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

Average Error: 0.3 → 0.2

Time: 7.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.3
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.3

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

2. Taylor expanded in x around 0 10.4

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

3. Simplified 0.2

   \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \left(3 \cdot y\right)} \]
   Proof
   (*.f64 (*.f64 y x) (*.f64 3 y)): 0 points increase in error, 0 points decrease in error
   (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 3 y) (*.f64 y x))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= associate-*r*_binary64 (*.f64 3 (*.f64 y (*.f64 y x)))): 45 points increase in error, 30 points decrease in error
   (*.f64 3 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y y) x))): 53 points increase in error, 15 points decrease in error
   (*.f64 3 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 y 2)) x)): 0 points increase in error, 0 points decrease in error

4. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.3
Cost	448

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

Alternative 2
Error	0.2
Cost	448

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

Alternative 3
Error	0.3
Cost	448

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

Alternative 4
Error	41.3
Cost	192

\[y \cdot 0 \]

Reproduce

herbie shell --seed 2022298 
(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))