Average Error: 0.1 → 0.1
Time: 19.4s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(z + \left(\left(x + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(z + \left(\left(x + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left(\sqrt[3]{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 r566280 = x;
        double r566281 = y;
        double r566282 = r566280 + r566281;
        double r566283 = z;
        double r566284 = r566282 + r566283;
        double r566285 = t;
        double r566286 = log(r566285);
        double r566287 = r566283 * r566286;
        double r566288 = r566284 - r566287;
        double r566289 = a;
        double r566290 = 0.5;
        double r566291 = r566289 - r566290;
        double r566292 = b;
        double r566293 = r566291 * r566292;
        double r566294 = r566288 + r566293;
        return r566294;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r566295 = z;
        double r566296 = x;
        double r566297 = y;
        double r566298 = r566296 + r566297;
        double r566299 = 2.0;
        double r566300 = t;
        double r566301 = cbrt(r566300);
        double r566302 = log(r566301);
        double r566303 = r566299 * r566302;
        double r566304 = r566303 * r566295;
        double r566305 = r566298 - r566304;
        double r566306 = r566295 + r566305;
        double r566307 = r566302 * r566295;
        double r566308 = r566306 - r566307;
        double r566309 = a;
        double r566310 = 0.5;
        double r566311 = r566309 - r566310;
        double r566312 = b;
        double r566313 = r566311 * r566312;
        double r566314 = r566308 + r566313;
        return r566314;
}

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. Applied associate--r+0.1

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

  7. Simplified0.1

    \[\leadsto \left(\color{blue}{\left(z + \left(\left(x + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right)} - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]

  8. Final simplification0.1

    \[\leadsto \left(\left(z + \left(\left(x + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2020043 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 0.5) b))

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