Average Error: 0.1 → 0.1
Time: 29.9s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(z + \left(y + x\right)\right) - \left(\left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right) + \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(z + \left(y + x\right)\right) - \left(\left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right) + \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r15879167 = x;
        double r15879168 = y;
        double r15879169 = r15879167 + r15879168;
        double r15879170 = z;
        double r15879171 = r15879169 + r15879170;
        double r15879172 = t;
        double r15879173 = log(r15879172);
        double r15879174 = r15879170 * r15879173;
        double r15879175 = r15879171 - r15879174;
        double r15879176 = a;
        double r15879177 = 0.5;
        double r15879178 = r15879176 - r15879177;
        double r15879179 = b;
        double r15879180 = r15879178 * r15879179;
        double r15879181 = r15879175 + r15879180;
        return r15879181;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r15879182 = z;
        double r15879183 = y;
        double r15879184 = x;
        double r15879185 = r15879183 + r15879184;
        double r15879186 = r15879182 + r15879185;
        double r15879187 = t;
        double r15879188 = cbrt(r15879187);
        double r15879189 = log(r15879188);
        double r15879190 = r15879182 * r15879189;
        double r15879191 = r15879190 + r15879190;
        double r15879192 = 1.0;
        double r15879193 = r15879192 / r15879187;
        double r15879194 = -0.3333333333333333;
        double r15879195 = pow(r15879193, r15879194);
        double r15879196 = log(r15879195);
        double r15879197 = r15879196 * r15879182;
        double r15879198 = r15879191 + r15879197;
        double r15879199 = r15879186 - r15879198;
        double r15879200 = a;
        double r15879201 = 0.5;
        double r15879202 = r15879200 - r15879201;
        double r15879203 = b;
        double r15879204 = r15879202 * r15879203;
        double r15879205 = r15879199 + r15879204;
        return r15879205;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.4
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right) + \left(a - 0.5\right) \cdot b\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\right) + \left(a - 0.5\right) \cdot b\]

  5. Applied distribute-rgt-in0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)}\right) + \left(a - 0.5\right) \cdot b\]

  6. Simplified0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\color{blue}{\left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)} + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]

  7. Taylor expanded around inf 0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))