Average Error: 0.0 → 0
Time: 5.7s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right) + \mathsf{fma}\left(-\frac{z}{\sqrt[3]{8}}, \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}, \frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right) + \mathsf{fma}\left(-\frac{z}{\sqrt[3]{8}}, \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}, \frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right)
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (x * y)) / 2.0)) - ((double) (z / 8.0))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) fma(x, ((double) (y / 2.0)), ((double) -(((double) (((double) (z / ((double) cbrt(8.0)))) * ((double) (1.0 / ((double) (((double) cbrt(8.0)) * ((double) cbrt(8.0)))))))))))) + ((double) fma(((double) -(((double) (z / ((double) cbrt(8.0)))))), ((double) (1.0 / ((double) (((double) cbrt(8.0)) * ((double) cbrt(8.0)))))), ((double) (((double) (z / ((double) cbrt(8.0)))) * ((double) (1.0 / ((double) (((double) cbrt(8.0)) * ((double) cbrt(8.0))))))))))));
}

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 0.0

    \[\frac{x \cdot y}{2} - \frac{z}{8}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto \frac{x \cdot y}{2} - \frac{z}{\color{blue}{\left(\sqrt[3]{8} \cdot \sqrt[3]{8}\right) \cdot \sqrt[3]{8}}}\]

  4. Applied *-un-lft-identity0.0

    \[\leadsto \frac{x \cdot y}{2} - \frac{\color{blue}{1 \cdot z}}{\left(\sqrt[3]{8} \cdot \sqrt[3]{8}\right) \cdot \sqrt[3]{8}}\]

  5. Applied times-frac0.0

    \[\leadsto \frac{x \cdot y}{2} - \color{blue}{\frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}} \cdot \frac{z}{\sqrt[3]{8}}}\]

  6. Applied add-sqr-sqrt27.9

    \[\leadsto \color{blue}{\sqrt{\frac{x \cdot y}{2}} \cdot \sqrt{\frac{x \cdot y}{2}}} - \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}} \cdot \frac{z}{\sqrt[3]{8}}\]

  7. Applied prod-diff27.9

    \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{x \cdot y}{2}}, \sqrt{\frac{x \cdot y}{2}}, -\frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right) + \mathsf{fma}\left(-\frac{z}{\sqrt[3]{8}}, \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}, \frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right)}\]

  8. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right)} + \mathsf{fma}\left(-\frac{z}{\sqrt[3]{8}}, \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}, \frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right)\]

  9. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right) + \mathsf{fma}\left(-\frac{z}{\sqrt[3]{8}}, \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}, \frac{z}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt[3]{8} \cdot \sqrt[3]{8}}\right)\]

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2) (/ z 8)))