Average Error: 0.1 → 0.1
Time: 12.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r48116 = x;
        double r48117 = y;
        double r48118 = log(r48117);
        double r48119 = r48116 * r48118;
        double r48120 = z;
        double r48121 = r48119 + r48120;
        double r48122 = t;
        double r48123 = r48121 + r48122;
        double r48124 = a;
        double r48125 = r48123 + r48124;
        double r48126 = b;
        double r48127 = 0.5;
        double r48128 = r48126 - r48127;
        double r48129 = c;
        double r48130 = log(r48129);
        double r48131 = r48128 * r48130;
        double r48132 = r48125 + r48131;
        double r48133 = i;
        double r48134 = r48117 * r48133;
        double r48135 = r48132 + r48134;
        return r48135;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r48136 = x;
        double r48137 = 2.0;
        double r48138 = y;
        double r48139 = cbrt(r48138);
        double r48140 = log(r48139);
        double r48141 = r48137 * r48140;
        double r48142 = r48136 * r48141;
        double r48143 = 1.0;
        double r48144 = r48143 / r48138;
        double r48145 = -0.3333333333333333;
        double r48146 = pow(r48144, r48145);
        double r48147 = log(r48146);
        double r48148 = r48136 * r48147;
        double r48149 = r48142 + r48148;
        double r48150 = z;
        double r48151 = r48149 + r48150;
        double r48152 = t;
        double r48153 = r48151 + r48152;
        double r48154 = a;
        double r48155 = r48153 + r48154;
        double r48156 = b;
        double r48157 = 0.5;
        double r48158 = r48156 - r48157;
        double r48159 = c;
        double r48160 = log(r48159);
        double r48161 = r48158 * r48160;
        double r48162 = r48155 + r48161;
        double r48163 = i;
        double r48164 = r48138 * r48163;
        double r48165 = r48162 + r48164;
        return r48165;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  7. Taylor expanded around inf 0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 +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)))