Average Error: 0.1 → 0.4
Time: 6.2s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r157376 = x;
        double r157377 = y;
        double r157378 = cos(r157377);
        double r157379 = r157376 + r157378;
        double r157380 = z;
        double r157381 = sin(r157377);
        double r157382 = r157380 * r157381;
        double r157383 = r157379 - r157382;
        return r157383;
}
↓
double f(double x, double y, double z) {
        double r157384 = x;
        double r157385 = y;
        double r157386 = cos(r157385);
        double r157387 = r157384 + r157386;
        double r157388 = z;
        double r157389 = cbrt(r157388);
        double r157390 = r157389 * r157389;
        double r157391 = cbrt(r157390);
        double r157392 = r157389 * r157391;
        double r157393 = cbrt(r157389);
        double r157394 = r157392 * r157393;
        double r157395 = sin(r157385);
        double r157396 = r157389 * r157395;
        double r157397 = r157394 * r157396;
        double r157398 = r157387 - r157397;
        return r157398;
}

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

    \[\left(x + \cos y\right) - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*l*0.4

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

  6. Applied add-cube-cbrt0.4

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

  7. Applied cbrt-prod0.4

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

  8. Applied associate-*r*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))