Average Error: 6.5 → 2.1
Time: 3.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\frac{z - x}{\frac{t}{y}} + x\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\frac{z - x}{\frac{t}{y}} + x
double f(double x, double y, double z, double t) {
        double r402563 = x;
        double r402564 = y;
        double r402565 = z;
        double r402566 = r402565 - r402563;
        double r402567 = r402564 * r402566;
        double r402568 = t;
        double r402569 = r402567 / r402568;
        double r402570 = r402563 + r402569;
        return r402570;
}
↓
double f(double x, double y, double z, double t) {
        double r402571 = z;
        double r402572 = x;
        double r402573 = r402571 - r402572;
        double r402574 = t;
        double r402575 = y;
        double r402576 = r402574 / r402575;
        double r402577 = r402573 / r402576;
        double r402578 = r402577 + r402572;
        return r402578;
}

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

Original6.5
Target2.2
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.5

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

  3. Applied clear-num6.5

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

  5. Applied associate-/r*2.2

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

  7. Applied *-un-lft-identity2.2

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

  8. Applied *-un-lft-identity2.2

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

  9. Applied *-un-lft-identity2.2

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

  10. Applied times-frac2.2

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

  11. Applied times-frac2.2

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

  12. Applied add-cube-cbrt2.2

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

  13. Applied times-frac2.2

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

  14. Simplified2.2

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

  15. Simplified2.1

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

  16. Final simplification2.1

    \[\leadsto \frac{z - x}{\frac{t}{y}} + x\]

Reproduce

herbie shell --seed 2020081 
(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)))