Average Error: 1.9 → 1.4
Time: 22.0s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\left(x \cdot \frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \frac{{\left(\frac{\sqrt[3]{1}}{\sqrt[3]{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\left(x \cdot \frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \frac{{\left(\frac{\sqrt[3]{1}}{\sqrt[3]{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r120048 = x;
        double r120049 = y;
        double r120050 = z;
        double r120051 = log(r120050);
        double r120052 = r120049 * r120051;
        double r120053 = t;
        double r120054 = 1.0;
        double r120055 = r120053 - r120054;
        double r120056 = a;
        double r120057 = log(r120056);
        double r120058 = r120055 * r120057;
        double r120059 = r120052 + r120058;
        double r120060 = b;
        double r120061 = r120059 - r120060;
        double r120062 = exp(r120061);
        double r120063 = r120048 * r120062;
        double r120064 = r120063 / r120049;
        return r120064;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r120065 = x;
        double r120066 = 1.0;
        double r120067 = cbrt(r120066);
        double r120068 = r120067 * r120067;
        double r120069 = a;
        double r120070 = cbrt(r120069);
        double r120071 = r120070 * r120070;
        double r120072 = r120068 / r120071;
        double r120073 = 1.0;
        double r120074 = pow(r120072, r120073);
        double r120075 = y;
        double r120076 = z;
        double r120077 = r120066 / r120076;
        double r120078 = log(r120077);
        double r120079 = r120075 * r120078;
        double r120080 = r120066 / r120069;
        double r120081 = log(r120080);
        double r120082 = t;
        double r120083 = r120081 * r120082;
        double r120084 = b;
        double r120085 = r120083 + r120084;
        double r120086 = r120079 + r120085;
        double r120087 = exp(r120086);
        double r120088 = sqrt(r120087);
        double r120089 = r120074 / r120088;
        double r120090 = r120065 * r120089;
        double r120091 = r120067 / r120070;
        double r120092 = pow(r120091, r120073);
        double r120093 = r120092 / r120088;
        double r120094 = r120090 * r120093;
        double r120095 = r120094 / r120075;
        return r120095;
}

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

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

  3. Simplified1.2

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

  5. Applied add-sqr-sqrt1.3

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

  6. Applied add-cube-cbrt1.4

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

  7. Applied add-cube-cbrt1.4

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

  8. Applied times-frac1.4

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

  9. Applied unpow-prod-down1.4

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

  10. Applied times-frac1.4

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

  11. Applied associate-*r*1.4

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

  12. Final simplification1.4

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

Reproduce

herbie shell --seed 2019322 
(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))