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

Average Accuracy: 100.0% → 100.0%

Time: 3.7s

Precision: binary64

Cost: 6720

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

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 100.0%

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

2. Simplified 100.0%

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

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

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	61.1%
Cost	652

\[\begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-77}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+104}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 2
Accuracy	84.1%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-76} \lor \neg \left(z \leq 1.65 \cdot 10^{-38}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	98.9%
Cost	585

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

Alternative 4
Accuracy	61.3%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-77}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Accuracy	100.0%
Cost	448

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

Alternative 6
Accuracy	36.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023160 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))