Average Error: 11.0 → 11.0
Time: 17.9s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - y \cdot z}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - y \cdot z}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r51495278 = x;
        double r51495279 = y;
        double r51495280 = z;
        double r51495281 = r51495279 * r51495280;
        double r51495282 = r51495278 - r51495281;
        double r51495283 = t;
        double r51495284 = a;
        double r51495285 = r51495284 * r51495280;
        double r51495286 = r51495283 - r51495285;
        double r51495287 = r51495282 / r51495286;
        return r51495287;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r51495288 = x;
        double r51495289 = y;
        double r51495290 = z;
        double r51495291 = r51495289 * r51495290;
        double r51495292 = r51495288 - r51495291;
        double r51495293 = t;
        double r51495294 = a;
        double r51495295 = r51495294 * r51495290;
        double r51495296 = r51495293 - r51495295;
        double r51495297 = r51495292 / r51495296;
        return r51495297;
}

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

Original11.0
Target1.7
Herbie11.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 11.0

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

  2. Final simplification11.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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