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

Average Error: 0.0 → 0.0

Time: 6.3s

Precision: binary64

Cost: 6848

Math

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

↓

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

FPCore

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

↓

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

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((1.0 - x), y, (x * z));
}

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(Float64(1.0 - x), y, Float64(x * z))
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[(N[(1.0 - x), $MachinePrecision] * y + N[(x * z), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	25.5
Cost	916

\[\begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+102}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -76.55260091418698:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.0873565926724834 \cdot 10^{-125}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.7961782705043693 \cdot 10^{-89}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 7.169444529973968 \cdot 10^{+19}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	12.0
Cost	716

\[\begin{array}{l} t_0 := y + x \cdot z\\ t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+96}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -76.55260091418698:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.169444529973968 \cdot 10^{+19}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	9.0
Cost	584

\[\begin{array}{l} t_0 := y - x \cdot y\\ \mathbf{if}\;y \leq -594893.0191040874:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.0943697288809915 \cdot 10^{+101}:\\ \;\;\;\;y + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.5
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -76.55260091418698:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.801897650124731 \cdot 10^{-28}:\\ \;\;\;\;y + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	1.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -76.55260091418698:\\ \;\;\;\;x \cdot z - x \cdot y\\ \mathbf{elif}\;x \leq 4.801897650124731 \cdot 10^{-28}:\\ \;\;\;\;y + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 6
Error	25.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -4.0873565926724834 \cdot 10^{-125}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.7961782705043693 \cdot 10^{-89}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 7
Error	0.0
Cost	448

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

Alternative 8
Error	34.7
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022300 
(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)))