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

Percentage Accurate: 99.8% → 99.8%

Time: 6.7s

Precision: binary64

Cost: 6784

• Unsound rule application detected in e-graph. Results may not be sound.

Math

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

↓

\[\mathsf{fma}\left(y \cdot x, 3, -z\right) \]

FPCore

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

↓

(FPCore (x y z) :precision binary64 (fma (* y x) 3.0 (- 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 fma((y * x), 3.0, -z);
}

Julia

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

↓

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

Wolfram

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

↓

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

Target

Original	99.8%
Target	99.8%
Herbie	99.8%

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around 0 99.9%

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

3. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot x, 3, -z\right)} \]
   Step-by-step derivation

   [Start] 99.9%	\[ 3 \cdot \left(y \cdot x\right) - z \]
   *-commutative [=>] 99.9%	\[ \color{blue}{\left(y \cdot x\right) \cdot 3} - z \]
   fma-neg [=>] 99.9%	\[ \color{blue}{\mathsf{fma}\left(y \cdot x, 3, -z\right)} \]

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(y \cdot x, 3, -z\right) \]

Alternatives

Alternative 1
Accuracy	99.8%
Cost	6784

\[\mathsf{fma}\left(y \cdot x, 3, -z\right) \]

Alternative 2
Accuracy	70.1%
Cost	849

\[\begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+27}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-103} \lor \neg \left(z \leq -1.56 \cdot 10^{-118}\right) \land z \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 3\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3
Accuracy	99.8%
Cost	448

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

Alternative 4
Accuracy	51.2%
Cost	128

\[-z \]

Alternative 5
Accuracy	2.3%
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023272 
(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))