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

Average Error: 10.4 → 0.3

Time: 6.2s

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	10.4
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 10.4

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

2. Simplified 0.3

   \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 \cdot y\right)\right)} \]
   Proof
   (*.f64 x (*.f64 x (*.f64 3 y))): 0 points increase in error, 0 points decrease in error
   (*.f64 x (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 3) y))): 34 points increase in error, 23 points decrease in error
   (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x (*.f64 x 3)) y)): 66 points increase in error, 27 points decrease in error
   (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 x 3) x)) y): 0 points increase in error, 0 points decrease in error

3. Final simplification 0.3

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

Alternatives

Alternative 1
Error	10.4
Cost	448

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

Alternative 2
Error	0.2
Cost	448

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

Alternative 3
Error	0.2
Cost	448

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

Reproduce

herbie shell --seed 2022297 
(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))