Average Error: 10.3 → 1.8
Time: 14.3s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\frac{x}{z} \cdot \left(y + 1\right) - x\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\frac{x}{z} \cdot \left(y + 1\right) - x
double f(double x, double y, double z) {
        double r872331 = x;
        double r872332 = y;
        double r872333 = z;
        double r872334 = r872332 - r872333;
        double r872335 = 1.0;
        double r872336 = r872334 + r872335;
        double r872337 = r872331 * r872336;
        double r872338 = r872337 / r872333;
        return r872338;
}
↓
double f(double x, double y, double z) {
        double r872339 = x;
        double r872340 = z;
        double r872341 = r872339 / r872340;
        double r872342 = y;
        double r872343 = 1.0;
        double r872344 = r872342 + r872343;
        double r872345 = r872341 * r872344;
        double r872346 = r872345 - r872339;
        return r872346;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.3
Target0.6
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Initial program 10.3

    \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]

  2. Taylor expanded around 0 3.1

    \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x}\]

  3. Simplified1.8

    \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + 1\right) - x}\]

  4. Final simplification1.8

    \[\leadsto \frac{x}{z} \cdot \left(y + 1\right) - x\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))