Average Error: 6.4 → 1.9
Time: 5.9s
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 r1752 = x;
        double r1753 = y;
        double r1754 = z;
        double r1755 = r1754 - r1752;
        double r1756 = r1753 * r1755;
        double r1757 = t;
        double r1758 = r1756 / r1757;
        double r1759 = r1752 + r1758;
        return r1759;
}
↓
double f(double x, double y, double z, double t) {
        double r1760 = z;
        double r1761 = x;
        double r1762 = r1760 - r1761;
        double r1763 = t;
        double r1764 = y;
        double r1765 = r1763 / r1764;
        double r1766 = r1762 / r1765;
        double r1767 = r1766 + r1761;
        return r1767;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.4
Target2.1
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.4

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

  3. Applied clear-num6.4

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

  5. Applied associate-/r*2.0

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

  7. Applied *-un-lft-identity2.0

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

  8. Applied *-un-lft-identity2.0

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

  9. Applied *-un-lft-identity2.0

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

  10. Applied times-frac2.0

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

  11. Applied times-frac2.0

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

  12. Applied add-cube-cbrt2.0

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

  13. Applied times-frac2.0

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

  14. Simplified2.0

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

  15. Simplified1.9

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

  16. Final simplification1.9

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

Reproduce

herbie shell --seed 2020025 
(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)))