Average Error: 6.2 → 2.0
Time: 8.7s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\left(x \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
\frac{x \cdot y}{z}
↓
\left(x \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}
double f(double x, double y, double z) {
        double r32297379 = x;
        double r32297380 = y;
        double r32297381 = r32297379 * r32297380;
        double r32297382 = z;
        double r32297383 = r32297381 / r32297382;
        return r32297383;
}
↓
double f(double x, double y, double z) {
        double r32297384 = x;
        double r32297385 = y;
        double r32297386 = cbrt(r32297385);
        double r32297387 = z;
        double r32297388 = cbrt(r32297387);
        double r32297389 = r32297386 / r32297388;
        double r32297390 = r32297389 * r32297389;
        double r32297391 = r32297384 * r32297390;
        double r32297392 = r32297391 * r32297389;
        return r32297392;
}

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

Target

Original6.2
Target6.1
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Initial program 6.2

    \[\frac{x \cdot y}{z}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity6.2

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot z}}\]

  4. Applied times-frac6.2

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{z}}\]

  5. Simplified6.2

    \[\leadsto \color{blue}{x} \cdot \frac{y}{z}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt7.0

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

  8. Applied add-cube-cbrt7.2

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

  9. Applied times-frac7.2

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

  10. Applied associate-*r*2.0

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

  11. Simplified2.0

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

  12. Final simplification2.0

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))