Average Error: 10.5 → 0.6
Time: 8.5s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -24086198947376115712 \lor \neg \left(x \le 9.896449769877687409365259539005345521731 \cdot 10^{-188}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -24086198947376115712 \lor \neg \left(x \le 9.896449769877687409365259539005345521731 \cdot 10^{-188}\right):\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r504661 = x;
        double r504662 = y;
        double r504663 = z;
        double r504664 = r504662 - r504663;
        double r504665 = 1.0;
        double r504666 = r504664 + r504665;
        double r504667 = r504661 * r504666;
        double r504668 = r504667 / r504663;
        return r504668;
}
↓
double f(double x, double y, double z) {
        double r504669 = x;
        double r504670 = -2.4086198947376116e+19;
        bool r504671 = r504669 <= r504670;
        double r504672 = 9.896449769877687e-188;
        bool r504673 = r504669 <= r504672;
        double r504674 = !r504673;
        bool r504675 = r504671 || r504674;
        double r504676 = z;
        double r504677 = y;
        double r504678 = r504677 - r504676;
        double r504679 = 1.0;
        double r504680 = r504678 + r504679;
        double r504681 = r504676 / r504680;
        double r504682 = r504669 / r504681;
        double r504683 = r504669 * r504677;
        double r504684 = r504683 / r504676;
        double r504685 = r504669 / r504676;
        double r504686 = r504679 * r504685;
        double r504687 = r504684 + r504686;
        double r504688 = r504687 - r504669;
        double r504689 = r504675 ? r504682 : r504688;
        return r504689;
}

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
Target0.4
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -2.4086198947376116e+19 or 9.896449769877687e-188 < x

    1. Initial program 18.5

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

    3. Applied associate-/l*0.9

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

    if -2.4086198947376116e+19 < x < 9.896449769877687e-188

    1. Initial program 0.2

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

    2. Taylor expanded around 0 0.1

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -24086198947376115712 \lor \neg \left(x \le 9.896449769877687409365259539005345521731 \cdot 10^{-188}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 
(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))