Average Error: 10.7 → 10.9
Time: 4.7s
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 r704247 = x;
        double r704248 = y;
        double r704249 = z;
        double r704250 = r704248 * r704249;
        double r704251 = r704247 - r704250;
        double r704252 = t;
        double r704253 = a;
        double r704254 = r704253 * r704249;
        double r704255 = r704252 - r704254;
        double r704256 = r704251 / r704255;
        return r704256;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r704257 = x;
        double r704258 = y;
        double r704259 = z;
        double r704260 = r704258 * r704259;
        double r704261 = r704257 - r704260;
        double r704262 = 1.0;
        double r704263 = t;
        double r704264 = a;
        double r704265 = r704264 * r704259;
        double r704266 = r704263 - r704265;
        double r704267 = r704262 / r704266;
        double r704268 = r704261 * r704267;
        return r704268;
}

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

Original10.7
Target1.6
Herbie10.9
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.7

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

  3. Applied div-inv10.9

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

  4. Final simplification10.9

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

Reproduce

herbie shell --seed 2019322 
(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))))