\[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]

↓

\[\begin{array}{l} \mathbf{if}\;c \le -4.5554482331281827 \cdot 10^{+198}:\\ \;\;\;\;\frac{-b}{\sqrt{d^2 + c^2}^*}\\ \mathbf{elif}\;c \le 2.251215078496209 \cdot 10^{+155}:\\ \;\;\;\;\frac{b \cdot c - d \cdot a}{\sqrt{d^2 + c^2}^*} \cdot \frac{1}{\sqrt{d^2 + c^2}^*}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{\sqrt{d^2 + c^2}^*}\\ \end{array}\]

double f(double a, double b, double c, double d) {
        double r17324927 = b;
        double r17324928 = c;
        double r17324929 = r17324927 * r17324928;
        double r17324930 = a;
        double r17324931 = d;
        double r17324932 = r17324930 * r17324931;
        double r17324933 = r17324929 - r17324932;
        double r17324934 = r17324928 * r17324928;
        double r17324935 = r17324931 * r17324931;
        double r17324936 = r17324934 + r17324935;
        double r17324937 = r17324933 / r17324936;
        return r17324937;
}

↓

double f(double a, double b, double c, double d) {
        double r17324938 = c;
        double r17324939 = -4.5554482331281827e+198;
        bool r17324940 = r17324938 <= r17324939;
        double r17324941 = b;
        double r17324942 = -r17324941;
        double r17324943 = d;
        double r17324944 = hypot(r17324943, r17324938);
        double r17324945 = r17324942 / r17324944;
        double r17324946 = 2.251215078496209e+155;
        bool r17324947 = r17324938 <= r17324946;
        double r17324948 = r17324941 * r17324938;
        double r17324949 = a;
        double r17324950 = r17324943 * r17324949;
        double r17324951 = r17324948 - r17324950;
        double r17324952 = r17324951 / r17324944;
        double r17324953 = 1.0;
        double r17324954 = r17324953 / r17324944;
        double r17324955 = r17324952 * r17324954;
        double r17324956 = r17324941 / r17324944;
        double r17324957 = r17324947 ? r17324955 : r17324956;
        double r17324958 = r17324940 ? r17324945 : r17324957;
        return r17324958;
}

\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}

↓

\begin{array}{l}
\mathbf{if}\;c \le -4.5554482331281827 \cdot 10^{+198}:\\
\;\;\;\;\frac{-b}{\sqrt{d^2 + c^2}^*}\\

\mathbf{elif}\;c \le 2.251215078496209 \cdot 10^{+155}:\\
\;\;\;\;\frac{b \cdot c - d \cdot a}{\sqrt{d^2 + c^2}^*} \cdot \frac{1}{\sqrt{d^2 + c^2}^*}\\

\mathbf{else}:\\
\;\;\;\;\frac{b}{\sqrt{d^2 + c^2}^*}\\

\end{array}

Original	25.5
Target	0.4
Herbie	12.6

Derivation

Split input into 3 regimes
if c < -4.5554482331281827e+198
1. Initial program 42.2
  \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]
2. Simplified42.2
  \[\leadsto \color{blue}{\frac{b \cdot c - a \cdot d}{(d \cdot d + \left(c \cdot c\right))_*}}\]
3. Using strategy rm
4. Applied add-sqr-sqrt42.2
  \[\leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*} \cdot \sqrt{(d \cdot d + \left(c \cdot c\right))_*}}}\]
5. Applied associate-/r*42.2
  \[\leadsto \color{blue}{\frac{\frac{b \cdot c - a \cdot d}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}}\]
6. Using strategy rm
7. Applied fma-udef42.2
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\sqrt{\color{blue}{d \cdot d + c \cdot c}}}}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}\]
8. Applied hypot-def42.2
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\color{blue}{\sqrt{d^2 + c^2}^*}}}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}\]
9. Using strategy rm
10. Applied fma-udef42.2
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\sqrt{d^2 + c^2}^*}}{\sqrt{\color{blue}{d \cdot d + c \cdot c}}}\]
11. Applied hypot-def28.4
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\sqrt{d^2 + c^2}^*}}{\color{blue}{\sqrt{d^2 + c^2}^*}}\]
12. Taylor expanded around -inf 11.7
  \[\leadsto \frac{\color{blue}{-1 \cdot b}}{\sqrt{d^2 + c^2}^*}\]
13. Simplified11.7
  \[\leadsto \frac{\color{blue}{-b}}{\sqrt{d^2 + c^2}^*}\]
if -4.5554482331281827e+198 < c < 2.251215078496209e+155
1. Initial program 20.6
  \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]
2. Simplified20.6
  \[\leadsto \color{blue}{\frac{b \cdot c - a \cdot d}{(d \cdot d + \left(c \cdot c\right))_*}}\]
3. Using strategy rm
4. Applied add-sqr-sqrt20.6
  \[\leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*} \cdot \sqrt{(d \cdot d + \left(c \cdot c\right))_*}}}\]
5. Applied associate-/r*20.5
  \[\leadsto \color{blue}{\frac{\frac{b \cdot c - a \cdot d}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}}\]
6. Using strategy rm
7. Applied fma-udef20.5
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\sqrt{\color{blue}{d \cdot d + c \cdot c}}}}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}\]
8. Applied hypot-def20.5
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\color{blue}{\sqrt{d^2 + c^2}^*}}}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}\]
9. Using strategy rm
10. Applied fma-udef20.5
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\sqrt{d^2 + c^2}^*}}{\sqrt{\color{blue}{d \cdot d + c \cdot c}}}\]
11. Applied hypot-def12.2
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\sqrt{d^2 + c^2}^*}}{\color{blue}{\sqrt{d^2 + c^2}^*}}\]
12. Using strategy rm
13. Applied div-inv12.4
  \[\leadsto \color{blue}{\frac{b \cdot c - a \cdot d}{\sqrt{d^2 + c^2}^*} \cdot \frac{1}{\sqrt{d^2 + c^2}^*}}\]
if 2.251215078496209e+155 < c
1. Initial program 44.2
  \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]
2. Simplified44.2
  \[\leadsto \color{blue}{\frac{b \cdot c - a \cdot d}{(d \cdot d + \left(c \cdot c\right))_*}}\]
3. Using strategy rm
4. Applied add-sqr-sqrt44.2
  \[\leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*} \cdot \sqrt{(d \cdot d + \left(c \cdot c\right))_*}}}\]
5. Applied associate-/r*44.2
  \[\leadsto \color{blue}{\frac{\frac{b \cdot c - a \cdot d}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}}\]
6. Using strategy rm
7. Applied fma-udef44.2
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\sqrt{\color{blue}{d \cdot d + c \cdot c}}}}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}\]
8. Applied hypot-def44.2
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\color{blue}{\sqrt{d^2 + c^2}^*}}}{\sqrt{(d \cdot d + \left(c \cdot c\right))_*}}\]
9. Using strategy rm
10. Applied fma-udef44.2
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\sqrt{d^2 + c^2}^*}}{\sqrt{\color{blue}{d \cdot d + c \cdot c}}}\]
11. Applied hypot-def28.2
  \[\leadsto \frac{\frac{b \cdot c - a \cdot d}{\sqrt{d^2 + c^2}^*}}{\color{blue}{\sqrt{d^2 + c^2}^*}}\]
12. Taylor expanded around inf 14.6
  \[\leadsto \frac{\color{blue}{b}}{\sqrt{d^2 + c^2}^*}\]
Recombined 3 regimes into one program.
Final simplification12.6
\[\leadsto \begin{array}{l} \mathbf{if}\;c \le -4.5554482331281827 \cdot 10^{+198}:\\ \;\;\;\;\frac{-b}{\sqrt{d^2 + c^2}^*}\\ \mathbf{elif}\;c \le 2.251215078496209 \cdot 10^{+155}:\\ \;\;\;\;\frac{b \cdot c - d \cdot a}{\sqrt{d^2 + c^2}^*} \cdot \frac{1}{\sqrt{d^2 + c^2}^*}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{\sqrt{d^2 + c^2}^*}\\ \end{array}\]

Error

Target

Derivation

`if c < -4.5554482331281827e+198`

`if -4.5554482331281827e+198 < c < 2.251215078496209e+155`

`if 2.251215078496209e+155 < c`

Reproduce