Average Error: 10.1 → 0.3
Time: 12.3s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.59946752196078414 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \frac{1 + y}{z} - x\\ \mathbf{elif}\;z \le 2.95754151107119427 \cdot 10^{32}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(\left(y - z\right) + 1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.59946752196078414 \cdot 10^{-62}:\\
\;\;\;\;x \cdot \frac{1 + y}{z} - x\\

\mathbf{elif}\;z \le 2.95754151107119427 \cdot 10^{32}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot \left(\left(y - z\right) + 1\right)}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r963036 = x;
        double r963037 = y;
        double r963038 = z;
        double r963039 = r963037 - r963038;
        double r963040 = 1.0;
        double r963041 = r963039 + r963040;
        double r963042 = r963036 * r963041;
        double r963043 = r963042 / r963038;
        return r963043;
}
↓
double f(double x, double y, double z) {
        double r963044 = z;
        double r963045 = -5.599467521960784e-62;
        bool r963046 = r963044 <= r963045;
        double r963047 = x;
        double r963048 = 1.0;
        double r963049 = y;
        double r963050 = r963048 + r963049;
        double r963051 = r963050 / r963044;
        double r963052 = r963047 * r963051;
        double r963053 = r963052 - r963047;
        double r963054 = 2.9575415110711943e+32;
        bool r963055 = r963044 <= r963054;
        double r963056 = 1.0;
        double r963057 = r963049 - r963044;
        double r963058 = r963057 + r963048;
        double r963059 = r963047 * r963058;
        double r963060 = r963044 / r963059;
        double r963061 = r963056 / r963060;
        double r963062 = r963044 / r963058;
        double r963063 = r963047 / r963062;
        double r963064 = r963055 ? r963061 : r963063;
        double r963065 = r963046 ? r963053 : r963064;
        return r963065;
}

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

Original10.1
Target0.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -5.599467521960784e-62

    1. Initial program 13.6

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

    2. Taylor expanded around 0 5.1

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

    3. Simplified2.3

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

    5. Applied div-inv2.3

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

    6. Applied associate-*l*0.4

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

    7. Simplified0.4

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

    if -5.599467521960784e-62 < z < 2.9575415110711943e+32

    1. Initial program 0.3

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

    3. Applied clear-num0.5

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

    if 2.9575415110711943e+32 < z

    1. Initial program 18.7

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

    3. Applied associate-/l*0.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.59946752196078414 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \frac{1 + y}{z} - x\\ \mathbf{elif}\;z \le 2.95754151107119427 \cdot 10^{32}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(\left(y - z\right) + 1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))