Average Error: 0.1 → 0.1
Time: 10.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{1} \cdot {c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i\]
\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) + \left(\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]{1} \cdot {c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r94099 = x;
        double r94100 = y;
        double r94101 = log(r94100);
        double r94102 = r94099 * r94101;
        double r94103 = z;
        double r94104 = r94102 + r94103;
        double r94105 = t;
        double r94106 = r94104 + r94105;
        double r94107 = a;
        double r94108 = r94106 + r94107;
        double r94109 = b;
        double r94110 = 0.5;
        double r94111 = r94109 - r94110;
        double r94112 = c;
        double r94113 = log(r94112);
        double r94114 = r94111 * r94113;
        double r94115 = r94108 + r94114;
        double r94116 = i;
        double r94117 = r94100 * r94116;
        double r94118 = r94115 + r94117;
        return r94118;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r94119 = x;
        double r94120 = y;
        double r94121 = log(r94120);
        double r94122 = r94119 * r94121;
        double r94123 = z;
        double r94124 = r94122 + r94123;
        double r94125 = t;
        double r94126 = r94124 + r94125;
        double r94127 = a;
        double r94128 = r94126 + r94127;
        double r94129 = b;
        double r94130 = 0.5;
        double r94131 = r94129 - r94130;
        double r94132 = 2.0;
        double r94133 = c;
        double r94134 = cbrt(r94133);
        double r94135 = log(r94134);
        double r94136 = r94132 * r94135;
        double r94137 = r94131 * r94136;
        double r94138 = 1.0;
        double r94139 = cbrt(r94138);
        double r94140 = 0.3333333333333333;
        double r94141 = pow(r94133, r94140);
        double r94142 = r94139 * r94141;
        double r94143 = log(r94142);
        double r94144 = r94131 * r94143;
        double r94145 = r94137 + r94144;
        double r94146 = r94128 + r94145;
        double r94147 = i;
        double r94148 = r94120 * r94147;
        double r94149 = r94146 + r94148;
        return r94149;
}

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. Using strategy rm

  8. Applied *-un-lft-identity0.1

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

  9. Applied cbrt-prod0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 
(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)))