Numeric.Histogram:binBounds from Chart-1.5.3

Average Error: 6.5 → 1.8

Time: 9.7s

Precision: 64

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 r428949 = x;
        double r428950 = y;
        double r428951 = r428950 - r428949;
        double r428952 = z;
        double r428953 = r428951 * r428952;
        double r428954 = t;
        double r428955 = r428953 / r428954;
        double r428956 = r428949 + r428955;
        return r428956;
}

↓

double f(double x, double y, double z, double t) {
        double r428957 = x;
        double r428958 = y;
        double r428959 = r428958 - r428957;
        double r428960 = t;
        double r428961 = z;
        double r428962 = r428960 / r428961;
        double r428963 = r428959 / r428962;
        double r428964 = r428957 + r428963;
        return r428964;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.5
Target	1.9
Herbie	1.8

\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Initial program 6.5

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

3. Applied associate-/l* 1.8

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

4. Final simplification 1.8

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.0255111955330046e-135) (- x (* (/ z t) (- x y))) (if (< x 4.2750321637007147e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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