Numeric.Histogram:binBounds from Chart-1.5.3

Average Error: 6.3 → 2.0

Time: 10.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r364140 = x;
        double r364141 = y;
        double r364142 = r364141 - r364140;
        double r364143 = z;
        double r364144 = r364142 * r364143;
        double r364145 = t;
        double r364146 = r364144 / r364145;
        double r364147 = r364140 + r364146;
        return r364147;
}

↓

double f(double x, double y, double z, double t) {
        double r364148 = x;
        double r364149 = z;
        double r364150 = t;
        double r364151 = r364149 / r364150;
        double r364152 = y;
        double r364153 = r364148 - r364152;
        double r364154 = r364151 * r364153;
        double r364155 = r364148 - r364154;
        return r364155;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.3
Target	2.1
Herbie	2.0

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

Derivation

1. Initial program 6.3

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

2. Simplified 2.0

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

3. Final simplification 2.0

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

Reproduce

herbie shell --seed 2019194 
(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)))