Average Error: 10.7 → 10.7
Time: 3.5s
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 r660560 = x;
        double r660561 = y;
        double r660562 = z;
        double r660563 = r660561 * r660562;
        double r660564 = r660560 - r660563;
        double r660565 = t;
        double r660566 = a;
        double r660567 = r660566 * r660562;
        double r660568 = r660565 - r660567;
        double r660569 = r660564 / r660568;
        return r660569;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r660570 = x;
        double r660571 = y;
        double r660572 = z;
        double r660573 = r660571 * r660572;
        double r660574 = r660570 - r660573;
        double r660575 = t;
        double r660576 = a;
        double r660577 = r660576 * r660572;
        double r660578 = r660575 - r660577;
        double r660579 = r660574 / r660578;
        return r660579;
}

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

Derivation

  1. Initial program 10.7

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

  2. Final simplification10.7

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

Reproduce

herbie shell --seed 2019353 
(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))))