Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Average Accuracy: 99.8% → 99.7%

Time: 4.0s

Precision: binary64

Cost: 448

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (3.0d0 * y)) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

↓

public static double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	99.8%
Target	99.7%
Herbie	99.7%

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

Derivation

1. Initial program 99.8%

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

2. Simplified 99.7%

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

   [Start] 99.8	\[ \left(x \cdot 3\right) \cdot y - z \]
   associate-*l* [=>] 99.7	\[ \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

3. Final simplification 99.7%

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

Alternatives

Alternative 1
Accuracy	74.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -2350000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-25}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 2
Accuracy	74.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -17500000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3
Accuracy	74.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -900000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4
Accuracy	99.8%
Cost	448

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

Alternative 5
Accuracy	58.5%
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2023129 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))