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

Percentage Accurate: 91.7% → 97.6%

Time: 8.8s

Alternatives: 9

Speedup: 0.5×

• 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: 91.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-z}{a}\\ t_2 := y \cdot x - t \cdot z\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(t\_1, t, \frac{x}{a} \cdot y\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+285}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-t\right) \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, t\_1 \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z) a)) (t_2 (- (* y x) (* t z))))
   (if (<= t_2 (- INFINITY))
     (fma t_1 t (* (/ x a) y))
     (if (<= t_2 1e+285)
       (/ (fma y x (* (- t) z)) a)
       (fma (/ x a) y (* t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -z / a;
	double t_2 = (y * x) - (t * z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(t_1, t, ((x / a) * y));
	} else if (t_2 <= 1e+285) {
		tmp = fma(y, x, (-t * z)) / a;
	} else {
		tmp = fma((x / a), y, (t_1 * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-z) / a)
	t_2 = Float64(Float64(y * x) - Float64(t * z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(t_1, t, Float64(Float64(x / a) * y));
	elseif (t_2 <= 1e+285)
		tmp = Float64(fma(y, x, Float64(Float64(-t) * z)) / a);
	else
		tmp = fma(Float64(x / a), y, Float64(t_1 * t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-z) / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 * t + N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+285], N[(N[(y * x + N[((-t) * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y + N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 57.1%

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

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 57.1

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 57.1

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 57.1

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

   4. Applied rewrites 57.1%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. div-inv N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. lift-/.f64 N/A

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

      12. div-inv N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*r/ N/A

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

      15. lift-/.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-neg.f64 N/A

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

      18. distribute-rgt-neg-out N/A

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

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

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

      20. lower-fma.f64 N/A

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

   6. Applied rewrites 99.9%

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

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

   1. Initial program 98.6%

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

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 98.6

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

   4. Applied rewrites 98.6%

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

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

   1. Initial program 69.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. 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 97.2

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

   4. Applied rewrites 97.2%

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

4. Final simplification 98.5%

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

Alternative 2: 97.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{a}, y, \frac{-z}{a} \cdot t\right)\\ t_2 := y \cdot x - t \cdot z\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+285}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-t\right) \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x a) y (* (/ (- z) a) t))) (t_2 (- (* y x) (* t z))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 1e+285) (/ (fma y x (* (- t) z)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / a), y, ((-z / a) * t));
	double t_2 = (y * x) - (t * z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1e+285) {
		tmp = fma(y, x, (-t * z)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / a), y, Float64(Float64(Float64(-z) / a) * t))
	t_2 = Float64(Float64(y * x) - Float64(t * z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1e+285)
		tmp = Float64(fma(y, x, Float64(Float64(-t) * z)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] * y + N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1e+285], N[(N[(y * x + N[((-t) * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 64.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 96.5

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

   4. Applied rewrites 96.5%

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

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

   1. Initial program 98.6%

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

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 98.6

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

   4. Applied rewrites 98.6%

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

4. Final simplification 98.1%

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

Alternative 3: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;t \cdot z \leq 10^{-17}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;t \cdot z \leq 10^{+90}:\\ \;\;\;\;\frac{\left(-t\right) \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* t z) -5e-22)
   (* (/ (- z) a) t)
   (if (<= (* t z) 1e-17)
     (/ (* y x) a)
     (if (<= (* t z) 1e+90) (/ (* (- t) z) a) (* (/ (- t) a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t * z) <= -5e-22) {
		tmp = (-z / a) * t;
	} else if ((t * z) <= 1e-17) {
		tmp = (y * x) / a;
	} else if ((t * z) <= 1e+90) {
		tmp = (-t * z) / a;
	} else {
		tmp = (-t / a) * z;
	}
	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) :: tmp
    if ((t * z) <= (-5d-22)) then
        tmp = (-z / a) * t
    else if ((t * z) <= 1d-17) then
        tmp = (y * x) / a
    else if ((t * z) <= 1d+90) then
        tmp = (-t * z) / a
    else
        tmp = (-t / a) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t * z) <= -5e-22) {
		tmp = (-z / a) * t;
	} else if ((t * z) <= 1e-17) {
		tmp = (y * x) / a;
	} else if ((t * z) <= 1e+90) {
		tmp = (-t * z) / a;
	} else {
		tmp = (-t / a) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t * z) <= -5e-22:
		tmp = (-z / a) * t
	elif (t * z) <= 1e-17:
		tmp = (y * x) / a
	elif (t * z) <= 1e+90:
		tmp = (-t * z) / a
	else:
		tmp = (-t / a) * z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(t * z) <= -5e-22)
		tmp = Float64(Float64(Float64(-z) / a) * t);
	elseif (Float64(t * z) <= 1e-17)
		tmp = Float64(Float64(y * x) / a);
	elseif (Float64(t * z) <= 1e+90)
		tmp = Float64(Float64(Float64(-t) * z) / a);
	else
		tmp = Float64(Float64(Float64(-t) / a) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t * z) <= -5e-22)
		tmp = (-z / a) * t;
	elseif ((t * z) <= 1e-17)
		tmp = (y * x) / a;
	elseif ((t * z) <= 1e+90)
		tmp = (-t * z) / a;
	else
		tmp = (-t / a) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(t * z), $MachinePrecision], -5e-22], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 1e-17], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 1e+90], N[(N[((-t) * z), $MachinePrecision] / a), $MachinePrecision], N[(N[((-t) / a), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -4.99999999999999954e-22

   1. Initial program 86.0%

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

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 81.3

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

   5. Applied rewrites 81.3%

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

   if -4.99999999999999954e-22 < (*.f64 z t) < 1.00000000000000007e-17

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.5

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

   5. Applied rewrites 76.5%

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

   if 1.00000000000000007e-17 < (*.f64 z t) < 9.99999999999999966e89

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 69.3

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

   5. Applied rewrites 69.3%

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

   if 9.99999999999999966e89 < (*.f64 z t)

   1. Initial program 82.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 19.0

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

   5. Applied rewrites 19.0%

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

   6. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 86.7

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

   8. Applied rewrites 86.7%

      \[\leadsto \color{blue}{\frac{-t}{a} \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;t \cdot z \leq 10^{-17}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;t \cdot z \leq 10^{+90}:\\ \;\;\;\;\frac{\left(-t\right) \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq -\infty:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;t \cdot z \leq 10^{+248}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-t\right) \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* t z) (- INFINITY))
   (* (/ (- z) a) t)
   (if (<= (* t z) 1e+248) (/ (fma y x (* (- t) z)) a) (* (/ (- t) a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t * z) <= -((double) INFINITY)) {
		tmp = (-z / a) * t;
	} else if ((t * z) <= 1e+248) {
		tmp = fma(y, x, (-t * z)) / a;
	} else {
		tmp = (-t / a) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(t * z) <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-z) / a) * t);
	elseif (Float64(t * z) <= 1e+248)
		tmp = Float64(fma(y, x, Float64(Float64(-t) * z)) / a);
	else
		tmp = Float64(Float64(Float64(-t) / a) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(t * z), $MachinePrecision], (-Infinity)], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 1e+248], N[(N[(y * x + N[((-t) * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[((-t) / a), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 68.4%

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

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 92.2

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

   5. Applied rewrites 92.2%

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

   if -inf.0 < (*.f64 z t) < 1.00000000000000005e248

   1. Initial program 95.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 95.7

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

   4. Applied rewrites 95.7%

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

   if 1.00000000000000005e248 < (*.f64 z t)

   1. Initial program 62.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 13.2

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

   5. Applied rewrites 13.2%

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

   6. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 88.9

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

   8. Applied rewrites 88.9%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -\infty:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;t \cdot z \leq 10^{+248}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-t\right) \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq -\infty:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;t \cdot z \leq 10^{+248}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* t z) (- INFINITY))
   (* (/ (- z) a) t)
   (if (<= (* t z) 1e+248) (/ (- (* y x) (* t z)) a) (* (/ (- t) a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t * z) <= -((double) INFINITY)) {
		tmp = (-z / a) * t;
	} else if ((t * z) <= 1e+248) {
		tmp = ((y * x) - (t * z)) / a;
	} else {
		tmp = (-t / a) * z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t * z) <= -Double.POSITIVE_INFINITY) {
		tmp = (-z / a) * t;
	} else if ((t * z) <= 1e+248) {
		tmp = ((y * x) - (t * z)) / a;
	} else {
		tmp = (-t / a) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t * z) <= -math.inf:
		tmp = (-z / a) * t
	elif (t * z) <= 1e+248:
		tmp = ((y * x) - (t * z)) / a
	else:
		tmp = (-t / a) * z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(t * z) <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-z) / a) * t);
	elseif (Float64(t * z) <= 1e+248)
		tmp = Float64(Float64(Float64(y * x) - Float64(t * z)) / a);
	else
		tmp = Float64(Float64(Float64(-t) / a) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t * z) <= -Inf)
		tmp = (-z / a) * t;
	elseif ((t * z) <= 1e+248)
		tmp = ((y * x) - (t * z)) / a;
	else
		tmp = (-t / a) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(t * z), $MachinePrecision], (-Infinity)], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 1e+248], N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[((-t) / a), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 68.4%

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

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 92.2

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

   5. Applied rewrites 92.2%

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

   if -inf.0 < (*.f64 z t) < 1.00000000000000005e248

   1. Initial program 95.7%

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

   if 1.00000000000000005e248 < (*.f64 z t)

   1. Initial program 62.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 13.2

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

   5. Applied rewrites 13.2%

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

   6. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 88.9

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

   8. Applied rewrites 88.9%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -\infty:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;t \cdot z \leq 10^{+248}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;t \cdot z \leq 10^{-17}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* t z) -5e-22)
   (* (/ (- z) a) t)
   (if (<= (* t z) 1e-17) (/ (* y x) a) (* (/ (- t) a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t * z) <= -5e-22) {
		tmp = (-z / a) * t;
	} else if ((t * z) <= 1e-17) {
		tmp = (y * x) / a;
	} else {
		tmp = (-t / a) * z;
	}
	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) :: tmp
    if ((t * z) <= (-5d-22)) then
        tmp = (-z / a) * t
    else if ((t * z) <= 1d-17) then
        tmp = (y * x) / a
    else
        tmp = (-t / a) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t * z) <= -5e-22) {
		tmp = (-z / a) * t;
	} else if ((t * z) <= 1e-17) {
		tmp = (y * x) / a;
	} else {
		tmp = (-t / a) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t * z) <= -5e-22:
		tmp = (-z / a) * t
	elif (t * z) <= 1e-17:
		tmp = (y * x) / a
	else:
		tmp = (-t / a) * z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(t * z) <= -5e-22)
		tmp = Float64(Float64(Float64(-z) / a) * t);
	elseif (Float64(t * z) <= 1e-17)
		tmp = Float64(Float64(y * x) / a);
	else
		tmp = Float64(Float64(Float64(-t) / a) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t * z) <= -5e-22)
		tmp = (-z / a) * t;
	elseif ((t * z) <= 1e-17)
		tmp = (y * x) / a;
	else
		tmp = (-t / a) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(t * z), $MachinePrecision], -5e-22], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 1e-17], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], N[(N[((-t) / a), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.99999999999999954e-22

   1. Initial program 86.0%

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

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 81.3

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

   5. Applied rewrites 81.3%

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

   if -4.99999999999999954e-22 < (*.f64 z t) < 1.00000000000000007e-17

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.5

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

   5. Applied rewrites 76.5%

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

   if 1.00000000000000007e-17 < (*.f64 z t)

   1. Initial program 87.5%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 23.6

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

   5. Applied rewrites 23.6%

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

   6. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 72.2

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

   8. Applied rewrites 72.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;t \cdot z \leq 10^{-17}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-z}{a} \cdot t\\ \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \cdot z \leq 10^{-17}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- z) a) t)))
   (if (<= (* t z) -5e-22) t_1 (if (<= (* t z) 1e-17) (/ (* y x) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-z / a) * t;
	double tmp;
	if ((t * z) <= -5e-22) {
		tmp = t_1;
	} else if ((t * z) <= 1e-17) {
		tmp = (y * x) / 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 = (-z / a) * t
    if ((t * z) <= (-5d-22)) then
        tmp = t_1
    else if ((t * z) <= 1d-17) then
        tmp = (y * x) / 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 = (-z / a) * t;
	double tmp;
	if ((t * z) <= -5e-22) {
		tmp = t_1;
	} else if ((t * z) <= 1e-17) {
		tmp = (y * x) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-z / a) * t
	tmp = 0
	if (t * z) <= -5e-22:
		tmp = t_1
	elif (t * z) <= 1e-17:
		tmp = (y * x) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(-z) / a) * t)
	tmp = 0.0
	if (Float64(t * z) <= -5e-22)
		tmp = t_1;
	elseif (Float64(t * z) <= 1e-17)
		tmp = Float64(Float64(y * x) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-z / a) * t;
	tmp = 0.0;
	if ((t * z) <= -5e-22)
		tmp = t_1;
	elseif ((t * z) <= 1e-17)
		tmp = (y * x) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(t * z), $MachinePrecision], -5e-22], t$95$1, If[LessEqual[N[(t * z), $MachinePrecision], 1e-17], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.99999999999999954e-22 or 1.00000000000000007e-17 < (*.f64 z t)

   1. Initial program 86.7%

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

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 78.3

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

   5. Applied rewrites 78.3%

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

   if -4.99999999999999954e-22 < (*.f64 z t) < 1.00000000000000007e-17

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.5

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

   5. Applied rewrites 76.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;t \cdot z \leq 10^{-17}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.52 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.52e+117) (* (/ x a) y) (* (/ y a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.52e+117) {
		tmp = (x / a) * y;
	} else {
		tmp = (y / a) * x;
	}
	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) :: tmp
    if (y <= 1.52d+117) then
        tmp = (x / a) * y
    else
        tmp = (y / a) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.52e+117) {
		tmp = (x / a) * y;
	} else {
		tmp = (y / a) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.52e+117:
		tmp = (x / a) * y
	else:
		tmp = (y / a) * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.52e+117)
		tmp = Float64(Float64(x / a) * y);
	else
		tmp = Float64(Float64(y / a) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.52e+117)
		tmp = (x / a) * y;
	else
		tmp = (y / a) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.52e+117], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.52e117

   1. Initial program 91.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 41.7

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

   5. Applied rewrites 41.7%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   7. 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 43.0

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

   8. Applied rewrites 43.0%

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

   if 1.52e117 < y

   1. Initial program 84.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 75.8

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   7. 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 64.6

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

   8. Applied rewrites 64.6%

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

   10. Applied rewrites 82.3%

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

Alternative 9: 51.1% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

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 / a) * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

3. Taylor expanded in t around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 46.0

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

5. Applied rewrites 46.0%

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

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
7. 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 45.7

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

8. Applied rewrites 45.7%

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

Developer Target 1: 91.2% 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 2024268 
(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))