Average Error: 0.1 → 0.1
Time: 37.8s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(z + \left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(z + \left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3390101 = x;
        double r3390102 = y;
        double r3390103 = log(r3390102);
        double r3390104 = r3390101 * r3390103;
        double r3390105 = z;
        double r3390106 = r3390104 + r3390105;
        double r3390107 = t;
        double r3390108 = r3390106 + r3390107;
        double r3390109 = a;
        double r3390110 = r3390108 + r3390109;
        double r3390111 = b;
        double r3390112 = 0.5;
        double r3390113 = r3390111 - r3390112;
        double r3390114 = c;
        double r3390115 = log(r3390114);
        double r3390116 = r3390113 * r3390115;
        double r3390117 = r3390110 + r3390116;
        double r3390118 = i;
        double r3390119 = r3390102 * r3390118;
        double r3390120 = r3390117 + r3390119;
        return r3390120;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3390121 = z;
        double r3390122 = y;
        double r3390123 = cbrt(r3390122);
        double r3390124 = r3390123 * r3390123;
        double r3390125 = log(r3390124);
        double r3390126 = x;
        double r3390127 = r3390125 * r3390126;
        double r3390128 = 0.3333333333333333;
        double r3390129 = pow(r3390122, r3390128);
        double r3390130 = log(r3390129);
        double r3390131 = r3390126 * r3390130;
        double r3390132 = r3390127 + r3390131;
        double r3390133 = r3390121 + r3390132;
        double r3390134 = t;
        double r3390135 = r3390133 + r3390134;
        double r3390136 = a;
        double r3390137 = r3390135 + r3390136;
        double r3390138 = c;
        double r3390139 = log(r3390138);
        double r3390140 = b;
        double r3390141 = 0.5;
        double r3390142 = r3390140 - r3390141;
        double r3390143 = r3390139 * r3390142;
        double r3390144 = r3390137 + r3390143;
        double r3390145 = i;
        double r3390146 = r3390122 * r3390145;
        double r3390147 = r3390144 + r3390146;
        return r3390147;
}

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. Using strategy rm

  7. Applied pow1/30.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))