Average Error: 6.4 → 2.5
Time: 7.4s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x + \frac{y}{a} \cdot \left(t - z\right)\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
x + \frac{y}{a} \cdot \left(t - z\right)
double code(double x, double y, double z, double t, double a) {
	return ((double) (x - ((double) (((double) (y * ((double) (z - t)))) / a))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y / a)) * ((double) (t - z))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.4
Target0.7
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.4

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

  3. Applied sub-neg6.4

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

  4. Applied distribute-lft-in6.4

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

  6. Applied sub-neg6.4

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

  7. Simplified2.5

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

  8. Final simplification2.5

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

Reproduce

herbie shell --seed 2020168 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))