Average Error: 10.2 → 3.2
Time: 20.9s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{1}{\frac{t - a \cdot z}{x}} - \frac{y}{\frac{t}{z} - a}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{1}{\frac{t - a \cdot z}{x}} - \frac{y}{\frac{t}{z} - a}
double f(double x, double y, double z, double t, double a) {
        double r510943 = x;
        double r510944 = y;
        double r510945 = z;
        double r510946 = r510944 * r510945;
        double r510947 = r510943 - r510946;
        double r510948 = t;
        double r510949 = a;
        double r510950 = r510949 * r510945;
        double r510951 = r510948 - r510950;
        double r510952 = r510947 / r510951;
        return r510952;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r510953 = 1.0;
        double r510954 = t;
        double r510955 = a;
        double r510956 = z;
        double r510957 = r510955 * r510956;
        double r510958 = r510954 - r510957;
        double r510959 = x;
        double r510960 = r510958 / r510959;
        double r510961 = r510953 / r510960;
        double r510962 = y;
        double r510963 = r510954 / r510956;
        double r510964 = r510963 - r510955;
        double r510965 = r510962 / r510964;
        double r510966 = r510961 - r510965;
        return r510966;
}

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

Original10.2
Target1.8
Herbie3.2
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.2

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

  3. Applied div-sub10.2

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

  4. Simplified7.8

    \[\leadsto \frac{x}{t - a \cdot z} - \color{blue}{y \cdot \frac{z}{t - a \cdot z}}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity7.8

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

  7. Applied associate-*l*7.8

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

  8. Simplified2.9

    \[\leadsto \frac{x}{t - a \cdot z} - 1 \cdot \color{blue}{\frac{y}{\frac{t}{z} - a}}\]
  9. Using strategy rm

  10. Applied clear-num3.2

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

  11. Final simplification3.2

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

Reproduce

herbie shell --seed 2019325 
(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))))