Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Average Error: 0.0 → 0.0

Time: 3.2s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	24.0
Cost	1312

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-90}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+28}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	18.7
Cost	849

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+132}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+89} \lor \neg \left(y \leq -7.5 \cdot 10^{-44}\right) \land y \leq 3.1 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3
Error	12.8
Cost	848

\[\begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-91}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 10^{-62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	24.3
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-26}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Error	0.0
Cost	448

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

Alternative 6
Error	34.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023056 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))