Average Error: 10.3 → 9.0
Time: 9.4s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)
double f(double x, double y, double z) {
        double r440438 = x;
        double r440439 = y;
        double r440440 = z;
        double r440441 = r440439 - r440440;
        double r440442 = 1.0;
        double r440443 = r440441 + r440442;
        double r440444 = r440438 * r440443;
        double r440445 = r440444 / r440440;
        return r440445;
}
↓
double f(double x, double y, double z) {
        double r440446 = x;
        double r440447 = z;
        double r440448 = r440446 / r440447;
        double r440449 = y;
        double r440450 = r440449 - r440447;
        double r440451 = 1.0;
        double r440452 = r440450 + r440451;
        double r440453 = r440448 * r440452;
        return r440453;
}

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
Herbie9.0
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -7.269742081445241e+26

    1. Initial program 29.9

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

    3. Applied associate-/l*0.1

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

    5. Applied clear-num0.2

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

    7. Applied div-inv0.3

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

    8. Applied add-sqr-sqrt0.3

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

    9. Applied times-frac0.3

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

    10. Simplified0.3

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

    11. Simplified0.1

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

    if -7.269742081445241e+26 < x < 6.18740927030149e-72

    1. Initial program 0.3

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

    2. Taylor expanded around 0 0.1

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

    if 6.18740927030149e-72 < x

    1. Initial program 19.0

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

    3. Applied associate-/l*0.4

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

    5. Applied associate-/r/0.8

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

  4. Final simplification9.0

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

Reproduce

herbie shell --seed 2019303 
(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))