Average Error: 6.4 → 1.9
Time: 11.9s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -4.784509795924599783439519186149299258721 \cdot 10^{-175}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 2.06509035370514777050973690805775237354 \cdot 10^{-309}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 2.556004766497536971746737596687333685074 \cdot 10^{232}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -4.784509795924599783439519186149299258721 \cdot 10^{-175}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 2.06509035370514777050973690805775237354 \cdot 10^{-309}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le 2.556004766497536971746737596687333685074 \cdot 10^{232}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r30531871 = x;
        double r30531872 = y;
        double r30531873 = r30531871 * r30531872;
        double r30531874 = z;
        double r30531875 = r30531873 / r30531874;
        return r30531875;
}
↓
double f(double x, double y, double z) {
        double r30531876 = x;
        double r30531877 = y;
        double r30531878 = r30531876 * r30531877;
        double r30531879 = -4.7845097959246e-175;
        bool r30531880 = r30531878 <= r30531879;
        double r30531881 = z;
        double r30531882 = r30531878 / r30531881;
        double r30531883 = 2.06509035370515e-309;
        bool r30531884 = r30531878 <= r30531883;
        double r30531885 = r30531881 / r30531877;
        double r30531886 = r30531876 / r30531885;
        double r30531887 = 2.556004766497537e+232;
        bool r30531888 = r30531878 <= r30531887;
        double r30531889 = r30531877 / r30531881;
        double r30531890 = r30531889 * r30531876;
        double r30531891 = r30531888 ? r30531882 : r30531890;
        double r30531892 = r30531884 ? r30531886 : r30531891;
        double r30531893 = r30531880 ? r30531882 : r30531892;
        return r30531893;
}

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

Original6.4
Target6.2
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -4.7845097959246e-175 or 2.06509035370515e-309 < (* x y) < 2.556004766497537e+232

    1. Initial program 2.4

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

    if -4.7845097959246e-175 < (* x y) < 2.06509035370515e-309

    1. Initial program 13.5

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

    3. Applied associate-/l*0.5

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

    if 2.556004766497537e+232 < (* x y)

    1. Initial program 31.8

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

    3. Applied *-un-lft-identity31.8

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -4.784509795924599783439519186149299258721 \cdot 10^{-175}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 2.06509035370514777050973690805775237354 \cdot 10^{-309}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 2.556004766497536971746737596687333685074 \cdot 10^{232}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 
(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))