Average Error: 0.1 → 0.3
Time: 8.7s
Precision: binary64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \sqrt[3]{{\cos y}^{2}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \sqrt[3]{{\cos y}^{2}}\right) \cdot \sqrt[3]{\cos y}
(FPCore (x y z) :precision binary64 (+ (* x (sin y)) (* z (cos y))))
↓
(FPCore (x y z)
 :precision binary64
 (+ (* x (sin y)) (* (* z (cbrt (pow (cos y) 2.0))) (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)) + ((z * cbrt(pow(cos(y), 2.0))) * 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_binary64_5450.4

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

  4. Applied associate-*r*_binary64_6330.4

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

  6. Applied add-cbrt-cube_binary64_5460.4

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

  7. Simplified0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{\color{blue}{{\cos y}^{2}}}\right) \cdot \sqrt[3]{\cos y}\]

  8. Final simplification0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{{\cos y}^{2}}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2020231 
(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))))