Average Error: 0.1 → 0.6
Time: 4.5s
Precision: binary64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\sqrt[3]{x \cdot \sin y} \cdot \left(\sqrt[3]{x} \cdot \left(\sqrt[3]{x \cdot \sin y} \cdot \sqrt[3]{\sin y}\right)\right) + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\sqrt[3]{x \cdot \sin y} \cdot \left(\sqrt[3]{x} \cdot \left(\sqrt[3]{x \cdot \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 (* x (sin y))) (* (cbrt x) (* (cbrt (* x (sin y))) (cbrt (sin y)))))
  (* z (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 (cbrt(x * sin(y)) * (cbrt(x) * (cbrt(x * sin(y)) * cbrt(sin(y))))) + (z * 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_binary640.6

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

  5. Applied cbrt-prod_binary640.6

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

  6. Applied associate-*l*_binary640.6

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

  7. Simplified0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2020232 
(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))))