Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H

Average Accuracy: 100.0% → 100.0%

Time: 5.9s

Precision: binary64

Cost: 6976

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

Math

\[\left(x + y\right) \cdot \left(1 - z\right) \]

↓

\[\mathsf{fma}\left(1 - z, y, \left(1 - z\right) \cdot x\right) \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

↓

(FPCore (x y z) :precision binary64 (fma (- 1.0 z) y (* (- 1.0 z) x)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

↓

double code(double x, double y, double z) {
	return fma((1.0 - z), y, ((1.0 - z) * x));
}

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

↓

function code(x, y, z)
	return fma(Float64(1.0 - z), y, Float64(Float64(1.0 - z) * x))
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * y + N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]

2. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 - z, y, \left(1 - z\right) \cdot x\right)} \]
   Proof

   [Start] 100.0	\[ \left(x + y\right) \cdot \left(1 - z\right) \]
   *-commutative [=>] 100.0	\[ \color{blue}{\left(1 - z\right) \cdot \left(x + y\right)} \]
   +-commutative [=>] 100.0	\[ \left(1 - z\right) \cdot \color{blue}{\left(y + x\right)} \]
   distribute-lft-in [=>] 100.0	\[ \color{blue}{\left(1 - z\right) \cdot y + \left(1 - z\right) \cdot x} \]
   fma-def [=>] 100.0	\[ \color{blue}{\mathsf{fma}\left(1 - z, y, \left(1 - z\right) \cdot x\right)} \]

3. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(1 - z, y, \left(1 - z\right) \cdot x\right) \]

Alternatives

Alternative 1
Accuracy	80.2%
Cost	1881

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;1 - z \leq -1 \cdot 10^{+219}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+189}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;1 - z \leq -500000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+163} \lor \neg \left(1 - z \leq 2 \cdot 10^{+200}\right):\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Accuracy	80.0%
Cost	785

\[\begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -8:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+187} \lor \neg \left(z \leq 1.08 \cdot 10^{+215}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	100.0%
Cost	704

\[\left(1 - z\right) \cdot x + \left(1 - z\right) \cdot y \]

Alternative 4
Accuracy	97.3%
Cost	649

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5
Accuracy	79.3%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -2800000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6
Accuracy	51.2%
Cost	460

\[\begin{array}{l} \mathbf{if}\;y \leq 1.32 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 25000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Accuracy	80.6%
Cost	452

\[\begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-103}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \end{array} \]

Alternative 8
Accuracy	100.0%
Cost	448

\[\left(1 - z\right) \cdot \left(y + x\right) \]

Alternative 9
Accuracy	62.7%
Cost	192

\[y + x \]

Alternative 10
Accuracy	31.6%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023151 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))