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

Percentage Accurate: 99.8% → 99.8%

Time: 5.4s

Precision: binary64

Cost: 6784

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

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (fma 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 fma(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 fma(x, Float64(3.0 * y), Float64(-z))
end

Wolfram

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

↓

code[x_, y_, z_] := N[(x * N[(3.0 * y), $MachinePrecision] + (-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. Simplified 99.9%

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

   [Start] 99.8%	\[ \left(x \cdot 3\right) \cdot y - z \]
   associate-*l* [=>] 99.9%	\[ \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]
   fma-neg [=>] 99.9%	\[ \color{blue}{\mathsf{fma}\left(x, 3 \cdot y, -z\right)} \]

3. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	99.8%
Cost	6784

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

Alternative 2
Accuracy	67.8%
Cost	850

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+92} \lor \neg \left(x \leq -5.7 \cdot 10^{+71}\right) \land \left(x \leq -5 \cdot 10^{+43} \lor \neg \left(x \leq 1.76 \cdot 10^{-140}\right)\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3
Accuracy	99.8%
Cost	448

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

Alternative 4
Accuracy	99.8%
Cost	448

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

Alternative 5
Accuracy	50.6%
Cost	128

\[-z \]

Alternative 6
Accuracy	2.3%
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023167 
(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))