Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3

Average Error: 0.0 → 0.0

Time: 4.3s

Precision: binary64

Cost: 6848

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

   [Start] 0.0	\[ x \cdot y + z \cdot \left(1 - y\right) \]
   fma-def [=>] 0.0	\[ \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	6720

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

Alternative 2
Error	23.4
Cost	852

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -7.7 \cdot 10^{+115}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1500000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-42}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3
Error	12.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-35} \lor \neg \left(y \leq 1.14 \cdot 10^{-41}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4
Error	0.9
Cost	585

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

Alternative 5
Error	23.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 10^{-41}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	34.4
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023060 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

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

  (+ (* x y) (* z (- 1.0 y))))