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

Percentage Accurate: 99.6% → 99.7%

Time: 4.1s

Precision: binary64

Cost: 448

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

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	99.6%
Target	99.7%
Herbie	99.7%

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

Derivation

1. Initial program 99.7%

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

2. Applied egg-rr 98.7%

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

   [Start] 99.7%	\[ \left(\left(x \cdot 3\right) \cdot y\right) \cdot y \]
   associate-*l* [=>] 99.7%	\[ \color{blue}{\left(x \cdot \left(3 \cdot y\right)\right)} \cdot y \]
   *-commutative [=>] 99.7%	\[ \color{blue}{\left(\left(3 \cdot y\right) \cdot x\right)} \cdot y \]
   add-cube-cbrt [=>] 98.8%	\[ \left(\color{blue}{\left(\left(\sqrt[3]{3 \cdot y} \cdot \sqrt[3]{3 \cdot y}\right) \cdot \sqrt[3]{3 \cdot y}\right)} \cdot x\right) \cdot y \]
   pow3 [=>] 98.8%	\[ \left(\color{blue}{{\left(\sqrt[3]{3 \cdot y}\right)}^{3}} \cdot x\right) \cdot y \]
   add-cube-cbrt [=>] 98.6%	\[ \left({\left(\sqrt[3]{3 \cdot y}\right)}^{3} \cdot \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)}\right) \cdot y \]
   pow3 [=>] 98.6%	\[ \left({\left(\sqrt[3]{3 \cdot y}\right)}^{3} \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{3}}\right) \cdot y \]
   pow-prod-down [=>] 98.7%	\[ \color{blue}{{\left(\sqrt[3]{3 \cdot y} \cdot \sqrt[3]{x}\right)}^{3}} \cdot y \]

3. Applied egg-rr 99.7%

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

   [Start] 98.7%	\[ {\left(\sqrt[3]{3 \cdot y} \cdot \sqrt[3]{x}\right)}^{3} \cdot y \]
   cbrt-unprod [=>] 98.7%	\[ {\color{blue}{\left(\sqrt[3]{\left(3 \cdot y\right) \cdot x}\right)}}^{3} \cdot y \]
   associate-*r* [<=] 98.7%	\[ {\left(\sqrt[3]{\color{blue}{3 \cdot \left(y \cdot x\right)}}\right)}^{3} \cdot y \]
   rem-cube-cbrt [=>] 99.6%	\[ \color{blue}{\left(3 \cdot \left(y \cdot x\right)\right)} \cdot y \]
   associate-*r* [=>] 99.7%	\[ \color{blue}{\left(\left(3 \cdot y\right) \cdot x\right)} \cdot y \]

4. Final simplification 99.7%

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

Alternatives

Alternative 1
Accuracy	99.7%
Cost	448

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

Alternative 2
Accuracy	99.7%
Cost	448

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

Alternative 3
Accuracy	99.7%
Cost	448

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

Alternative 4
Accuracy	99.7%
Cost	448

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

Reproduce

herbie shell --seed 2023165 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

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

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