Average Error: 10.8 → 11.2
Time: 12.7s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{1}{\frac{t - a \cdot z}{x - y \cdot z}}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{1}{\frac{t - a \cdot z}{x - y \cdot z}}
double f(double x, double y, double z, double t, double a) {
        double r491548 = x;
        double r491549 = y;
        double r491550 = z;
        double r491551 = r491549 * r491550;
        double r491552 = r491548 - r491551;
        double r491553 = t;
        double r491554 = a;
        double r491555 = r491554 * r491550;
        double r491556 = r491553 - r491555;
        double r491557 = r491552 / r491556;
        return r491557;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r491558 = 1.0;
        double r491559 = t;
        double r491560 = a;
        double r491561 = z;
        double r491562 = r491560 * r491561;
        double r491563 = r491559 - r491562;
        double r491564 = x;
        double r491565 = y;
        double r491566 = r491565 * r491561;
        double r491567 = r491564 - r491566;
        double r491568 = r491563 / r491567;
        double r491569 = r491558 / r491568;
        return r491569;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.8
Target1.8
Herbie11.2
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  3. Applied clear-num11.2

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

  4. Final simplification11.2

    \[\leadsto \frac{1}{\frac{t - a \cdot z}{x - y \cdot z}}\]

Reproduce

herbie shell --seed 2019209 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.51395223729782958e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))