Average Error: 3.7 → 3.0
Time: 38.7s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{a + t}}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)} + x}\]
\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}
↓
\frac{x}{y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{a + t}}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)} + x}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r2789241 = x;
        double r2789242 = y;
        double r2789243 = 2.0;
        double r2789244 = z;
        double r2789245 = t;
        double r2789246 = a;
        double r2789247 = r2789245 + r2789246;
        double r2789248 = sqrt(r2789247);
        double r2789249 = r2789244 * r2789248;
        double r2789250 = r2789249 / r2789245;
        double r2789251 = b;
        double r2789252 = c;
        double r2789253 = r2789251 - r2789252;
        double r2789254 = 5.0;
        double r2789255 = 6.0;
        double r2789256 = r2789254 / r2789255;
        double r2789257 = r2789246 + r2789256;
        double r2789258 = 3.0;
        double r2789259 = r2789245 * r2789258;
        double r2789260 = r2789243 / r2789259;
        double r2789261 = r2789257 - r2789260;
        double r2789262 = r2789253 * r2789261;
        double r2789263 = r2789250 - r2789262;
        double r2789264 = r2789243 * r2789263;
        double r2789265 = exp(r2789264);
        double r2789266 = r2789242 * r2789265;
        double r2789267 = r2789241 + r2789266;
        double r2789268 = r2789241 / r2789267;
        return r2789268;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r2789269 = x;
        double r2789270 = y;
        double r2789271 = 2.0;
        double r2789272 = z;
        double r2789273 = t;
        double r2789274 = a;
        double r2789275 = r2789274 + r2789273;
        double r2789276 = sqrt(r2789275);
        double r2789277 = r2789273 / r2789276;
        double r2789278 = r2789272 / r2789277;
        double r2789279 = 5.0;
        double r2789280 = 6.0;
        double r2789281 = r2789279 / r2789280;
        double r2789282 = r2789281 + r2789274;
        double r2789283 = 3.0;
        double r2789284 = r2789273 * r2789283;
        double r2789285 = r2789271 / r2789284;
        double r2789286 = r2789282 - r2789285;
        double r2789287 = b;
        double r2789288 = c;
        double r2789289 = r2789287 - r2789288;
        double r2789290 = r2789286 * r2789289;
        double r2789291 = r2789278 - r2789290;
        double r2789292 = r2789271 * r2789291;
        double r2789293 = exp(r2789292);
        double r2789294 = r2789270 * r2789293;
        double r2789295 = r2789294 + r2789269;
        double r2789296 = r2789269 / r2789295;
        return r2789296;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.7

    \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
  2. Using strategy rm

  3. Applied associate-/l*3.0

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\frac{t}{\sqrt{t + a}}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

  4. Final simplification3.0

    \[\leadsto \frac{x}{y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{a + t}}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)} + x}\]

Reproduce

herbie shell --seed 2019135 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))