Average Error: 10.7 → 0.2
Time: 9.9s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -115950917863283103134100794376192:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 1.699875720445952633498395020587009021763 \cdot 10^{46}:\\ \;\;\;\;\left(\frac{x}{z} \cdot 1 + \frac{x \cdot y}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -115950917863283103134100794376192:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;z \le 1.699875720445952633498395020587009021763 \cdot 10^{46}:\\
\;\;\;\;\left(\frac{x}{z} \cdot 1 + \frac{x \cdot y}{z}\right) - x\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\end{array}
double f(double x, double y, double z) {
        double r40340294 = x;
        double r40340295 = y;
        double r40340296 = z;
        double r40340297 = r40340295 - r40340296;
        double r40340298 = 1.0;
        double r40340299 = r40340297 + r40340298;
        double r40340300 = r40340294 * r40340299;
        double r40340301 = r40340300 / r40340296;
        return r40340301;
}
↓
double f(double x, double y, double z) {
        double r40340302 = z;
        double r40340303 = -1.159509178632831e+32;
        bool r40340304 = r40340302 <= r40340303;
        double r40340305 = x;
        double r40340306 = y;
        double r40340307 = r40340306 - r40340302;
        double r40340308 = 1.0;
        double r40340309 = r40340307 + r40340308;
        double r40340310 = r40340302 / r40340309;
        double r40340311 = r40340305 / r40340310;
        double r40340312 = 1.6998757204459526e+46;
        bool r40340313 = r40340302 <= r40340312;
        double r40340314 = r40340305 / r40340302;
        double r40340315 = r40340314 * r40340308;
        double r40340316 = r40340305 * r40340306;
        double r40340317 = r40340316 / r40340302;
        double r40340318 = r40340315 + r40340317;
        double r40340319 = r40340318 - r40340305;
        double r40340320 = r40340313 ? r40340319 : r40340311;
        double r40340321 = r40340304 ? r40340311 : r40340320;
        return r40340321;
}

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

Original10.7
Target0.4
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.159509178632831e+32 or 1.6998757204459526e+46 < z

    1. Initial program 19.3

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

    3. Applied associate-/l*0.1

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

    if -1.159509178632831e+32 < z < 1.6998757204459526e+46

    1. Initial program 0.6

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

    2. Taylor expanded around 0 0.4

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -115950917863283103134100794376192:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 1.699875720445952633498395020587009021763 \cdot 10^{46}:\\ \;\;\;\;\left(\frac{x}{z} \cdot 1 + \frac{x \cdot y}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))