Average Error: 6.3 → 0.9
Time: 8.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{1}{\frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\frac{z - x}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{1}{\frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\frac{z - x}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}}}
double code(double x, double y, double z, double t) {
	return (x + ((y * (z - x)) / t));
}
↓
double code(double x, double y, double z, double t) {
	return (x + (1.0 / (((cbrt(t) * cbrt(t)) / (cbrt(y) * cbrt(y))) / ((z - x) / (cbrt(t) / cbrt(y))))));
}

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
Target2.0
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. Using strategy rm

  3. Applied sub-neg6.3

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

  4. Applied distribute-lft-in6.3

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

  6. Applied clear-num6.4

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

  7. Simplified1.9

    \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z - x}}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt2.4

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

  10. Applied add-cube-cbrt2.5

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

  11. Applied times-frac2.5

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

  12. Applied associate-/l*0.9

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

  13. Final simplification0.9

    \[\leadsto x + \frac{1}{\frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\frac{z - x}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}}}\]

Reproduce

herbie shell --seed 2020053 
(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)) (* (- z) (/ y t))))

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