Average Error: 10.2 → 10.4
Time: 17.0s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{\frac{1}{t - z \cdot a}}{\frac{1}{x - z \cdot y}}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{\frac{1}{t - z \cdot a}}{\frac{1}{x - z \cdot y}}
double f(double x, double y, double z, double t, double a) {
        double r36390237 = x;
        double r36390238 = y;
        double r36390239 = z;
        double r36390240 = r36390238 * r36390239;
        double r36390241 = r36390237 - r36390240;
        double r36390242 = t;
        double r36390243 = a;
        double r36390244 = r36390243 * r36390239;
        double r36390245 = r36390242 - r36390244;
        double r36390246 = r36390241 / r36390245;
        return r36390246;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r36390247 = 1.0;
        double r36390248 = t;
        double r36390249 = z;
        double r36390250 = a;
        double r36390251 = r36390249 * r36390250;
        double r36390252 = r36390248 - r36390251;
        double r36390253 = r36390247 / r36390252;
        double r36390254 = x;
        double r36390255 = y;
        double r36390256 = r36390249 * r36390255;
        double r36390257 = r36390254 - r36390256;
        double r36390258 = r36390247 / r36390257;
        double r36390259 = r36390253 / r36390258;
        return r36390259;
}

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
Target1.6
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344.0:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.2

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

  3. Applied sub-neg10.2

    \[\leadsto \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}}\]
  4. Using strategy rm

  5. Applied clear-num10.6

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

  6. Simplified10.6

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

  8. Applied div-inv10.6

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

  9. Applied associate-/r*10.4

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

  10. Final simplification10.4

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

Reproduce

herbie shell --seed 2019163 
(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 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))