Average Error: 10.2 → 10.2
Time: 9.1s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
double f(double x, double y, double z) {
        double r549175 = x;
        double r549176 = y;
        double r549177 = z;
        double r549178 = r549176 - r549177;
        double r549179 = 1.0;
        double r549180 = r549178 + r549179;
        double r549181 = r549175 * r549180;
        double r549182 = r549181 / r549177;
        return r549182;
}
↓
double f(double x, double y, double z) {
        double r549183 = x;
        double r549184 = y;
        double r549185 = z;
        double r549186 = r549184 - r549185;
        double r549187 = 1.0;
        double r549188 = r549186 + r549187;
        double r549189 = r549183 * r549188;
        double r549190 = r549189 / r549185;
        return r549190;
}

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

Original10.2
Target0.5
Herbie10.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -0.4122874216555284 or 2355.8937832261954 < z

    1. Initial program 17.0

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.1

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

    if -0.4122874216555284 < z < 2355.8937832261954

    1. Initial program 0.1

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.2

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

Reproduce

herbie shell --seed 2019294 
(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))