\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]

↓

\[2 \cdot \sqrt[3]{\left(a + \left(d + \left(c + b\right)\right)\right) \cdot \left(\left(a + \left(d + \left(c + b\right)\right)\right) \cdot \log \left(e^{\left(b + d\right) + \left(c + a\right)}\right)\right)}\]

double f(double a, double b, double c, double d) {
        double r11212165 = a;
        double r11212166 = b;
        double r11212167 = c;
        double r11212168 = d;
        double r11212169 = r11212167 + r11212168;
        double r11212170 = r11212166 + r11212169;
        double r11212171 = r11212165 + r11212170;
        double r11212172 = 2.0;
        double r11212173 = r11212171 * r11212172;
        return r11212173;
}

↓

double f(double a, double b, double c, double d) {
        double r11212174 = 2.0;
        double r11212175 = a;
        double r11212176 = d;
        double r11212177 = c;
        double r11212178 = b;
        double r11212179 = r11212177 + r11212178;
        double r11212180 = r11212176 + r11212179;
        double r11212181 = r11212175 + r11212180;
        double r11212182 = r11212178 + r11212176;
        double r11212183 = r11212177 + r11212175;
        double r11212184 = r11212182 + r11212183;
        double r11212185 = exp(r11212184);
        double r11212186 = log(r11212185);
        double r11212187 = r11212181 * r11212186;
        double r11212188 = r11212181 * r11212187;
        double r11212189 = cbrt(r11212188);
        double r11212190 = r11212174 * r11212189;
        return r11212190;
}

\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2

↓

2 \cdot \sqrt[3]{\left(a + \left(d + \left(c + b\right)\right)\right) \cdot \left(\left(a + \left(d + \left(c + b\right)\right)\right) \cdot \log \left(e^{\left(b + d\right) + \left(c + a\right)}\right)\right)}

Original	3.7
Target	3.8
Herbie	2.7

Derivation

Initial program 3.7
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
Using strategy rm
Applied associate-+r+2.7
\[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
Using strategy rm
Applied add-cbrt-cube2.9
\[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)}} \cdot 2\]
Using strategy rm
Applied associate-+r+2.7
\[\leadsto \sqrt[3]{\left(\color{blue}{\left(\left(a + \left(b + c\right)\right) + d\right)} \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]
Using strategy rm
Applied add-log-exp2.7
\[\leadsto \sqrt[3]{\left(\left(\left(a + \left(b + c\right)\right) + \color{blue}{\log \left(e^{d}\right)}\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]
Applied add-log-exp2.7
\[\leadsto \sqrt[3]{\left(\left(\color{blue}{\log \left(e^{a + \left(b + c\right)}\right)} + \log \left(e^{d}\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]
Applied sum-log2.8
\[\leadsto \sqrt[3]{\left(\color{blue}{\log \left(e^{a + \left(b + c\right)} \cdot e^{d}\right)} \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]
Simplified2.7
\[\leadsto \sqrt[3]{\left(\log \color{blue}{\left(e^{\left(a + c\right) + \left(b + d\right)}\right)} \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]
Final simplification2.7
\[\leadsto 2 \cdot \sqrt[3]{\left(a + \left(d + \left(c + b\right)\right)\right) \cdot \left(\left(a + \left(d + \left(c + b\right)\right)\right) \cdot \log \left(e^{\left(b + d\right) + \left(c + a\right)}\right)\right)}\]

Error

Target

Derivation

Reproduce