Average Error: 10.5 → 0.2
Time: 11.3s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.001862668948682683719019062200331892161 \cdot 10^{54}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 1900831.650325161404907703399658203125:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.001862668948682683719019062200331892161 \cdot 10^{54}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;z \le 1900831.650325161404907703399658203125:\\
\;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r30392320 = x;
        double r30392321 = y;
        double r30392322 = z;
        double r30392323 = r30392321 - r30392322;
        double r30392324 = 1.0;
        double r30392325 = r30392323 + r30392324;
        double r30392326 = r30392320 * r30392325;
        double r30392327 = r30392326 / r30392322;
        return r30392327;
}
↓
double f(double x, double y, double z) {
        double r30392328 = z;
        double r30392329 = -2.0018626689486827e+54;
        bool r30392330 = r30392328 <= r30392329;
        double r30392331 = x;
        double r30392332 = y;
        double r30392333 = r30392332 - r30392328;
        double r30392334 = 1.0;
        double r30392335 = r30392333 + r30392334;
        double r30392336 = r30392328 / r30392335;
        double r30392337 = r30392331 / r30392336;
        double r30392338 = 1900831.6503251614;
        bool r30392339 = r30392328 <= r30392338;
        double r30392340 = r30392331 * r30392335;
        double r30392341 = r30392340 / r30392328;
        double r30392342 = r30392339 ? r30392341 : r30392337;
        double r30392343 = r30392330 ? r30392337 : r30392342;
        return r30392343;
}

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

Original10.5
Target0.5
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 < -2.0018626689486827e+54 or 1900831.6503251614 < z

    1. Initial program 18.4

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

    3. Applied associate-/l*0.1

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

    if -2.0018626689486827e+54 < z < 1900831.6503251614

    1. Initial program 0.5

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.001862668948682683719019062200331892161 \cdot 10^{54}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 1900831.650325161404907703399658203125:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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))