Average Error: 0.1 → 0.1
Time: 30.8s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - \log \left(\sqrt{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - \log \left(\sqrt{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r304168 = x;
        double r304169 = y;
        double r304170 = r304168 + r304169;
        double r304171 = z;
        double r304172 = r304170 + r304171;
        double r304173 = t;
        double r304174 = log(r304173);
        double r304175 = r304171 * r304174;
        double r304176 = r304172 - r304175;
        double r304177 = a;
        double r304178 = 0.5;
        double r304179 = r304177 - r304178;
        double r304180 = b;
        double r304181 = r304179 * r304180;
        double r304182 = r304176 + r304181;
        return r304182;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r304183 = x;
        double r304184 = y;
        double r304185 = r304183 + r304184;
        double r304186 = z;
        double r304187 = r304185 + r304186;
        double r304188 = t;
        double r304189 = sqrt(r304188);
        double r304190 = log(r304189);
        double r304191 = r304190 * r304186;
        double r304192 = r304187 - r304191;
        double r304193 = r304192 - r304191;
        double r304194 = a;
        double r304195 = 0.5;
        double r304196 = r304194 - r304195;
        double r304197 = b;
        double r304198 = r304196 * r304197;
        double r304199 = r304193 + r304198;
        return r304199;
}

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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate--r+0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019199 
(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)))