Average Error: 3.9 → 1.6
Time: 22.9s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\frac{\frac{2}{t}}{3} - \left(a + \frac{5}{6}\right), b - c, \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right)\right)}, x\right)}\]
\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}
↓
\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\frac{\frac{2}{t}}{3} - \left(a + \frac{5}{6}\right), b - c, \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right)\right)}, x\right)}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r52188 = x;
        double r52189 = y;
        double r52190 = 2.0;
        double r52191 = z;
        double r52192 = t;
        double r52193 = a;
        double r52194 = r52192 + r52193;
        double r52195 = sqrt(r52194);
        double r52196 = r52191 * r52195;
        double r52197 = r52196 / r52192;
        double r52198 = b;
        double r52199 = c;
        double r52200 = r52198 - r52199;
        double r52201 = 5.0;
        double r52202 = 6.0;
        double r52203 = r52201 / r52202;
        double r52204 = r52193 + r52203;
        double r52205 = 3.0;
        double r52206 = r52192 * r52205;
        double r52207 = r52190 / r52206;
        double r52208 = r52204 - r52207;
        double r52209 = r52200 * r52208;
        double r52210 = r52197 - r52209;
        double r52211 = r52190 * r52210;
        double r52212 = exp(r52211);
        double r52213 = r52189 * r52212;
        double r52214 = r52188 + r52213;
        double r52215 = r52188 / r52214;
        return r52215;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r52216 = x;
        double r52217 = y;
        double r52218 = 2.0;
        double r52219 = exp(r52218);
        double r52220 = t;
        double r52221 = r52218 / r52220;
        double r52222 = 3.0;
        double r52223 = r52221 / r52222;
        double r52224 = a;
        double r52225 = 5.0;
        double r52226 = 6.0;
        double r52227 = r52225 / r52226;
        double r52228 = r52224 + r52227;
        double r52229 = r52223 - r52228;
        double r52230 = b;
        double r52231 = c;
        double r52232 = r52230 - r52231;
        double r52233 = z;
        double r52234 = cbrt(r52220);
        double r52235 = r52234 * r52234;
        double r52236 = r52233 / r52235;
        double r52237 = r52220 + r52224;
        double r52238 = sqrt(r52237);
        double r52239 = r52238 / r52234;
        double r52240 = r52236 * r52239;
        double r52241 = fma(r52229, r52232, r52240);
        double r52242 = pow(r52219, r52241);
        double r52243 = fma(r52217, r52242, r52216);
        double r52244 = r52216 / r52243;
        return r52244;
}

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

Derivation

  1. Initial program 3.9

    \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

  2. Simplified2.7

    \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\frac{\frac{2}{t}}{3} - \left(a + \frac{5}{6}\right), b - c, \frac{z \cdot \sqrt{t + a}}{t}\right)\right)}, x\right)}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt2.7

    \[\leadsto \frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\frac{\frac{2}{t}}{3} - \left(a + \frac{5}{6}\right), b - c, \frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\right)\right)}, x\right)}\]

  5. Applied times-frac1.6

    \[\leadsto \frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\frac{\frac{2}{t}}{3} - \left(a + \frac{5}{6}\right), b - c, \color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}}\right)\right)}, x\right)}\]

  6. Final simplification1.6

    \[\leadsto \frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\frac{\frac{2}{t}}{3} - \left(a + \frac{5}{6}\right), b - c, \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right)\right)}, x\right)}\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))