Diagrams.Color.HSV:lerp from diagrams-contrib-1.3.0.5

Average Accuracy: 100.0% → 100.0%

Time: 4.4s

Precision: binary64

Cost: 6848

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 100.0%

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

2. Applied egg-rr 100.0%

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

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

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	6720

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

Alternative 2
Accuracy	68.3%
Cost	849

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+122}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-70} \lor \neg \left(z \leq 1.8 \cdot 10^{+23}\right) \land z \leq 4.2 \cdot 10^{+126}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3
Accuracy	62.4%
Cost	652

\[\begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-26}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-64}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{+45}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 4
Accuracy	81.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -62000 \lor \neg \left(x \leq 7.8 \cdot 10^{-64}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \end{array} \]

Alternative 5
Accuracy	98.5%
Cost	585

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

Alternative 6
Accuracy	100.0%
Cost	576

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

Alternative 7
Accuracy	62.6%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-64}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 8
Accuracy	100.0%
Cost	448

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

Alternative 9
Accuracy	44.5%
Cost	64

\[y \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

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

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