Numeric.Histogram:binBounds from Chart-1.5.3

Average Error: 6.5 → 1.7

Time: 12.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r483514 = x;
        double r483515 = y;
        double r483516 = r483515 - r483514;
        double r483517 = z;
        double r483518 = r483516 * r483517;
        double r483519 = t;
        double r483520 = r483518 / r483519;
        double r483521 = r483514 + r483520;
        return r483521;
}

↓

double f(double x, double y, double z, double t) {
        double r483522 = x;
        double r483523 = y;
        double r483524 = r483523 - r483522;
        double r483525 = t;
        double r483526 = z;
        double r483527 = r483525 / r483526;
        double r483528 = r483524 / r483527;
        double r483529 = r483522 + r483528;
        return r483529;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.5
Target	1.8
Herbie	1.7

\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Initial program 6.5

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

3. Applied associate-/l* 1.7

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

4. Final simplification 1.7

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

Reproduce

herbie shell --seed 2020043 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :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)))