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

Average Accuracy: 83.9% → 99.6%

Time: 4.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return x * (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) * x) * y
end function

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	83.9%
Target	99.6%
Herbie	99.6%

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

Derivation

1. Initial program 83.9%

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

2. Applied egg-rr 68.6%

   \[\leadsto \color{blue}{\left(1 + x \cdot \left(\left(x \cdot 3\right) \cdot y\right)\right) - 1} \]
   Proof

   [Start] 83.9	\[ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
   expm1-log1p-u [=>] 70.9	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\right)\right)} \]
   expm1-udef [=>] 47.6	\[ \color{blue}{e^{\mathsf{log1p}\left(\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\right)} - 1} \]
   log1p-udef [=>] 47.6	\[ e^{\color{blue}{\log \left(1 + \left(\left(x \cdot 3\right) \cdot x\right) \cdot y\right)}} - 1 \]
   add-exp-log [<=] 60.6	\[ \color{blue}{\left(1 + \left(\left(x \cdot 3\right) \cdot x\right) \cdot y\right)} - 1 \]
   *-commutative [=>] 60.6	\[ \left(1 + \color{blue}{\left(x \cdot \left(x \cdot 3\right)\right)} \cdot y\right) - 1 \]
   associate-*l* [=>] 68.6	\[ \left(1 + \color{blue}{x \cdot \left(\left(x \cdot 3\right) \cdot y\right)}\right) - 1 \]

3. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\left(x \cdot \left(3 \cdot y\right)\right) \cdot x} \]
   Proof

   [Start] 68.6	\[ \left(1 + x \cdot \left(\left(x \cdot 3\right) \cdot y\right)\right) - 1 \]
   add-exp-log [=>] 51.3	\[ \color{blue}{e^{\log \left(1 + x \cdot \left(\left(x \cdot 3\right) \cdot y\right)\right)}} - 1 \]
   log1p-udef [<=] 51.3	\[ e^{\color{blue}{\mathsf{log1p}\left(x \cdot \left(\left(x \cdot 3\right) \cdot y\right)\right)}} - 1 \]
   expm1-udef [<=] 82.2	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(\left(x \cdot 3\right) \cdot y\right)\right)\right)} \]
   expm1-log1p-u [<=] 99.6	\[ \color{blue}{x \cdot \left(\left(x \cdot 3\right) \cdot y\right)} \]
   *-commutative [=>] 99.6	\[ \color{blue}{\left(\left(x \cdot 3\right) \cdot y\right) \cdot x} \]
   associate-*l* [=>] 99.6	\[ \color{blue}{\left(x \cdot \left(3 \cdot y\right)\right)} \cdot x \]

4. Final simplification 99.6%

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

Alternatives

Alternative 1
Accuracy	99.6%
Cost	448

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

Alternative 2
Accuracy	99.6%
Cost	448

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

Reproduce

herbie shell --seed 2023151 
(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))