64(-z), t, Float64(y * x)) / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+226], N[Not[LessEqual[t$95$1, 5e+120]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * y + N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-z) * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000005e226 or 5.00000000000000019e120 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 85.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-/l* N/A

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

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

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

      15. lower-*.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lower-/.f64 96.1

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

   4. Applied rewrites 96.1%

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

   if -5.0000000000000005e226 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000019e120

   1. Initial program 98.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 99.0

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 99.0

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

   4. Applied rewrites 99.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+226} \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, y \cdot x\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.2% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (* (- z) (/ t a))
   (if (<= (* z t) 4e+146) (/ (fma (- z) t (* y x)) a) (/ (- t) (/ a z)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = -z * (t / a);
	} else if ((z * t) <= 4e+146) {
		tmp = fma(-z, t, (y * x)) / a;
	} else {
		tmp = -t / (a / z);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(-z) * Float64(t / a));
	elseif (Float64(z * t) <= 4e+146)
		tmp = Float64(fma(Float64(-z), t, Float64(y * x)) / a);
	else
		tmp = Float64(Float64(-t) / Float64(a / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e+146], N[(N[((-z) * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 60.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 93.8

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

   5. Applied rewrites 93.8%

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

   if -inf.0 < (*.f64 z t) < 3.99999999999999973e146

   1. Initial program 97.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 97.4

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 97.4

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

   4. Applied rewrites 97.4%

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

   if 3.99999999999999973e146 < (*.f64 z t)

   1. Initial program 79.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 79.1

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 79.1

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

   4. Applied rewrites 79.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 99.7

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

   7. Applied rewrites 99.7%

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

   9. Applied rewrites 99.7%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+146}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, y \cdot x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.2% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (* (- z) (/ t a))
   (if (<= (* z t) 4e+146) (/ (- (* x y) (* z t)) a) (/ (- t) (/ a z)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = -z * (t / a);
	} else if ((z * t) <= 4e+146) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = -t / (a / z);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = -z * (t / a);
	} else if ((z * t) <= 4e+146) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = -t / (a / z);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = -z * (t / a)
	elif (z * t) <= 4e+146:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = -t / (a / z)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(-z) * Float64(t / a));
	elseif (Float64(z * t) <= 4e+146)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(-t) / Float64(a / z));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = -z * (t / a);
	elseif ((z * t) <= 4e+146)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = -t / (a / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e+146], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 60.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 93.8

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

   5. Applied rewrites 93.8%

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

   if -inf.0 < (*.f64 z t) < 3.99999999999999973e146

   1. Initial program 97.4%

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

   if 3.99999999999999973e146 < (*.f64 z t)

   1. Initial program 79.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 79.1

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 79.1

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

   4. Applied rewrites 79.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 99.7

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

   7. Applied rewrites 99.7%

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

   9. Applied rewrites 99.7%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+146}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+67} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -2e+67) (not (<= (* x y) 2e+61)))
   (/ x (/ a y))
   (/ (* (- z) t) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+67) || !((x * y) <= 2e+61)) {
		tmp = x / (a / y);
	} else {
		tmp = (-z * t) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x * y) <= (-2d+67)) .or. (.not. ((x * y) <= 2d+61))) then
        tmp = x / (a / y)
    else
        tmp = (-z * t) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+67) || !((x * y) <= 2e+61)) {
		tmp = x / (a / y);
	} else {
		tmp = (-z * t) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -2e+67) or not ((x * y) <= 2e+61):
		tmp = x / (a / y)
	else:
		tmp = (-z * t) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+67) || !(Float64(x * y) <= 2e+61))
		tmp = Float64(x / Float64(a / y));
	else
		tmp = Float64(Float64(Float64(-z) * t) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -2e+67) || ~(((x * y) <= 2e+61)))
		tmp = x / (a / y);
	else
		tmp = (-z * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+67], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+61]], $MachinePrecision]], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(N[((-z) * t), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999997e67 or 1.9999999999999999e61 < (*.f64 x y)

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 83.2

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

   5. Applied rewrites 83.2%

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

   7. Applied rewrites 83.3%

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

   9. Applied rewrites 84.3%

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

   if -1.99999999999999997e67 < (*.f64 x y) < 1.9999999999999999e61

   1. Initial program 95.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 76.1

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

   5. Applied rewrites 76.1%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+67} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{+150}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, y \cdot x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a}, \frac{y \cdot x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 5e+150)
   (/ (fma (- z) t (* y x)) a)
   (fma (- t) (/ z a) (/ (* y x) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 5e+150) {
		tmp = fma(-z, t, (y * x)) / a;
	} else {
		tmp = fma(-t, (z / a), ((y * x) / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 5e+150)
		tmp = Float64(fma(Float64(-z), t, Float64(y * x)) / a);
	else
		tmp = fma(Float64(-t), Float64(z / a), Float64(Float64(y * x) / a));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 5e+150], N[(N[((-z) * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-t) * N[(z / a), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.00000000000000009e150

   1. Initial program 94.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 94.6

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 94.6

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

   4. Applied rewrites 94.6%

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

   if 5.00000000000000009e150 < a

   1. Initial program 87.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-/.f64 99.0

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 99.0

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

   4. Applied rewrites 99.0%

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

Alternative 7: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+67} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -2e+67) (not (<= (* x y) 2e+61)))
   (* x (/ y a))
   (/ (* (- z) t) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+67) || !((x * y) <= 2e+61)) {
		tmp = x * (y / a);
	} else {
		tmp = (-z * t) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x * y) <= (-2d+67)) .or. (.not. ((x * y) <= 2d+61))) then
        tmp = x * (y / a)
    else
        tmp = (-z * t) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+67) || !((x * y) <= 2e+61)) {
		tmp = x * (y / a);
	} else {
		tmp = (-z * t) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -2e+67) or not ((x * y) <= 2e+61):
		tmp = x * (y / a)
	else:
		tmp = (-z * t) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+67) || !(Float64(x * y) <= 2e+61))
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(Float64(Float64(-z) * t) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -2e+67) || ~(((x * y) <= 2e+61)))
		tmp = x * (y / a);
	else
		tmp = (-z * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+67], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+61]], $MachinePrecision]], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[((-z) * t), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999997e67 or 1.9999999999999999e61 < (*.f64 x y)

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 83.2

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

   5. Applied rewrites 83.2%

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

   7. Applied rewrites 83.3%

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

   if -1.99999999999999997e67 < (*.f64 x y) < 1.9999999999999999e61

   1. Initial program 95.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 76.1

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

   5. Applied rewrites 76.1%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+67} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{-52} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{-22}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* z t) -2e-52) (not (<= (* z t) 2e-22)))
   (* (- z) (/ t a))
   (/ (* y x) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -2e-52) || !((z * t) <= 2e-22)) {
		tmp = -z * (t / a);
	} else {
		tmp = (y * x) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z * t) <= (-2d-52)) .or. (.not. ((z * t) <= 2d-22))) then
        tmp = -z * (t / a)
    else
        tmp = (y * x) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -2e-52) || !((z * t) <= 2e-22)) {
		tmp = -z * (t / a);
	} else {
		tmp = (y * x) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((z * t) <= -2e-52) or not ((z * t) <= 2e-22):
		tmp = -z * (t / a)
	else:
		tmp = (y * x) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z * t) <= -2e-52) || !(Float64(z * t) <= 2e-22))
		tmp = Float64(Float64(-z) * Float64(t / a));
	else
		tmp = Float64(Float64(y * x) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z * t) <= -2e-52) || ~(((z * t) <= 2e-22)))
		tmp = -z * (t / a);
	else
		tmp = (y * x) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -2e-52], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e-22]], $MachinePrecision]], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2e-52 or 2.0000000000000001e-22 < (*.f64 z t)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 76.8

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

   5. Applied rewrites 76.8%

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

   if -2e-52 < (*.f64 z t) < 2.0000000000000001e-22

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{-52} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{-22}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+89} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -1e+89) (not (<= (* x y) 2e+61)))
   (* x (/ y a))
   (* (/ (- z) a) t)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -1e+89) || !((x * y) <= 2e+61)) {
		tmp = x * (y / a);
	} else {
		tmp = (-z / a) * t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x * y) <= (-1d+89)) .or. (.not. ((x * y) <= 2d+61))) then
        tmp = x * (y / a)
    else
        tmp = (-z / a) * t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -1e+89) || !((x * y) <= 2e+61)) {
		tmp = x * (y / a);
	} else {
		tmp = (-z / a) * t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -1e+89) or not ((x * y) <= 2e+61):
		tmp = x * (y / a)
	else:
		tmp = (-z / a) * t
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+89) || !(Float64(x * y) <= 2e+61))
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(Float64(Float64(-z) / a) * t);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -1e+89) || ~(((x * y) <= 2e+61)))
		tmp = x * (y / a);
	else
		tmp = (-z / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+89], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+61]], $MachinePrecision]], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.99999999999999995e88 or 1.9999999999999999e61 < (*.f64 x y)

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 84.8

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

   5. Applied rewrites 84.8%

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

   7. Applied rewrites 84.9%

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

   if -9.99999999999999995e88 < (*.f64 x y) < 1.9999999999999999e61

   1. Initial program 94.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 94.7

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 94.7

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

   4. Applied rewrites 94.7%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 74.8

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

   7. Applied rewrites 74.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+89} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.3% accurate, 1.5× speedup

Math

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

FPCore

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

C

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.
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;
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])
def code(x, y, z, t, a):
	return (x / a) * y

Julia

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])){:}
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.
code[x_, y_, z_, t_, a_] := N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in x around inf

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 47.5

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

5. Applied rewrites 47.5%

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

7. Applied rewrites 46.6%

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

8. Final simplification 46.6%

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

Alternative 11: 51.3% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in x around inf

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 47.5

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

5. Applied rewrites 47.5%

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

7. Applied rewrites 47.2%

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

8. Final simplification 47.2%

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

Developer Target 1: 91.1% 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 2024324 
(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))