Average Error: 0.1 → 0.2
Time: 20.2s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) + z \cdot \sin y
double f(double x, double y, double z) {
        double r7908384 = x;
        double r7908385 = y;
        double r7908386 = cos(r7908385);
        double r7908387 = r7908384 * r7908386;
        double r7908388 = z;
        double r7908389 = sin(r7908385);
        double r7908390 = r7908388 * r7908389;
        double r7908391 = r7908387 + r7908390;
        return r7908391;
}
↓
double f(double x, double y, double z) {
        double r7908392 = y;
        double r7908393 = cos(r7908392);
        double r7908394 = cbrt(r7908393);
        double r7908395 = r7908393 * r7908393;
        double r7908396 = 0.3333333333333333;
        double r7908397 = pow(r7908395, r7908396);
        double r7908398 = x;
        double r7908399 = r7908397 * r7908398;
        double r7908400 = r7908394 * r7908399;
        double r7908401 = z;
        double r7908402 = sin(r7908392);
        double r7908403 = r7908401 * r7908402;
        double r7908404 = r7908400 + r7908403;
        return r7908404;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.4

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

  7. Applied pow1/316.3

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

  8. Applied pow-prod-down0.2

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

  9. Final simplification0.2

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

Reproduce

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