Average Error: 10.6 → 10.6
Time: 17.8s
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 r32129220 = x;
        double r32129221 = y;
        double r32129222 = z;
        double r32129223 = r32129221 * r32129222;
        double r32129224 = r32129220 - r32129223;
        double r32129225 = t;
        double r32129226 = a;
        double r32129227 = r32129226 * r32129222;
        double r32129228 = r32129225 - r32129227;
        double r32129229 = r32129224 / r32129228;
        return r32129229;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r32129230 = x;
        double r32129231 = y;
        double r32129232 = z;
        double r32129233 = r32129231 * r32129232;
        double r32129234 = r32129230 - r32129233;
        double r32129235 = t;
        double r32129236 = a;
        double r32129237 = r32129236 * r32129232;
        double r32129238 = r32129235 - r32129237;
        double r32129239 = r32129234 / r32129238;
        return r32129239;
}

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

Original10.6
Target1.7
Herbie10.6
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.6

    \[\frac{x - y \cdot z}{t - a \cdot z}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity10.6

    \[\leadsto \frac{x - y \cdot z}{\color{blue}{1 \cdot \left(t - a \cdot z\right)}}\]

  4. Applied associate-/r*10.6

    \[\leadsto \color{blue}{\frac{\frac{x - y \cdot z}{1}}{t - a \cdot z}}\]

  5. Simplified10.6

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

  6. Final simplification10.6

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

Reproduce

herbie shell --seed 2019192 +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))))