Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Average Error: 6.7 → 0.8

Time: 11.4s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 3.055507619344911093835800045301061034504 \cdot 10^{304}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r276961 = x;
        double r276962 = y;
        double r276963 = z;
        double r276964 = r276963 - r276961;
        double r276965 = r276962 * r276964;
        double r276966 = t;
        double r276967 = r276965 / r276966;
        double r276968 = r276961 + r276967;
        return r276968;
}

↓

double f(double x, double y, double z, double t) {
        double r276969 = x;
        double r276970 = y;
        double r276971 = z;
        double r276972 = r276971 - r276969;
        double r276973 = r276970 * r276972;
        double r276974 = t;
        double r276975 = r276973 / r276974;
        double r276976 = r276969 + r276975;
        double r276977 = -inf.0;
        bool r276978 = r276976 <= r276977;
        double r276979 = 3.055507619344911e+304;
        bool r276980 = r276976 <= r276979;
        double r276981 = !r276980;
        bool r276982 = r276978 || r276981;
        double r276983 = r276974 / r276972;
        double r276984 = r276970 / r276983;
        double r276985 = r276969 + r276984;
        double r276986 = r276982 ? r276985 : r276976;
        return r276986;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.7
Target	2.0
Herbie	0.8

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

Derivation

1. Split input into 2 regimes

2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 3.055507619344911e+304 < (+ x (/ (* y (- z x)) t))

   1. Initial program 62.1

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

   3. Applied associate-/l* 0.9

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

   if -inf.0 < (+ x (/ (* y (- z x)) t)) < 3.055507619344911e+304

   1. Initial program 0.8

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 3.055507619344911093835800045301061034504 \cdot 10^{304}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(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)))