Average Error: 6.0 → 2.3
Time: 4.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x + \frac{\frac{y}{a}}{\frac{1}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
x + \frac{\frac{y}{a}}{\frac{1}{z - t}}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) a)))
↓
(FPCore (x y z t a) :precision binary64 (+ x (/ (/ y a) (/ 1.0 (- z t)))))
double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / a);
}
↓
double code(double x, double y, double z, double t, double a) {
	return x + ((y / a) / (1.0 / (z - t)));
}

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

Original6.0
Target0.7
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.0

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

  3. Applied associate-/l*_binary645.5

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

  5. Applied div-inv_binary645.6

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

  6. Applied associate-/r*_binary642.3

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

  7. Final simplification2.3

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

Reproduce

herbie shell --seed 2020224 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))