Average Error: 1.6 → 1.6
Time: 34.5s
Precision: 64
\[\frac{\left(\left(-b\right) - \left(\sqrt{\left(\left(b \cdot b\right) - \left(\left(4\right) \cdot \left(a \cdot c\right)\right)\right)}\right)\right)}{\left(\left(2\right) \cdot a\right)}\]
↓
\[\frac{\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2}}{a}\]
\frac{\left(\left(-b\right) - \left(\sqrt{\left(\left(b \cdot b\right) - \left(\left(4\right) \cdot \left(a \cdot c\right)\right)\right)}\right)\right)}{\left(\left(2\right) \cdot a\right)}
↓
\frac{\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2}}{a}
double f(double a, double b, double c) {
        double r2612353 = b;
        double r2612354 = -r2612353;
        double r2612355 = r2612353 * r2612353;
        double r2612356 = 4.0;
        double r2612357 = /* ERROR: no posit support in C */;
        double r2612358 = a;
        double r2612359 = c;
        double r2612360 = r2612358 * r2612359;
        double r2612361 = r2612357 * r2612360;
        double r2612362 = r2612355 - r2612361;
        double r2612363 = sqrt(r2612362);
        double r2612364 = r2612354 - r2612363;
        double r2612365 = 2.0;
        double r2612366 = /* ERROR: no posit support in C */;
        double r2612367 = r2612366 * r2612358;
        double r2612368 = r2612364 / r2612367;
        return r2612368;
}
↓
double f(double a, double b, double c) {
        double r2612369 = b;
        double r2612370 = -r2612369;
        double r2612371 = r2612369 * r2612369;
        double r2612372 = 4.0;
        double r2612373 = a;
        double r2612374 = c;
        double r2612375 = r2612373 * r2612374;
        double r2612376 = r2612372 * r2612375;
        double r2612377 = r2612371 - r2612376;
        double r2612378 = sqrt(r2612377);
        double r2612379 = r2612370 - r2612378;
        double r2612380 = 2.0;
        double r2612381 = r2612379 / r2612380;
        double r2612382 = r2612381 / r2612373;
        return r2612382;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 1.6

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

  3. Applied associate-/r*1.6

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

  4. Final simplification1.6

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

Reproduce

herbie shell --seed 2019133 
(FPCore (a b c)
  :name "quadm (p42, negative)"
  (/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a)))