Average Error: 10.5 → 10.6
Time: 3.5s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r794188 = x;
        double r794189 = y;
        double r794190 = z;
        double r794191 = r794189 * r794190;
        double r794192 = r794188 - r794191;
        double r794193 = t;
        double r794194 = a;
        double r794195 = r794194 * r794190;
        double r794196 = r794193 - r794195;
        double r794197 = r794192 / r794196;
        return r794197;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r794198 = x;
        double r794199 = y;
        double r794200 = z;
        double r794201 = r794199 * r794200;
        double r794202 = r794198 - r794201;
        double r794203 = 1.0;
        double r794204 = t;
        double r794205 = a;
        double r794206 = r794205 * r794200;
        double r794207 = r794204 - r794206;
        double r794208 = r794203 / r794207;
        double r794209 = r794202 * r794208;
        return r794209;
}

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

Original10.5
Target1.9
Herbie10.6
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.5

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

  3. Applied div-inv10.6

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

  4. Final simplification10.6

    \[\leadsto \left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\]

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(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 3.5139522372978296e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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