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

Average Error: 10.6 → 0.3

Time: 3.7s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 * y)) * 3.0d0
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 * y)) * 3.0;
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	10.6
Target	0.3
Herbie	0.3

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

Derivation

1. Initial program 10.6

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

2. Taylor expanded in x around 0 10.6

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

3. Simplified 10.6

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

4. Applied egg-rr 20.8

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

5. Applied egg-rr 0.3

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

6. Final simplification 0.3

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

Reproduce

herbie shell --seed 2022217 
(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))