Numeric.Histogram:binBounds from Chart-1.5.3

Average Error: 6.2 → 1.1

Time: 1.8m

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 2.4829011027507563 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r37968988 = x;
        double r37968989 = y;
        double r37968990 = r37968989 - r37968988;
        double r37968991 = z;
        double r37968992 = r37968990 * r37968991;
        double r37968993 = t;
        double r37968994 = r37968992 / r37968993;
        double r37968995 = r37968988 + r37968994;
        return r37968995;
}

↓

double f(double x, double y, double z, double t) {
        double r37968996 = x;
        double r37968997 = y;
        double r37968998 = r37968997 - r37968996;
        double r37968999 = z;
        double r37969000 = r37968998 * r37968999;
        double r37969001 = t;
        double r37969002 = r37969000 / r37969001;
        double r37969003 = r37968996 + r37969002;
        double r37969004 = -inf.0;
        bool r37969005 = r37969003 <= r37969004;
        double r37969006 = r37969001 / r37968998;
        double r37969007 = r37968999 / r37969006;
        double r37969008 = r37968996 + r37969007;
        double r37969009 = 2.4829011027507563e+286;
        bool r37969010 = r37969003 <= r37969009;
        double r37969011 = r37969010 ? r37969003 : r37969008;
        double r37969012 = r37969005 ? r37969008 : r37969011;
        return r37969012;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.2
Target	2.0
Herbie	1.1

\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (+ x (/ (* (- y x) z) t)) < -inf.0 or 2.4829011027507563e+286 < (+ x (/ (* (- y x) z) t))

   1. Initial program 49.9

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

   3. Applied *-commutative 49.9

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

   4. Applied associate-/l* 3.4

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

   if -inf.0 < (+ x (/ (* (- y x) z) t)) < 2.4829011027507563e+286

   1. Initial program 0.8

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

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 2.4829011027507563 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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