Average Error: 34.2 → 11.9
Time: 14.3s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.547666603636537260513437138645901028344 \cdot 10^{50}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 7.455592343308264166675918758902222662503 \cdot 10^{-170}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\begin{array}{l}
\mathbf{if}\;b \le -1.547666603636537260513437138645901028344 \cdot 10^{50}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 7.455592343308264166675918758902222662503 \cdot 10^{-170}:\\
\;\;\;\;\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}\\

\mathbf{else}:\\
\;\;\;\;-1 \cdot \frac{c}{b}\\

\end{array}
double f(double a, double b, double c) {
        double r37463 = b;
        double r37464 = -r37463;
        double r37465 = r37463 * r37463;
        double r37466 = 4.0;
        double r37467 = a;
        double r37468 = r37466 * r37467;
        double r37469 = c;
        double r37470 = r37468 * r37469;
        double r37471 = r37465 - r37470;
        double r37472 = sqrt(r37471);
        double r37473 = r37464 + r37472;
        double r37474 = 2.0;
        double r37475 = r37474 * r37467;
        double r37476 = r37473 / r37475;
        return r37476;
}
↓
double f(double a, double b, double c) {
        double r37477 = b;
        double r37478 = -1.5476666036365373e+50;
        bool r37479 = r37477 <= r37478;
        double r37480 = 1.0;
        double r37481 = c;
        double r37482 = r37481 / r37477;
        double r37483 = a;
        double r37484 = r37477 / r37483;
        double r37485 = r37482 - r37484;
        double r37486 = r37480 * r37485;
        double r37487 = 7.455592343308264e-170;
        bool r37488 = r37477 <= r37487;
        double r37489 = 1.0;
        double r37490 = 2.0;
        double r37491 = r37490 * r37483;
        double r37492 = r37477 * r37477;
        double r37493 = 4.0;
        double r37494 = r37493 * r37483;
        double r37495 = r37494 * r37481;
        double r37496 = r37492 - r37495;
        double r37497 = sqrt(r37496);
        double r37498 = r37497 - r37477;
        double r37499 = r37491 / r37498;
        double r37500 = r37489 / r37499;
        double r37501 = -1.0;
        double r37502 = r37501 * r37482;
        double r37503 = r37488 ? r37500 : r37502;
        double r37504 = r37479 ? r37486 : r37503;
        return r37504;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if b < -1.5476666036365373e+50

    1. Initial program 37.8

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

    2. Taylor expanded around -inf 5.8

      \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]

    3. Simplified5.8

      \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]

    if -1.5476666036365373e+50 < b < 7.455592343308264e-170

    1. Initial program 12.4

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
    2. Using strategy rm

    3. Applied clear-num12.5

      \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}\]

    4. Simplified12.5

      \[\leadsto \frac{1}{\color{blue}{\frac{2 \cdot a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}}\]

    if 7.455592343308264e-170 < b

    1. Initial program 48.9

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

    2. Taylor expanded around inf 14.1

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification11.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.547666603636537260513437138645901028344 \cdot 10^{50}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 7.455592343308264166675918758902222662503 \cdot 10^{-170}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (a b c)
  :name "Quadratic roots, full range"
  :precision binary64
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))