Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 88.2% → 99.7%

Time: 5.8s

Precision: binary64

Cost: 448

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Math

\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]

↓

\[x \cdot \left(3 \cdot \left(x \cdot y\right)\right) \]

FPCore

(FPCore (x y) :precision binary64 (* (* (* x 3.0) x) y))

↓

(FPCore (x y) :precision binary64 (* x (* 3.0 (* x y))))

C

double code(double x, double y) {
	return ((x * 3.0) * x) * y;
}

↓

double code(double x, double y) {
	return x * (3.0 * (x * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 3.0d0) * x) * y
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (3.0d0 * (x * y))
end function

Java

public static double code(double x, double y) {
	return ((x * 3.0) * x) * y;
}

↓

public static double code(double x, double y) {
	return x * (3.0 * (x * y));
}

Python

def code(x, y):
	return ((x * 3.0) * x) * y

↓

def code(x, y):
	return x * (3.0 * (x * y))

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 3.0) * x) * y)
end

↓

function code(x, y)
	return Float64(x * Float64(3.0 * Float64(x * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 3.0) * x) * y;
end

↓

function tmp = code(x, y)
	tmp = x * (3.0 * (x * y));
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] * y), $MachinePrecision]

↓

code[x_, y_] := N[(x * N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	88.2%
Target	99.7%
Herbie	99.7%

\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right) \]

Derivation

1. Initial program 89.4%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]

2. Simplified 89.3%

   \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right) \cdot y} \]
   Step-by-step derivation

   [Start] 89.4%	\[ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
   *-commutative [=>] 89.4%	\[ \left(\color{blue}{\left(3 \cdot x\right)} \cdot x\right) \cdot y \]
   associate-*l* [=>] 89.3%	\[ \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right)} \cdot y \]

3. Applied egg-rr 75.7%

   \[\leadsto \color{blue}{\left(1 + 3 \cdot \left(x \cdot \left(x \cdot y\right)\right)\right) - 1} \]
   Step-by-step derivation

   [Start] 89.3%	\[ \left(3 \cdot \left(x \cdot x\right)\right) \cdot y \]
   associate-*r* [=>] 89.4%	\[ \color{blue}{\left(\left(3 \cdot x\right) \cdot x\right)} \cdot y \]
   *-commutative [<=] 89.4%	\[ \left(\color{blue}{\left(x \cdot 3\right)} \cdot x\right) \cdot y \]
   associate-*r* [<=] 99.7%	\[ \color{blue}{\left(x \cdot 3\right) \cdot \left(x \cdot y\right)} \]
   expm1-log1p-u [=>] 74.9%	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\right)\right)} \]
   expm1-udef [=>] 50.8%	\[ \color{blue}{e^{\mathsf{log1p}\left(\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\right)} - 1} \]
   log1p-udef [=>] 50.8%	\[ e^{\color{blue}{\log \left(1 + \left(x \cdot 3\right) \cdot \left(x \cdot y\right)\right)}} - 1 \]
   add-exp-log [<=] 75.6%	\[ \color{blue}{\left(1 + \left(x \cdot 3\right) \cdot \left(x \cdot y\right)\right)} - 1 \]
   *-commutative [=>] 75.6%	\[ \left(1 + \color{blue}{\left(3 \cdot x\right)} \cdot \left(x \cdot y\right)\right) - 1 \]
   associate-*l* [=>] 75.7%	\[ \left(1 + \color{blue}{3 \cdot \left(x \cdot \left(x \cdot y\right)\right)}\right) - 1 \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot y\right)\right) \cdot x} \]
   Step-by-step derivation

   [Start] 75.7%	\[ \left(1 + 3 \cdot \left(x \cdot \left(x \cdot y\right)\right)\right) - 1 \]
   add-exp-log [=>] 50.8%	\[ \color{blue}{e^{\log \left(\left(1 + 3 \cdot \left(x \cdot \left(x \cdot y\right)\right)\right) - 1\right)}} \]
   associate--l+ [=>] 50.8%	\[ e^{\log \color{blue}{\left(1 + \left(3 \cdot \left(x \cdot \left(x \cdot y\right)\right) - 1\right)\right)}} \]
   log1p-def [=>] 50.8%	\[ e^{\color{blue}{\mathsf{log1p}\left(3 \cdot \left(x \cdot \left(x \cdot y\right)\right) - 1\right)}} \]
   associate-*r* [=>] 48.6%	\[ e^{\mathsf{log1p}\left(3 \cdot \color{blue}{\left(\left(x \cdot x\right) \cdot y\right)} - 1\right)} \]
   *-commutative [<=] 48.6%	\[ e^{\mathsf{log1p}\left(3 \cdot \color{blue}{\left(y \cdot \left(x \cdot x\right)\right)} - 1\right)} \]
   associate-*r* [=>] 48.6%	\[ e^{\mathsf{log1p}\left(\color{blue}{\left(3 \cdot y\right) \cdot \left(x \cdot x\right)} - 1\right)} \]
   *-commutative [<=] 48.6%	\[ e^{\mathsf{log1p}\left(\color{blue}{\left(x \cdot x\right) \cdot \left(3 \cdot y\right)} - 1\right)} \]
   add-exp-log [=>] 48.2%	\[ e^{\mathsf{log1p}\left(\color{blue}{e^{\log \left(\left(x \cdot x\right) \cdot \left(3 \cdot y\right)\right)}} - 1\right)} \]
   expm1-def [=>] 48.2%	\[ e^{\mathsf{log1p}\left(\color{blue}{\mathsf{expm1}\left(\log \left(\left(x \cdot x\right) \cdot \left(3 \cdot y\right)\right)\right)}\right)} \]
   log1p-expm1-u [<=] 58.6%	\[ e^{\color{blue}{\log \left(\left(x \cdot x\right) \cdot \left(3 \cdot y\right)\right)}} \]
   associate-*r* [=>] 58.6%	\[ e^{\log \color{blue}{\left(\left(\left(x \cdot x\right) \cdot 3\right) \cdot y\right)}} \]
   log-prod [=>] 47.7%	\[ e^{\color{blue}{\log \left(\left(x \cdot x\right) \cdot 3\right) + \log y}} \]
   add-sqr-sqrt [=>] 47.7%	\[ e^{\log \left(\left(x \cdot x\right) \cdot \color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)}\right) + \log y} \]
   swap-sqr [<=] 47.7%	\[ e^{\log \color{blue}{\left(\left(x \cdot \sqrt{3}\right) \cdot \left(x \cdot \sqrt{3}\right)\right)} + \log y} \]
   unpow2 [<=] 47.7%	\[ e^{\log \color{blue}{\left({\left(x \cdot \sqrt{3}\right)}^{2}\right)} + \log y} \]
   log-prod [<=] 58.6%	\[ e^{\color{blue}{\log \left({\left(x \cdot \sqrt{3}\right)}^{2} \cdot y\right)}} \]
   add-exp-log [<=] 89.1%	\[ \color{blue}{{\left(x \cdot \sqrt{3}\right)}^{2} \cdot y} \]

5. Final simplification 99.8%

   \[\leadsto x \cdot \left(3 \cdot \left(x \cdot y\right)\right) \]

Alternatives

Alternative 1
Accuracy	99.7%
Cost	448

\[x \cdot \left(3 \cdot \left(x \cdot y\right)\right) \]

Alternative 2
Accuracy	88.1%
Cost	448

\[3 \cdot \left(y \cdot \left(x \cdot x\right)\right) \]

Alternative 3
Accuracy	88.1%
Cost	448

\[y \cdot \left(3 \cdot \left(x \cdot x\right)\right) \]

Reproduce

herbie shell --seed 2023277 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* (* x 3.0) (* x y))

  (* (* (* x 3.0) x) y))