Average Error: 0.1 → 0.1
Time: 6.6s
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
Cost13248
\[\sin y \cdot z + x \cdot \cos y \]
Alternative 2
Error8.8
Cost6984
\[\begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;x \leq -0.0135:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.00082:\\ \;\;\;\;x + \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error16.3
Cost6856
\[\begin{array}{l} t_0 := \sin y \cdot z\\ \mathbf{if}\;y \leq -0.026:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0078:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error16.1
Cost6856
\[\begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;x \leq -8 \cdot 10^{-54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;\sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 5
Error37.5
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-126}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 6
Error31.1
Cost320
\[x + y \cdot z \]
Alternative 7
Error39.0
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022329 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))