Average Error: 10.3 → 1.6
Time: 23.0s
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 r470652 = x;
        double r470653 = y;
        double r470654 = z;
        double r470655 = r470653 - r470654;
        double r470656 = 1.0;
        double r470657 = r470655 + r470656;
        double r470658 = r470652 * r470657;
        double r470659 = r470658 / r470654;
        return r470659;
}
↓
double f(double x, double y, double z) {
        double r470660 = x;
        double r470661 = z;
        double r470662 = r470660 / r470661;
        double r470663 = y;
        double r470664 = 1.0;
        double r470665 = r470663 + r470664;
        double r470666 = r470662 * r470665;
        double r470667 = r470666 - r470660;
        return r470667;
}

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
Target0.4
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Initial program 10.3

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

  2. Taylor expanded around 0 3.7

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

  3. Simplified1.6

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

  4. Final simplification1.6

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

Reproduce

herbie shell --seed 2019303 +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 -2.7148310671343599e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.87410881643954616e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

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