Average Error: 6.3 → 0.9
Time: 3.7s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{z - x} \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{z - x}}{{\left(\sqrt[3]{t}\right)}^{2}}\right)\right)\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{z - x} \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{z - x}}{{\left(\sqrt[3]{t}\right)}^{2}}\right)\right)\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (((double) (((double) cbrt(y)) * ((double) cbrt(y)))) * ((double) (((double) cbrt(((double) (z - x)))) * ((double) (((double) cbrt(y)) * ((double) (((double) cbrt(((double) (z - x)))) / ((double) pow(((double) cbrt(t)), 2.0)))))))))) * ((double) (((double) cbrt(((double) (z - x)))) / ((double) cbrt(t))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.3
Target2.2
Herbie0.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.3

    \[x + \frac{y \cdot \left(z - x\right)}{t}\]

  2. Simplified6.6

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

  4. Applied add-cube-cbrt7.1

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

  5. Applied add-cube-cbrt7.2

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

  6. Applied times-frac7.2

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

  7. Applied associate-*r*1.7

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

  8. Simplified1.7

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

  10. Applied add-cube-cbrt1.8

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

  11. Applied associate-*l*1.8

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

  12. Simplified0.9

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

  13. Final simplification0.9

    \[\leadsto x + \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{z - x} \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{z - x}}{{\left(\sqrt[3]{t}\right)}^{2}}\right)\right)\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (neg z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))