Average Error: 10.5 → 10.8
Time: 4.7s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{1}{\frac{t - a \cdot z}{x - y \cdot z}}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{1}{\frac{t - a \cdot z}{x - y \cdot z}}
double f(double x, double y, double z, double t, double a) {
        double r706040 = x;
        double r706041 = y;
        double r706042 = z;
        double r706043 = r706041 * r706042;
        double r706044 = r706040 - r706043;
        double r706045 = t;
        double r706046 = a;
        double r706047 = r706046 * r706042;
        double r706048 = r706045 - r706047;
        double r706049 = r706044 / r706048;
        return r706049;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r706050 = 1.0;
        double r706051 = t;
        double r706052 = a;
        double r706053 = z;
        double r706054 = r706052 * r706053;
        double r706055 = r706051 - r706054;
        double r706056 = x;
        double r706057 = y;
        double r706058 = r706057 * r706053;
        double r706059 = r706056 - r706058;
        double r706060 = r706055 / r706059;
        double r706061 = r706050 / r706060;
        return r706061;
}

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
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.5

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

  3. Applied clear-num10.8

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

  4. Final simplification10.8

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

Reproduce

herbie shell --seed 2020083 
(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))))