Average Error: 10.3 → 3.5
Time: 3.5s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[x \cdot \frac{\left(y - z\right) + 1}{z}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
x \cdot \frac{\left(y - z\right) + 1}{z}
double f(double x, double y, double z) {
        double r470641 = x;
        double r470642 = y;
        double r470643 = z;
        double r470644 = r470642 - r470643;
        double r470645 = 1.0;
        double r470646 = r470644 + r470645;
        double r470647 = r470641 * r470646;
        double r470648 = r470647 / r470643;
        return r470648;
}
↓
double f(double x, double y, double z) {
        double r470649 = x;
        double r470650 = y;
        double r470651 = z;
        double r470652 = r470650 - r470651;
        double r470653 = 1.0;
        double r470654 = r470652 + r470653;
        double r470655 = r470654 / r470651;
        double r470656 = r470649 * r470655;
        return r470656;
}

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
Target0.5
Herbie3.5
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.83651324945672e+16 or 8797080640.399511 < z

    1. Initial program 17.5

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

    3. Applied *-un-lft-identity17.5

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if -1.83651324945672e+16 < z < 8797080640.399511

    1. Initial program 0.2

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

    3. Applied distribute-lft-in0.2

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

  4. Final simplification3.5

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

Reproduce

herbie shell --seed 1978988140 
(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))