?

Average Error: 0.1 → 0.1
Time: 10.7s
Precision: binary64
Cost: 19520

?

\[x \cdot \cos y + z \cdot \sin y \]
↓
\[\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right) \]
(FPCore (x y z) :precision binary64 (+ (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z) :precision binary64 (fma (sin y) z (* x (cos y))))
double code(double x, double y, double z) {
	return (x * cos(y)) + (z * sin(y));
}
↓
double code(double x, double y, double z) {
	return fma(sin(y), z, (x * cos(y)));
}

function code(x, y, z)
	return Float64(Float64(x * cos(y)) + Float64(z * sin(y)))
end
↓
function code(x, y, z)
	return fma(sin(y), z, Float64(x * cos(y)))
end

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

x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right)

Error?

Derivation?

  1. Initial program 0.1

    \[x \cdot \cos y + z \cdot \sin y \]

  2. Applied egg-rr0.1

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

  3. Final simplification0.1

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

Alternatives

Alternative 1
Error0.1
Cost19520
\[\mathsf{fma}\left(x, \cos y, \sin y \cdot z\right) \]
Alternative 2
Error0.1
Cost13248
\[x \cdot \cos y + \sin y \cdot z \]
Alternative 3
Error15.9
Cost7120
\[\begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := \sin y \cdot z\\ \mathbf{if}\;y \leq -6 \cdot 10^{+249}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.0012:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00027:\\ \;\;\;\;y \cdot z + \left(x + -0.5 \cdot \left(x \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+249}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error8.6
Cost6985
\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-101} \lor \neg \left(z \leq 2.2 \cdot 10^{-83}\right):\\ \;\;\;\;x + \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
Alternative 5
Error15.6
Cost6857
\[\begin{array}{l} \mathbf{if}\;y \leq -0.00015 \lor \neg \left(y \leq 0.000195\right):\\ \;\;\;\;\sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + -0.5 \cdot \left(x \cdot \left(y \cdot y\right)\right)\right)\\ \end{array} \]
Alternative 6
Error37.5
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+83}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
Alternative 7
Error30.6
Cost320
\[x + y \cdot z \]
Alternative 8
Error38.8
Cost64
\[x \]

Error

Reproduce?

herbie shell --seed 2023027 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))