\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]

↓

\[\left(\left(\left(\left(z + \left(y + x\right)\right) - \left(z + z\right) \cdot \log \left({t}^{\frac{1}{6}}\right)\right) - \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot z\right) - z \cdot \log \left(\sqrt{t}\right)\right) + b \cdot \left(a - 0.5\right)\]

\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b

↓

\left(\left(\left(\left(z + \left(y + x\right)\right) - \left(z + z\right) \cdot \log \left({t}^{\frac{1}{6}}\right)\right) - \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot z\right) - z \cdot \log \left(\sqrt{t}\right)\right) + b \cdot \left(a - 0.5\right)

double f(double x, double y, double z, double t, double a, double b) {
        double r19205183 = x;
        double r19205184 = y;
        double r19205185 = r19205183 + r19205184;
        double r19205186 = z;
        double r19205187 = r19205185 + r19205186;
        double r19205188 = t;
        double r19205189 = log(r19205188);
        double r19205190 = r19205186 * r19205189;
        double r19205191 = r19205187 - r19205190;
        double r19205192 = a;
        double r19205193 = 0.5;
        double r19205194 = r19205192 - r19205193;
        double r19205195 = b;
        double r19205196 = r19205194 * r19205195;
        double r19205197 = r19205191 + r19205196;
        return r19205197;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r19205198 = z;
        double r19205199 = y;
        double r19205200 = x;
        double r19205201 = r19205199 + r19205200;
        double r19205202 = r19205198 + r19205201;
        double r19205203 = r19205198 + r19205198;
        double r19205204 = t;
        double r19205205 = 0.16666666666666666;
        double r19205206 = pow(r19205204, r19205205);
        double r19205207 = log(r19205206);
        double r19205208 = r19205203 * r19205207;
        double r19205209 = r19205202 - r19205208;
        double r19205210 = sqrt(r19205204);
        double r19205211 = cbrt(r19205210);
        double r19205212 = log(r19205211);
        double r19205213 = r19205212 * r19205198;
        double r19205214 = r19205209 - r19205213;
        double r19205215 = log(r19205210);
        double r19205216 = r19205198 * r19205215;
        double r19205217 = r19205214 - r19205216;
        double r19205218 = b;
        double r19205219 = a;
        double r19205220 = 0.5;
        double r19205221 = r19205219 - r19205220;
        double r19205222 = r19205218 * r19205221;
        double r19205223 = r19205217 + r19205222;
        return r19205223;
}

Original	0.1
Target	0.3
Herbie	0.1

Derivation

Initial program 0.1
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
Using strategy rm
Applied add-sqr-sqrt0.1
\[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}\right) + \left(a - 0.5\right) \cdot b\]
Applied log-prod0.1
\[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \color{blue}{\left(\log \left(\sqrt{t}\right) + \log \left(\sqrt{t}\right)\right)}\right) + \left(a - 0.5\right) \cdot b\]
Applied distribute-lft-in0.1
\[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(z \cdot \log \left(\sqrt{t}\right) + z \cdot \log \left(\sqrt{t}\right)\right)}\right) + \left(a - 0.5\right) \cdot b\]
Applied associate--r+0.1
\[\leadsto \color{blue}{\left(\left(\left(\left(x + y\right) + z\right) - z \cdot \log \left(\sqrt{t}\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right)} + \left(a - 0.5\right) \cdot b\]
Using strategy rm
Applied add-cube-cbrt0.1
\[\leadsto \left(\left(\left(\left(x + y\right) + z\right) - z \cdot \log \color{blue}{\left(\left(\sqrt[3]{\sqrt{t}} \cdot \sqrt[3]{\sqrt{t}}\right) \cdot \sqrt[3]{\sqrt{t}}\right)}\right) - z \cdot \log \left(\sqrt{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
Applied log-prod0.1
\[\leadsto \left(\left(\left(\left(x + y\right) + z\right) - z \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt{t}} \cdot \sqrt[3]{\sqrt{t}}\right) + \log \left(\sqrt[3]{\sqrt{t}}\right)\right)}\right) - z \cdot \log \left(\sqrt{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
Applied distribute-rgt-in0.1
\[\leadsto \left(\left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\log \left(\sqrt[3]{\sqrt{t}} \cdot \sqrt[3]{\sqrt{t}}\right) \cdot z + \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot z\right)}\right) - z \cdot \log \left(\sqrt{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
Applied associate--r+0.1
\[\leadsto \left(\color{blue}{\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt[3]{\sqrt{t}} \cdot \sqrt[3]{\sqrt{t}}\right) \cdot z\right) - \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot z\right)} - z \cdot \log \left(\sqrt{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
Simplified0.1
\[\leadsto \left(\left(\color{blue}{\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot \left(z + z\right)\right)} - \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot z\right) - z \cdot \log \left(\sqrt{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
Taylor expanded around 0 0.1
\[\leadsto \left(\left(\left(\left(\left(x + y\right) + z\right) - \log \color{blue}{\left({t}^{\frac{1}{6}}\right)} \cdot \left(z + z\right)\right) - \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot z\right) - z \cdot \log \left(\sqrt{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
Final simplification0.1
\[\leadsto \left(\left(\left(\left(z + \left(y + x\right)\right) - \left(z + z\right) \cdot \log \left({t}^{\frac{1}{6}}\right)\right) - \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot z\right) - z \cdot \log \left(\sqrt{t}\right)\right) + b \cdot \left(a - 0.5\right)\]

Error

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Target

Derivation

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