Average Error: 6.0 → 5.9
Time: 5.1s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[x \cdot \frac{y}{z}\]
\frac{x \cdot y}{z}
↓
x \cdot \frac{y}{z}
double f(double x, double y, double z) {
        double r447064 = x;
        double r447065 = y;
        double r447066 = r447064 * r447065;
        double r447067 = z;
        double r447068 = r447066 / r447067;
        return r447068;
}
↓
double f(double x, double y, double z) {
        double r447069 = x;
        double r447070 = y;
        double r447071 = z;
        double r447072 = r447070 / r447071;
        double r447073 = r447069 * r447072;
        return r447073;
}

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
Target5.8
Herbie5.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -7.814875792411794e-205 or 2.3509053306716985e-193 < (* x y) < 1.376680785759135e+84

    1. Initial program 2.7

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

    3. Applied *-un-lft-identity2.7

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

    4. Applied times-frac8.5

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

    5. Simplified8.5

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

    7. Applied associate-*r/2.7

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

    if -7.814875792411794e-205 < (* x y) < 2.3509053306716985e-193

    1. Initial program 9.8

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

    3. Applied *-un-lft-identity9.8

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    if 1.376680785759135e+84 < (* x y)

    1. Initial program 12.8

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

    3. Applied associate-/l*5.2

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

    5. Applied associate-/r/4.5

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

  4. Final simplification5.9

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

Reproduce

herbie shell --seed 2019291 
(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 1.70421306606504721e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))