Average Error: 0.1 → 0.1
Time: 21.6s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[x - \left(\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(0.5 - a\right) \cdot b\right)\right) - \left(z + y\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
x - \left(\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(0.5 - a\right) \cdot b\right)\right) - \left(z + y\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r299195 = x;
        double r299196 = y;
        double r299197 = r299195 + r299196;
        double r299198 = z;
        double r299199 = r299197 + r299198;
        double r299200 = t;
        double r299201 = log(r299200);
        double r299202 = r299198 * r299201;
        double r299203 = r299199 - r299202;
        double r299204 = a;
        double r299205 = 0.5;
        double r299206 = r299204 - r299205;
        double r299207 = b;
        double r299208 = r299206 * r299207;
        double r299209 = r299203 + r299208;
        return r299209;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r299210 = x;
        double r299211 = t;
        double r299212 = cbrt(r299211);
        double r299213 = r299212 * r299212;
        double r299214 = log(r299213);
        double r299215 = z;
        double r299216 = r299214 * r299215;
        double r299217 = log(r299212);
        double r299218 = r299215 * r299217;
        double r299219 = 0.5;
        double r299220 = a;
        double r299221 = r299219 - r299220;
        double r299222 = b;
        double r299223 = r299221 * r299222;
        double r299224 = r299218 + r299223;
        double r299225 = r299216 + r299224;
        double r299226 = y;
        double r299227 = r299215 + r299226;
        double r299228 = r299225 - r299227;
        double r299229 = r299210 - r299228;
        return r299229;
}

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
Target0.3
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. Simplified0.1

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied log-prod0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Applied associate-+l+0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(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)))