Average Error: 6.3 → 1.9
Time: 3.3s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{1}{\frac{\frac{t}{y}}{z - x}}
double f(double x, double y, double z, double t) {
        double r338534 = x;
        double r338535 = y;
        double r338536 = z;
        double r338537 = r338536 - r338534;
        double r338538 = r338535 * r338537;
        double r338539 = t;
        double r338540 = r338538 / r338539;
        double r338541 = r338534 + r338540;
        return r338541;
}
↓
double f(double x, double y, double z, double t) {
        double r338542 = x;
        double r338543 = 1.0;
        double r338544 = t;
        double r338545 = y;
        double r338546 = r338544 / r338545;
        double r338547 = z;
        double r338548 = r338547 - r338542;
        double r338549 = r338546 / r338548;
        double r338550 = r338543 / r338549;
        double r338551 = r338542 + r338550;
        return r338551;
}

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

Derivation

  1. Initial program 6.3

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

  3. Applied clear-num6.3

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

  5. Applied associate-/r*1.9

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

  6. Final simplification1.9

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

Reproduce

herbie shell --seed 2020018 
(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)))