Average Error: 10.0 → 10.0
Time: 7.5s
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 r571675 = x;
        double r571676 = y;
        double r571677 = z;
        double r571678 = r571676 - r571677;
        double r571679 = 1.0;
        double r571680 = r571678 + r571679;
        double r571681 = r571675 * r571680;
        double r571682 = r571681 / r571677;
        return r571682;
}
↓
double f(double x, double y, double z) {
        double r571683 = x;
        double r571684 = y;
        double r571685 = z;
        double r571686 = r571684 - r571685;
        double r571687 = 1.0;
        double r571688 = r571686 + r571687;
        double r571689 = r571683 * r571688;
        double r571690 = r571689 / r571685;
        return r571690;
}

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

Original10.0
Target0.5
Herbie10.0
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -5.1532315076989797e+73

    1. Initial program 34.2

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

    3. Applied *-un-lft-identity34.2

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    7. Applied div-inv0.2

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

    if -5.1532315076989797e+73 < x < 9.872650849754673e-49

    1. Initial program 0.9

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

    2. Taylor expanded around 0 0.3

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

    if 9.872650849754673e-49 < x

    1. Initial program 20.5

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

    3. Applied *-un-lft-identity20.5

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

    4. Applied times-frac0.2

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

    5. Simplified0.2

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

  4. Final simplification10.0

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

Reproduce

herbie shell --seed 2019298 
(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))