Average Error: 33.0 → 10.4
Time: 20.0s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -6.615151909502748 \cdot 10^{-87}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 3.5387363548079373 \cdot 10^{+99}:\\ \;\;\;\;\left(-\frac{b}{2 \cdot a}\right) - \frac{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array}\]
\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}
↓
\begin{array}{l}
\mathbf{if}\;b \le -6.615151909502748 \cdot 10^{-87}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 3.5387363548079373 \cdot 10^{+99}:\\
\;\;\;\;\left(-\frac{b}{2 \cdot a}\right) - \frac{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}{2 \cdot a}\\

\mathbf{else}:\\
\;\;\;\;\frac{-b}{a}\\

\end{array}
double f(double a, double b, double c) {
        double r3215920 = b;
        double r3215921 = -r3215920;
        double r3215922 = r3215920 * r3215920;
        double r3215923 = 4.0;
        double r3215924 = a;
        double r3215925 = c;
        double r3215926 = r3215924 * r3215925;
        double r3215927 = r3215923 * r3215926;
        double r3215928 = r3215922 - r3215927;
        double r3215929 = sqrt(r3215928);
        double r3215930 = r3215921 - r3215929;
        double r3215931 = 2.0;
        double r3215932 = r3215931 * r3215924;
        double r3215933 = r3215930 / r3215932;
        return r3215933;
}
↓
double f(double a, double b, double c) {
        double r3215934 = b;
        double r3215935 = -6.615151909502748e-87;
        bool r3215936 = r3215934 <= r3215935;
        double r3215937 = c;
        double r3215938 = r3215937 / r3215934;
        double r3215939 = -r3215938;
        double r3215940 = 3.5387363548079373e+99;
        bool r3215941 = r3215934 <= r3215940;
        double r3215942 = 2.0;
        double r3215943 = a;
        double r3215944 = r3215942 * r3215943;
        double r3215945 = r3215934 / r3215944;
        double r3215946 = -r3215945;
        double r3215947 = r3215934 * r3215934;
        double r3215948 = r3215943 * r3215937;
        double r3215949 = 4.0;
        double r3215950 = r3215948 * r3215949;
        double r3215951 = r3215947 - r3215950;
        double r3215952 = sqrt(r3215951);
        double r3215953 = r3215952 / r3215944;
        double r3215954 = r3215946 - r3215953;
        double r3215955 = -r3215934;
        double r3215956 = r3215955 / r3215943;
        double r3215957 = r3215941 ? r3215954 : r3215956;
        double r3215958 = r3215936 ? r3215939 : r3215957;
        return r3215958;
}

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

Target

Original33.0
Target20.1
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -6.615151909502748e-87

    1. Initial program 51.9

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

    3. Applied div-inv52.0

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

    4. Simplified52.0

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

    5. Taylor expanded around -inf 10.0

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

    6. Simplified10.0

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

    if -6.615151909502748e-87 < b < 3.5387363548079373e+99

    1. Initial program 12.8

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

    3. Applied div-sub12.8

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

    if 3.5387363548079373e+99 < b

    1. Initial program 44.4

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

    3. Applied *-un-lft-identity44.4

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

    4. Applied associate-/l*44.5

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

    5. Taylor expanded around 0 3.9

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

    6. Simplified3.9

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

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -6.615151909502748 \cdot 10^{-87}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 3.5387363548079373 \cdot 10^{+99}:\\ \;\;\;\;\left(-\frac{b}{2 \cdot a}\right) - \frac{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019133 
(FPCore (a b c)
  :name "quadm (p42, negative)"

  :herbie-target
  (if (< b 0) (/ c (* a (/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))) (/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))

  (/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))