Average Error: 1.4 → 0.8
Time: 12.8s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{y} \cdot 1} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right)\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{y} \cdot 1} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right)\right|
double code(double x, double y, double z) {
	return fabs((((x + 4.0) / y) - ((x / y) * z)));
}
↓
double code(double x, double y, double z) {
	return fabs((((x + 4.0) / y) - (((cbrt(x) * cbrt((cbrt(x) * cbrt(x)))) / (cbrt(y) * 1.0)) * ((cbrt(cbrt(x)) / cbrt(y)) * ((cbrt(x) / cbrt(y)) * 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

Derivation

  1. Initial program 1.4

    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.7

    \[\leadsto \left|\frac{x + 4}{y} - \frac{x}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}} \cdot z\right|\]

  4. Applied add-cube-cbrt1.8

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot z\right|\]

  5. Applied times-frac1.8

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)} \cdot z\right|\]

  6. Applied associate-*l*0.6

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)}\right|\]
  7. Using strategy rm

  8. Applied *-un-lft-identity0.6

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \color{blue}{\left(1 \cdot \sqrt[3]{y}\right)}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]

  9. Applied associate-*r*0.6

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\color{blue}{\left(\sqrt[3]{y} \cdot 1\right) \cdot \sqrt[3]{y}}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]

  10. Applied add-cube-cbrt0.6

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}}{\left(\sqrt[3]{y} \cdot 1\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]

  11. Applied cbrt-prod0.6

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)}}{\left(\sqrt[3]{y} \cdot 1\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]

  12. Applied associate-*r*0.6

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \sqrt[3]{\sqrt[3]{x}}}}{\left(\sqrt[3]{y} \cdot 1\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]

  13. Applied times-frac0.6

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{y} \cdot 1} \cdot \frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{y}}\right)} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]

  14. Applied associate-*l*0.8

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{y} \cdot 1} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right)}\right|\]

  15. Final simplification0.8

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{y} \cdot 1} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right)\right|\]

Reproduce

herbie shell --seed 2020066 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))