Average Error: 6.0 → 0.4
Time: 10.4s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -2.166521247594354925726439343625696917212 \cdot 10^{205}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.343713460892298755823259752013121029537 \cdot 10^{-191}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 4.152478566064296352109998791440075706057 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 9.404611212472955651642851083785275703569 \cdot 10^{253}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -2.166521247594354925726439343625696917212 \cdot 10^{205}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -1.343713460892298755823259752013121029537 \cdot 10^{-191}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 4.152478566064296352109998791440075706057 \cdot 10^{-204}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;x \cdot y \le 9.404611212472955651642851083785275703569 \cdot 10^{253}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r29340131 = x;
        double r29340132 = y;
        double r29340133 = r29340131 * r29340132;
        double r29340134 = z;
        double r29340135 = r29340133 / r29340134;
        return r29340135;
}
↓
double f(double x, double y, double z) {
        double r29340136 = x;
        double r29340137 = y;
        double r29340138 = r29340136 * r29340137;
        double r29340139 = -2.166521247594355e+205;
        bool r29340140 = r29340138 <= r29340139;
        double r29340141 = z;
        double r29340142 = r29340141 / r29340137;
        double r29340143 = r29340136 / r29340142;
        double r29340144 = -1.3437134608922988e-191;
        bool r29340145 = r29340138 <= r29340144;
        double r29340146 = r29340138 / r29340141;
        double r29340147 = 4.152478566064296e-204;
        bool r29340148 = r29340138 <= r29340147;
        double r29340149 = r29340137 / r29340141;
        double r29340150 = r29340149 * r29340136;
        double r29340151 = 9.404611212472956e+253;
        bool r29340152 = r29340138 <= r29340151;
        double r29340153 = r29340152 ? r29340146 : r29340150;
        double r29340154 = r29340148 ? r29340150 : r29340153;
        double r29340155 = r29340145 ? r29340146 : r29340154;
        double r29340156 = r29340140 ? r29340143 : r29340155;
        return r29340156;
}

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
Target6.2
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -2.166521247594355e+205

    1. Initial program 27.2

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

    3. Applied associate-/l*1.5

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

    if -2.166521247594355e+205 < (* x y) < -1.3437134608922988e-191 or 4.152478566064296e-204 < (* x y) < 9.404611212472956e+253

    1. Initial program 0.2

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

    if -1.3437134608922988e-191 < (* x y) < 4.152478566064296e-204 or 9.404611212472956e+253 < (* x y)

    1. Initial program 13.8

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

    3. Applied *-un-lft-identity13.8

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

    4. Applied times-frac0.5

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

    5. Simplified0.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -2.166521247594354925726439343625696917212 \cdot 10^{205}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.343713460892298755823259752013121029537 \cdot 10^{-191}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 4.152478566064296352109998791440075706057 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 9.404611212472955651642851083785275703569 \cdot 10^{253}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"

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

  (/ (* x y) z))