Average Error: 6.3 → 2.1
Time: 15.9s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\left(z - x\right) \cdot \frac{y}{t} + x\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\left(z - x\right) \cdot \frac{y}{t} + x
double f(double x, double y, double z, double t) {
        double r363662 = x;
        double r363663 = y;
        double r363664 = z;
        double r363665 = r363664 - r363662;
        double r363666 = r363663 * r363665;
        double r363667 = t;
        double r363668 = r363666 / r363667;
        double r363669 = r363662 + r363668;
        return r363669;
}
↓
double f(double x, double y, double z, double t) {
        double r363670 = z;
        double r363671 = x;
        double r363672 = r363670 - r363671;
        double r363673 = y;
        double r363674 = t;
        double r363675 = r363673 / r363674;
        double r363676 = r363672 * r363675;
        double r363677 = r363676 + r363671;
        return r363677;
}

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

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 clear-num6.3

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

  6. Simplified2.0

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

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

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

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

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

  10. Applied distribute-lft-out2.0

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

  11. Simplified2.1

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

  12. Final simplification2.1

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

Reproduce

herbie shell --seed 2019350 
(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)))