Average Error: 10.7 → 10.7
Time: 3.4s
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 r630551 = x;
        double r630552 = y;
        double r630553 = z;
        double r630554 = r630552 * r630553;
        double r630555 = r630551 - r630554;
        double r630556 = t;
        double r630557 = a;
        double r630558 = r630557 * r630553;
        double r630559 = r630556 - r630558;
        double r630560 = r630555 / r630559;
        return r630560;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r630561 = x;
        double r630562 = y;
        double r630563 = z;
        double r630564 = r630562 * r630563;
        double r630565 = r630561 - r630564;
        double r630566 = t;
        double r630567 = a;
        double r630568 = r630567 * r630563;
        double r630569 = r630566 - r630568;
        double r630570 = r630565 / r630569;
        return r630570;
}

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
Target1.8
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.7

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

  2. Final simplification10.7

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

Reproduce

herbie shell --seed 2020064 
(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))))