Average Error: 0.1 → 0.3
Time: 20.4s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right)\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right)
double f(double x, double y, double z) {
        double r8061534 = x;
        double r8061535 = y;
        double r8061536 = sin(r8061535);
        double r8061537 = r8061534 * r8061536;
        double r8061538 = z;
        double r8061539 = cos(r8061535);
        double r8061540 = r8061538 * r8061539;
        double r8061541 = r8061537 + r8061540;
        return r8061541;
}
↓
double f(double x, double y, double z) {
        double r8061542 = x;
        double r8061543 = y;
        double r8061544 = sin(r8061543);
        double r8061545 = r8061542 * r8061544;
        double r8061546 = z;
        double r8061547 = cos(r8061543);
        double r8061548 = r8061547 * r8061547;
        double r8061549 = 0.3333333333333333;
        double r8061550 = pow(r8061548, r8061549);
        double r8061551 = r8061546 * r8061550;
        double r8061552 = cbrt(r8061547);
        double r8061553 = exp(r8061552);
        double r8061554 = log(r8061553);
        double r8061555 = r8061551 * r8061554;
        double r8061556 = r8061545 + r8061555;
        return r8061556;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.4

    \[\leadsto x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  7. Applied pow1/316.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \left(\color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}} \cdot {\left(\cos y\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  8. Applied pow-prod-down0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}\]
  9. Using strategy rm

  10. Applied add-log-exp0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \color{blue}{\log \left(e^{\sqrt[3]{\cos y}}\right)}\]

  11. Final simplification0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right)\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))