Average Error: 6.4 → 1.9
Time: 2.7s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\left(x \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
\frac{x \cdot y}{z}
↓
\left(x \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}
double code(double x, double y, double z) {
	return ((double) (((double) (x * y)) / z));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (((double) cbrt(y)) * ((double) (((double) cbrt(y)) / ((double) (((double) cbrt(z)) * ((double) cbrt(z)))))))))) * ((double) (((double) cbrt(y)) / ((double) cbrt(z))))));
}

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

Original6.4
Target6.0
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Initial program 6.4

    \[\frac{x \cdot y}{z}\]

  2. Simplified5.9

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

  4. Applied add-cube-cbrt6.7

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

  5. Applied add-cube-cbrt6.9

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

  6. Applied times-frac6.9

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

  7. Applied associate-*r*1.9

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

  8. Simplified1.9

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

  9. Final simplification1.9

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

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

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

  (/ (* x y) z))