Average Error: 6.7 → 0.9
Time: 10.3s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\frac{z - x}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\frac{z - x}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}
double f(double x, double y, double z, double t) {
        double r401463 = x;
        double r401464 = y;
        double r401465 = z;
        double r401466 = r401465 - r401463;
        double r401467 = r401464 * r401466;
        double r401468 = t;
        double r401469 = r401467 / r401468;
        double r401470 = r401463 + r401469;
        return r401470;
}
↓
double f(double x, double y, double z, double t) {
        double r401471 = x;
        double r401472 = z;
        double r401473 = r401472 - r401471;
        double r401474 = t;
        double r401475 = cbrt(r401474);
        double r401476 = r401475 * r401475;
        double r401477 = y;
        double r401478 = cbrt(r401477);
        double r401479 = r401478 * r401478;
        double r401480 = r401476 / r401479;
        double r401481 = r401473 / r401480;
        double r401482 = r401475 / r401478;
        double r401483 = r401481 / r401482;
        double r401484 = r401471 + r401483;
        return r401484;
}

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

Original6.7
Target2.0
Herbie0.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.7

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

  3. Applied *-un-lft-identity6.7

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

  4. Applied *-un-lft-identity6.7

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

  5. Applied distribute-lft-out6.7

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

  6. Simplified1.9

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

  8. Applied add-cube-cbrt2.4

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

  9. Applied add-cube-cbrt2.6

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

  10. Applied times-frac2.6

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

  11. Applied associate-/r*0.9

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

  12. Final simplification0.9

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

Reproduce

herbie shell --seed 2020047 
(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)))