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

Average Error: 10.3 → 0.3

Time: 2.8s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return 3.0 * (x * (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 = 3.0d0 * (x * (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 3.0 * (x * (x * y));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	10.3
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 10.3

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

2. Simplified 0.2

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

   [Start] 10.3	\[ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
   associate-*l* [=>] 0.2	\[ \color{blue}{\left(x \cdot 3\right) \cdot \left(x \cdot y\right)} \]

3. Taylor expanded in x around 0 10.3

   \[\leadsto \color{blue}{3 \cdot \left(y \cdot {x}^{2}\right)} \]

4. Simplified 0.3

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

   [Start] 10.3	\[ 3 \cdot \left(y \cdot {x}^{2}\right) \]
   *-commutative [=>] 10.3	\[ 3 \cdot \color{blue}{\left({x}^{2} \cdot y\right)} \]
   unpow2 [=>] 10.3	\[ 3 \cdot \left(\color{blue}{\left(x \cdot x\right)} \cdot y\right) \]
   associate-*l* [=>] 0.3	\[ 3 \cdot \color{blue}{\left(x \cdot \left(x \cdot y\right)\right)} \]
   *-commutative [=>] 0.3	\[ 3 \cdot \left(x \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

5. Final simplification 0.3

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

Reproduce

herbie shell --seed 2023012 
(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))