Average Error: 1.9 → 2.1
Time: 19.2s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{e^{\left(-\log a\right) \cdot \left(1 - t\right) - \left(b - y \cdot \log z\right)}}{y} \cdot x\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{e^{\left(-\log a\right) \cdot \left(1 - t\right) - \left(b - y \cdot \log z\right)}}{y} \cdot x
double f(double x, double y, double z, double t, double a, double b) {
        double r85058 = x;
        double r85059 = y;
        double r85060 = z;
        double r85061 = log(r85060);
        double r85062 = r85059 * r85061;
        double r85063 = t;
        double r85064 = 1.0;
        double r85065 = r85063 - r85064;
        double r85066 = a;
        double r85067 = log(r85066);
        double r85068 = r85065 * r85067;
        double r85069 = r85062 + r85068;
        double r85070 = b;
        double r85071 = r85069 - r85070;
        double r85072 = exp(r85071);
        double r85073 = r85058 * r85072;
        double r85074 = r85073 / r85059;
        return r85074;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r85075 = a;
        double r85076 = log(r85075);
        double r85077 = -r85076;
        double r85078 = 1.0;
        double r85079 = t;
        double r85080 = r85078 - r85079;
        double r85081 = r85077 * r85080;
        double r85082 = b;
        double r85083 = y;
        double r85084 = z;
        double r85085 = log(r85084);
        double r85086 = r85083 * r85085;
        double r85087 = r85082 - r85086;
        double r85088 = r85081 - r85087;
        double r85089 = exp(r85088);
        double r85090 = r85089 / r85083;
        double r85091 = x;
        double r85092 = r85090 * r85091;
        return r85092;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.9

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]

  2. Taylor expanded around inf 1.9

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

  3. Simplified2.1

    \[\leadsto \color{blue}{\frac{e^{\left(-\log a\right) \cdot \left(1 - t\right) - \left(b - y \cdot \log z\right)}}{y} \cdot x}\]

  4. Final simplification2.1

    \[\leadsto \frac{e^{\left(-\log a\right) \cdot \left(1 - t\right) - \left(b - y \cdot \log z\right)}}{y} \cdot x\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))