Average Error: 33.6 → 11.2
Time: 27.6s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.2890050783826923 \cdot 10^{-183}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 1.9396144761399596 \cdot 10^{+100}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]
\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 -1.2890050783826923 \cdot 10^{-183}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 1.9396144761399596 \cdot 10^{+100}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r3716940 = b;
        double r3716941 = -r3716940;
        double r3716942 = r3716940 * r3716940;
        double r3716943 = 4.0;
        double r3716944 = a;
        double r3716945 = c;
        double r3716946 = r3716944 * r3716945;
        double r3716947 = r3716943 * r3716946;
        double r3716948 = r3716942 - r3716947;
        double r3716949 = sqrt(r3716948);
        double r3716950 = r3716941 - r3716949;
        double r3716951 = 2.0;
        double r3716952 = r3716951 * r3716944;
        double r3716953 = r3716950 / r3716952;
        return r3716953;
}
↓
double f(double a, double b, double c) {
        double r3716954 = b;
        double r3716955 = -1.2890050783826923e-183;
        bool r3716956 = r3716954 <= r3716955;
        double r3716957 = c;
        double r3716958 = r3716957 / r3716954;
        double r3716959 = -r3716958;
        double r3716960 = 1.9396144761399596e+100;
        bool r3716961 = r3716954 <= r3716960;
        double r3716962 = -r3716954;
        double r3716963 = r3716954 * r3716954;
        double r3716964 = a;
        double r3716965 = r3716957 * r3716964;
        double r3716966 = 4.0;
        double r3716967 = r3716965 * r3716966;
        double r3716968 = r3716963 - r3716967;
        double r3716969 = sqrt(r3716968);
        double r3716970 = r3716962 - r3716969;
        double r3716971 = 2.0;
        double r3716972 = r3716964 * r3716971;
        double r3716973 = r3716970 / r3716972;
        double r3716974 = r3716954 / r3716964;
        double r3716975 = r3716958 - r3716974;
        double r3716976 = r3716961 ? r3716973 : r3716975;
        double r3716977 = r3716956 ? r3716959 : r3716976;
        return r3716977;
}

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

Original33.6
Target20.5
Herbie11.2
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -1.2890050783826923e-183

    1. Initial program 48.2

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

    2. Taylor expanded around -inf 14.3

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

    3. Simplified14.3

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

    if -1.2890050783826923e-183 < b < 1.9396144761399596e+100

    1. Initial program 10.5

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

    2. Taylor expanded around -inf 10.5

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

    3. Simplified10.5

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

    if 1.9396144761399596e+100 < b

    1. Initial program 44.2

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

    2. Taylor expanded around -inf 44.2

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

    3. Simplified44.2

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

    4. Taylor expanded around inf 3.4

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

  4. Final simplification11.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.2890050783826923 \cdot 10^{-183}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 1.9396144761399596 \cdot 10^{+100}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019151 
(FPCore (a b c)
  :name "The quadratic formula (r2)"

  :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)))