Average Error: 10.5 → 10.5
Time: 4.7s
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 r775497 = x;
        double r775498 = y;
        double r775499 = z;
        double r775500 = r775498 * r775499;
        double r775501 = r775497 - r775500;
        double r775502 = t;
        double r775503 = a;
        double r775504 = r775503 * r775499;
        double r775505 = r775502 - r775504;
        double r775506 = r775501 / r775505;
        return r775506;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r775507 = x;
        double r775508 = y;
        double r775509 = z;
        double r775510 = r775508 * r775509;
        double r775511 = r775507 - r775510;
        double r775512 = t;
        double r775513 = a;
        double r775514 = r775513 * r775509;
        double r775515 = r775512 - r775514;
        double r775516 = r775511 / r775515;
        return r775516;
}

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
Target1.9
Herbie10.5
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.5

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

  2. Final simplification10.5

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(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))))