Average Error: 10.5 → 10.5
Time: 16.6s
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 r522602 = x;
        double r522603 = y;
        double r522604 = z;
        double r522605 = r522603 * r522604;
        double r522606 = r522602 - r522605;
        double r522607 = t;
        double r522608 = a;
        double r522609 = r522608 * r522604;
        double r522610 = r522607 - r522609;
        double r522611 = r522606 / r522610;
        return r522611;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r522612 = x;
        double r522613 = y;
        double r522614 = z;
        double r522615 = r522613 * r522614;
        double r522616 = r522612 - r522615;
        double r522617 = t;
        double r522618 = a;
        double r522619 = r522618 * r522614;
        double r522620 = r522617 - r522619;
        double r522621 = r522616 / r522620;
        return r522621;
}

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

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 2019198 +o rules:numerics
(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))))