Average Error: 10.5 → 10.6
Time: 15.3s
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 r1411624 = x;
        double r1411625 = y;
        double r1411626 = z;
        double r1411627 = r1411625 * r1411626;
        double r1411628 = r1411624 - r1411627;
        double r1411629 = t;
        double r1411630 = a;
        double r1411631 = r1411630 * r1411626;
        double r1411632 = r1411629 - r1411631;
        double r1411633 = r1411628 / r1411632;
        return r1411633;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1411634 = x;
        double r1411635 = y;
        double r1411636 = z;
        double r1411637 = r1411635 * r1411636;
        double r1411638 = r1411634 - r1411637;
        double r1411639 = 1.0;
        double r1411640 = t;
        double r1411641 = a;
        double r1411642 = r1411641 * r1411636;
        double r1411643 = r1411640 - r1411642;
        double r1411644 = r1411639 / r1411643;
        double r1411645 = r1411638 * r1411644;
        return r1411645;
}

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
Target1.8
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 2019198 
(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))))