Average Error: 0.1 → 0.1
Time: 40.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-1} \cdot \sqrt[3]{-c}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]
\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(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-1} \cdot \sqrt[3]{-c}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66052 = x;
        double r66053 = y;
        double r66054 = log(r66053);
        double r66055 = r66052 * r66054;
        double r66056 = z;
        double r66057 = r66055 + r66056;
        double r66058 = t;
        double r66059 = r66057 + r66058;
        double r66060 = a;
        double r66061 = r66059 + r66060;
        double r66062 = b;
        double r66063 = 0.5;
        double r66064 = r66062 - r66063;
        double r66065 = c;
        double r66066 = log(r66065);
        double r66067 = r66064 * r66066;
        double r66068 = r66061 + r66067;
        double r66069 = i;
        double r66070 = r66053 * r66069;
        double r66071 = r66068 + r66070;
        return r66071;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66072 = x;
        double r66073 = y;
        double r66074 = log(r66073);
        double r66075 = r66072 * r66074;
        double r66076 = z;
        double r66077 = r66075 + r66076;
        double r66078 = t;
        double r66079 = r66077 + r66078;
        double r66080 = a;
        double r66081 = r66079 + r66080;
        double r66082 = -1.0;
        double r66083 = cbrt(r66082);
        double r66084 = c;
        double r66085 = -r66084;
        double r66086 = cbrt(r66085);
        double r66087 = r66083 * r66086;
        double r66088 = log(r66087);
        double r66089 = 3.0;
        double r66090 = b;
        double r66091 = r66089 * r66090;
        double r66092 = 1.5;
        double r66093 = r66091 - r66092;
        double r66094 = r66088 * r66093;
        double r66095 = r66081 + r66094;
        double r66096 = i;
        double r66097 = r66073 * r66096;
        double r66098 = r66095 + r66097;
        return r66098;
}

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-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  7. Taylor expanded around -inf 64.0

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(3 \cdot \left(b \cdot \log \left({\left(-1 \cdot c\right)}^{\frac{1}{3}} \cdot \sqrt[3]{-1}\right)\right) - 1.5 \cdot \log \left({\left(-1 \cdot c\right)}^{\frac{1}{3}} \cdot \sqrt[3]{-1}\right)\right)}\right) + y \cdot i\]

  8. Simplified0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\log \left(\sqrt[3]{-1} \cdot \sqrt[3]{-c}\right) \cdot \left(3 \cdot b - 1.5\right)}\right) + y \cdot i\]

  9. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-1} \cdot \sqrt[3]{-c}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(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)))