Average Error: 0.1 → 0.9
Time: 8.4s
Precision: binary64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\sqrt[3]{x \cdot \cos y} \cdot \left(\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\cos y}\right) + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\sqrt[3]{x \cdot \cos y} \cdot \left(\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\cos y}\right) + z \cdot \sin y
(FPCore (x y z) :precision binary64 (+ (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z)
 :precision binary64
 (+
  (* (cbrt (* x (cos y))) (* (* (cbrt (* x (cos y))) (cbrt x)) (cbrt (cos y))))
  (* z (sin 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 (cbrt(x * cos(y)) * ((cbrt(x * cos(y)) * cbrt(x)) * cbrt(cos(y)))) + (z * sin(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

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

  3. Applied add-cube-cbrt_binary64_18290.9

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

  5. Applied cbrt-prod_binary64_18250.9

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

  6. Applied associate-*r*_binary64_19170.9

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

  7. Final simplification0.9

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

Reproduce

herbie shell --seed 2020231 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))