Average Error: 0.1 → 0.6
Time: 4.9s
Precision: binary64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\sqrt[3]{\sin y} \cdot \left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\sqrt[3]{\sin y} \cdot \left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) + z \cdot \cos y
(FPCore (x y z) :precision binary64 (+ (* x (sin y)) (* z (cos y))))
↓
(FPCore (x y z)
 :precision binary64
 (+ (* (cbrt (sin y)) (* x (* (cbrt (sin y)) (cbrt (sin y))))) (* z (cos y))))
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) sin(y)))) + ((double) (z * ((double) cos(y))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) cbrt(((double) sin(y)))) * ((double) (x * ((double) (((double) cbrt(((double) sin(y)))) * ((double) cbrt(((double) sin(y)))))))))) + ((double) (z * ((double) cos(y))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.1 bits

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrtError: 0.6 bits

    \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{\sin y}\right)} + z \cdot \cos y\]

  4. Applied associate-*r*Error: 0.6 bits

    \[\leadsto \color{blue}{\left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y}} + z \cdot \cos y\]

  5. Final simplificationError: 0.6 bits

    \[\leadsto \sqrt[3]{\sin y} \cdot \left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) + z \cdot \cos y\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))