Average Error: 10.5 → 0.1
Time: 19.3s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -99364267727785690513269327921152:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \mathbf{elif}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 7.306690792946160753438066249762784977198 \cdot 10^{59}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -99364267727785690513269327921152:\\
\;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\

\mathbf{elif}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 7.306690792946160753438066249762784977198 \cdot 10^{59}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r88491006 = x;
        double r88491007 = y;
        double r88491008 = z;
        double r88491009 = r88491007 - r88491008;
        double r88491010 = 1.0;
        double r88491011 = r88491009 + r88491010;
        double r88491012 = r88491006 * r88491011;
        double r88491013 = r88491012 / r88491008;
        return r88491013;
}
↓
double f(double x, double y, double z) {
        double r88491014 = x;
        double r88491015 = y;
        double r88491016 = z;
        double r88491017 = r88491015 - r88491016;
        double r88491018 = 1.0;
        double r88491019 = r88491017 + r88491018;
        double r88491020 = r88491014 * r88491019;
        double r88491021 = r88491020 / r88491016;
        double r88491022 = -9.936426772778569e+31;
        bool r88491023 = r88491021 <= r88491022;
        double r88491024 = r88491014 / r88491016;
        double r88491025 = r88491015 + r88491018;
        double r88491026 = r88491024 * r88491025;
        double r88491027 = r88491026 - r88491014;
        double r88491028 = 7.306690792946161e+59;
        bool r88491029 = r88491021 <= r88491028;
        double r88491030 = r88491016 / r88491019;
        double r88491031 = r88491014 / r88491030;
        double r88491032 = r88491029 ? r88491031 : r88491027;
        double r88491033 = r88491023 ? r88491027 : r88491032;
        return r88491033;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (+ (- y z) 1.0)) z) < -9.936426772778569e+31 or 7.306690792946161e+59 < (/ (* x (+ (- y z) 1.0)) z)

    1. Initial program 19.8

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

    2. Taylor expanded around 0 6.8

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

    3. Simplified0.1

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

    4. Taylor expanded around 0 6.8

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

    5. Simplified0.1

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

    if -9.936426772778569e+31 < (/ (* x (+ (- y z) 1.0)) z) < 7.306690792946161e+59

    1. Initial program 0.1

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

    3. Applied associate-/l*0.2

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -99364267727785690513269327921152:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \mathbf{elif}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 7.306690792946160753438066249762784977198 \cdot 10^{59}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(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))