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

Average Error: 10.5 → 0.3

Time: 4.1s

Precision: binary64

Cost: 13376

Math

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

↓

\[\frac{3 \cdot \left(y \cdot \left|x\right|\right)}{\frac{1}{\left|x\right|}} \]

FPCore

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

↓

(FPCore (x y) :precision binary64 (/ (* 3.0 (* y (fabs x))) (/ 1.0 (fabs x))))

C

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

↓

double code(double x, double y) {
	return (3.0 * (y * fabs(x))) / (1.0 / fabs(x));
}

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 * (y * abs(x))) / (1.0d0 / abs(x))
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 * (y * Math.abs(x))) / (1.0 / Math.abs(x));
}

Python

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

↓

def code(x, y):
	return (3.0 * (y * math.fabs(x))) / (1.0 / math.fabs(x))

Julia

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

↓

function code(x, y)
	return Float64(Float64(3.0 * Float64(y * abs(x))) / Float64(1.0 / abs(x)))
end

MATLAB

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

↓

function tmp = code(x, y)
	tmp = (3.0 * (y * abs(x))) / (1.0 / abs(x));
end

Wolfram

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

↓

code[x_, y_] := N[(N[(3.0 * N[(y * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	10.5
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 10.5

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

2. Simplified 10.4

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

   [Start] 10.5	\[ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
   rational.json-simplify-2 [=>] 10.5	\[ \color{blue}{y \cdot \left(\left(x \cdot 3\right) \cdot x\right)} \]
   rational.json-simplify-2 [=>] 10.5	\[ y \cdot \color{blue}{\left(x \cdot \left(x \cdot 3\right)\right)} \]
   rational.json-simplify-43 [<=] 10.5	\[ y \cdot \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right)} \]
   rational.json-simplify-43 [=>] 10.4	\[ \color{blue}{3 \cdot \left(\left(x \cdot x\right) \cdot y\right)} \]

3. Applied egg-rr 0.3

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

4. Final simplification 0.3

   \[\leadsto \frac{3 \cdot \left(y \cdot \left|x\right|\right)}{\frac{1}{\left|x\right|}} \]

Alternatives

Alternative 1
Error	10.4
Cost	448

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

Alternative 2
Error	0.3
Cost	448

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

Reproduce

herbie shell --seed 2023064 
(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))