Average Error: 0.1 → 0.4
Time: 4.2s
Precision: binary64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right)\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right)
(FPCore (x y z) :precision binary64 (+ (* x (sin y)) (* z (cos y))))
↓
(FPCore (x y z)
 :precision binary64
 (+ (* x (sin y)) (* (cbrt (cos y)) (* z (* (cbrt (cos y)) (cbrt (cos y)))))))
double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(y));
}
↓
double code(double x, double y, double z) {
	return (x * sin(y)) + (cbrt(cos(y)) * (z * (cbrt(cos(y)) * cbrt(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 0.1

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

  3. Applied add-cube-cbrt_binary640.4

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

  4. Applied associate-*r*_binary640.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2020224 
(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))))