Average Error: 6.0 → 0.5
Time: 1.9s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -8.92420091480522906 \cdot 10^{-307}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 0.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 3.0241590046493684 \cdot 10^{292}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le -8.92420091480522906 \cdot 10^{-307}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le 0.0:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le 3.0241590046493684 \cdot 10^{292}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\end{array}
double f(double x, double y, double z) {
        double r1425223 = x;
        double r1425224 = y;
        double r1425225 = r1425223 * r1425224;
        double r1425226 = z;
        double r1425227 = r1425225 / r1425226;
        return r1425227;
}
↓
double f(double x, double y, double z) {
        double r1425228 = x;
        double r1425229 = y;
        double r1425230 = r1425228 * r1425229;
        double r1425231 = z;
        double r1425232 = r1425230 / r1425231;
        double r1425233 = -inf.0;
        bool r1425234 = r1425232 <= r1425233;
        double r1425235 = 1.0;
        double r1425236 = r1425231 / r1425228;
        double r1425237 = r1425236 / r1425229;
        double r1425238 = r1425235 / r1425237;
        double r1425239 = -8.924200914805229e-307;
        bool r1425240 = r1425232 <= r1425239;
        double r1425241 = 0.0;
        bool r1425242 = r1425232 <= r1425241;
        double r1425243 = r1425231 / r1425229;
        double r1425244 = r1425228 / r1425243;
        double r1425245 = 3.0241590046493684e+292;
        bool r1425246 = r1425232 <= r1425245;
        double r1425247 = r1425229 / r1425231;
        double r1425248 = r1425228 * r1425247;
        double r1425249 = r1425246 ? r1425232 : r1425248;
        double r1425250 = r1425242 ? r1425244 : r1425249;
        double r1425251 = r1425240 ? r1425232 : r1425250;
        double r1425252 = r1425234 ? r1425238 : r1425251;
        return r1425252;
}

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

Original6.0
Target6.1
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (/ (* x y) z) < -inf.0

    1. Initial program 64.0

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied clear-num64.0

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
    4. Using strategy rm

    5. Applied associate-/r*0.3

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

    if -inf.0 < (/ (* x y) z) < -8.924200914805229e-307 or 0.0 < (/ (* x y) z) < 3.0241590046493684e+292

    1. Initial program 0.5

      \[\frac{x \cdot y}{z}\]

    if -8.924200914805229e-307 < (/ (* x y) z) < 0.0

    1. Initial program 10.7

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.4

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]

    if 3.0241590046493684e+292 < (/ (* x y) z)

    1. Initial program 53.3

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity53.3

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

    4. Applied times-frac3.1

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

    5. Simplified3.1

      \[\leadsto \color{blue}{x} \cdot \frac{y}{z}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -8.92420091480522906 \cdot 10^{-307}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 0.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 3.0241590046493684 \cdot 10^{292}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))