Average Error: 0.1 → 0.1
Time: 27.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(a + \left(\log \left(\sqrt{y}\right) \cdot \left(x + x\right) + \left(z + t\right)\right)\right) + y \cdot i\right) + \left(3 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - \frac{1}{2}\right)\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(a + \left(\log \left(\sqrt{y}\right) \cdot \left(x + x\right) + \left(z + t\right)\right)\right) + y \cdot i\right) + \left(3 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - \frac{1}{2}\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70015 = x;
        double r70016 = y;
        double r70017 = log(r70016);
        double r70018 = r70015 * r70017;
        double r70019 = z;
        double r70020 = r70018 + r70019;
        double r70021 = t;
        double r70022 = r70020 + r70021;
        double r70023 = a;
        double r70024 = r70022 + r70023;
        double r70025 = b;
        double r70026 = 0.5;
        double r70027 = r70025 - r70026;
        double r70028 = c;
        double r70029 = log(r70028);
        double r70030 = r70027 * r70029;
        double r70031 = r70024 + r70030;
        double r70032 = i;
        double r70033 = r70016 * r70032;
        double r70034 = r70031 + r70033;
        return r70034;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70035 = a;
        double r70036 = y;
        double r70037 = sqrt(r70036);
        double r70038 = log(r70037);
        double r70039 = x;
        double r70040 = r70039 + r70039;
        double r70041 = r70038 * r70040;
        double r70042 = z;
        double r70043 = t;
        double r70044 = r70042 + r70043;
        double r70045 = r70041 + r70044;
        double r70046 = r70035 + r70045;
        double r70047 = i;
        double r70048 = r70036 * r70047;
        double r70049 = r70046 + r70048;
        double r70050 = 3.0;
        double r70051 = c;
        double r70052 = cbrt(r70051);
        double r70053 = log(r70052);
        double r70054 = r70050 * r70053;
        double r70055 = b;
        double r70056 = 1.0;
        double r70057 = 2.0;
        double r70058 = r70056 / r70057;
        double r70059 = r70055 - r70058;
        double r70060 = r70054 * r70059;
        double r70061 = r70049 + r70060;
        return r70061;
}

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

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  7. Applied add-cube-cbrt0.1

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

  8. Applied log-prod0.1

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

  9. Applied distribute-lft-in0.1

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

  10. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log \left(\sqrt{y}\right) + x \cdot \log \left(\sqrt{y}\right)\right) + z\right) + t\right) + a\right) + \left(\color{blue}{\left(b - \frac{1}{2}\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right)} + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i\]

  11. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log \left(\sqrt{y}\right) + x \cdot \log \left(\sqrt{y}\right)\right) + z\right) + t\right) + a\right) + \left(\left(b - \frac{1}{2}\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log \left(\sqrt[3]{c}\right)}\right)\right) + y \cdot i\]

  12. Final simplification0.1

    \[\leadsto \left(\left(a + \left(\log \left(\sqrt{y}\right) \cdot \left(x + x\right) + \left(z + t\right)\right)\right) + y \cdot i\right) + \left(3 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - \frac{1}{2}\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))