Average Error: 10.8 → 11.0
Time: 24.0s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\left(x - z \cdot y\right) \cdot \frac{1}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\left(x - z \cdot y\right) \cdot \frac{1}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r30183005 = x;
        double r30183006 = y;
        double r30183007 = z;
        double r30183008 = r30183006 * r30183007;
        double r30183009 = r30183005 - r30183008;
        double r30183010 = t;
        double r30183011 = a;
        double r30183012 = r30183011 * r30183007;
        double r30183013 = r30183010 - r30183012;
        double r30183014 = r30183009 / r30183013;
        return r30183014;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30183015 = x;
        double r30183016 = z;
        double r30183017 = y;
        double r30183018 = r30183016 * r30183017;
        double r30183019 = r30183015 - r30183018;
        double r30183020 = 1.0;
        double r30183021 = t;
        double r30183022 = a;
        double r30183023 = r30183022 * r30183016;
        double r30183024 = r30183021 - r30183023;
        double r30183025 = r30183020 / r30183024;
        double r30183026 = r30183019 * r30183025;
        return r30183026;
}

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

Original10.8
Target1.7
Herbie11.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  3. Applied div-inv11.0

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

  4. Final simplification11.0

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

Reproduce

herbie shell --seed 2019172 +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))))