Average Error: 10.6 → 3.5
Time: 8.5s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\frac{x}{\frac{z}{\left(y - z\right) + 1}}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\frac{x}{\frac{z}{\left(y - z\right) + 1}}
double f(double x, double y, double z) {
        double r485960 = x;
        double r485961 = y;
        double r485962 = z;
        double r485963 = r485961 - r485962;
        double r485964 = 1.0;
        double r485965 = r485963 + r485964;
        double r485966 = r485960 * r485965;
        double r485967 = r485966 / r485962;
        return r485967;
}
↓
double f(double x, double y, double z) {
        double r485968 = x;
        double r485969 = z;
        double r485970 = y;
        double r485971 = r485970 - r485969;
        double r485972 = 1.0;
        double r485973 = r485971 + r485972;
        double r485974 = r485969 / r485973;
        double r485975 = r485968 / r485974;
        return r485975;
}

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

Original10.6
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 x < -2.4335967943887723e+55 or 8.931640994224886e-49 < x

    1. Initial program 26.2

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

    3. Applied associate-/l*0.1

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

    if -2.4335967943887723e+55 < x < 8.931640994224886e-49

    1. Initial program 0.5

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

    2. Taylor expanded around 0 0.2

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

  4. Final simplification3.5

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

Reproduce

herbie shell --seed 2019297 
(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))