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

Average Error: 0.3 → 0.2

Time: 6.8s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

↓

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

Python

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

↓

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

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(3.0 * y))
end

MATLAB

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

↓

function tmp = code(x, y)
	tmp = (y * x) * (3.0 * y);
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[(3.0 * y), $MachinePrecision]), $MachinePrecision]

Target

Original	0.3
Target	0.3
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. Simplified 10.5

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

   [Start] 0.3	\[ \left(\left(x \cdot 3\right) \cdot y\right) \cdot y \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.3	\[ \color{blue}{y \cdot \left(\left(x \cdot 3\right) \cdot y\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.3	\[ y \cdot \color{blue}{\left(y \cdot \left(x \cdot 3\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.3	\[ y \cdot \color{blue}{\left(x \cdot \left(y \cdot 3\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 10.5	\[ \color{blue}{x \cdot \left(y \cdot \left(y \cdot 3\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 10.5	\[ x \cdot \left(y \cdot \color{blue}{\left(3 \cdot y\right)}\right) \]

3. Applied egg-rr 10.5

   \[\leadsto \color{blue}{0 - x \cdot \left(y \cdot \left(y \cdot -3\right)\right)} \]

4. Simplified 0.2

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

   [Start] 10.5	\[ 0 - x \cdot \left(y \cdot \left(y \cdot -3\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.3	\[ 0 - \color{blue}{y \cdot \left(x \cdot \left(y \cdot -3\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-38 [<=] 0.3	\[ \color{blue}{\left(x \cdot y\right) \cdot 0} - y \cdot \left(x \cdot \left(y \cdot -3\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-74 [<=] 0.3	\[ \color{blue}{0 \cdot \left(x \cdot y\right)} - y \cdot \left(x \cdot \left(y \cdot -3\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.3	\[ 0 \cdot \left(x \cdot y\right) - y \cdot \color{blue}{\left(\left(y \cdot -3\right) \cdot x\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.2	\[ 0 \cdot \left(x \cdot y\right) - \color{blue}{\left(y \cdot -3\right) \cdot \left(y \cdot x\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [<=] 0.2	\[ 0 \cdot \left(x \cdot y\right) - \left(y \cdot -3\right) \cdot \color{blue}{\left(x \cdot y\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [<=] 0.2	\[ 0 \cdot \left(x \cdot y\right) - \color{blue}{\left(x \cdot y\right) \cdot \left(y \cdot -3\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-13 [<=] 0.2	\[ \color{blue}{\left(x \cdot y\right) \cdot \left(0 - y \cdot -3\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.2	\[ \color{blue}{\left(y \cdot x\right)} \cdot \left(0 - y \cdot -3\right) \]
   rational_best_oopsla_all_46_json_45_simplify-5 [=>] 0.2	\[ \left(y \cdot x\right) \cdot \color{blue}{\left(-y \cdot -3\right)} \]

5. Applied egg-rr 0.2

   \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \left(y \cdot 3\right) + 0} \]

6. Simplified 0.2

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

   [Start] 0.2	\[ \left(y \cdot x\right) \cdot \left(y \cdot 3\right) + 0 \]
   rational_best_oopsla_all_46_json_45_simplify-85 [=>] 0.2	\[ \color{blue}{\left(y \cdot x\right) \cdot \left(y \cdot 3\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.2	\[ \left(y \cdot x\right) \cdot \color{blue}{\left(3 \cdot y\right)} \]

7. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.3
Cost	448

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

Alternative 2
Error	0.3
Cost	448

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

Reproduce

herbie shell --seed 2023090 
(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))