Average Error: 3.5 → 3.0
Time: 34.5s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{y \cdot e^{2.0 \cdot \left(\frac{\sqrt{a + t}}{t} \cdot z - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)} + x}\]
\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{\sqrt{a + t}}{t} \cdot z - \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 r3059043 = x;
        double r3059044 = y;
        double r3059045 = 2.0;
        double r3059046 = z;
        double r3059047 = t;
        double r3059048 = a;
        double r3059049 = r3059047 + r3059048;
        double r3059050 = sqrt(r3059049);
        double r3059051 = r3059046 * r3059050;
        double r3059052 = r3059051 / r3059047;
        double r3059053 = b;
        double r3059054 = c;
        double r3059055 = r3059053 - r3059054;
        double r3059056 = 5.0;
        double r3059057 = 6.0;
        double r3059058 = r3059056 / r3059057;
        double r3059059 = r3059048 + r3059058;
        double r3059060 = 3.0;
        double r3059061 = r3059047 * r3059060;
        double r3059062 = r3059045 / r3059061;
        double r3059063 = r3059059 - r3059062;
        double r3059064 = r3059055 * r3059063;
        double r3059065 = r3059052 - r3059064;
        double r3059066 = r3059045 * r3059065;
        double r3059067 = exp(r3059066);
        double r3059068 = r3059044 * r3059067;
        double r3059069 = r3059043 + r3059068;
        double r3059070 = r3059043 / r3059069;
        return r3059070;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3059071 = x;
        double r3059072 = y;
        double r3059073 = 2.0;
        double r3059074 = a;
        double r3059075 = t;
        double r3059076 = r3059074 + r3059075;
        double r3059077 = sqrt(r3059076);
        double r3059078 = r3059077 / r3059075;
        double r3059079 = z;
        double r3059080 = r3059078 * r3059079;
        double r3059081 = 5.0;
        double r3059082 = 6.0;
        double r3059083 = r3059081 / r3059082;
        double r3059084 = r3059083 + r3059074;
        double r3059085 = 3.0;
        double r3059086 = r3059075 * r3059085;
        double r3059087 = r3059073 / r3059086;
        double r3059088 = r3059084 - r3059087;
        double r3059089 = b;
        double r3059090 = c;
        double r3059091 = r3059089 - r3059090;
        double r3059092 = r3059088 * r3059091;
        double r3059093 = r3059080 - r3059092;
        double r3059094 = r3059073 * r3059093;
        double r3059095 = exp(r3059094);
        double r3059096 = r3059072 * r3059095;
        double r3059097 = r3059096 + r3059071;
        double r3059098 = r3059071 / r3059097;
        return r3059098;
}

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 3.5

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

  3. Applied *-un-lft-identity3.5

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{1 \cdot t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

  4. Applied times-frac3.0

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{1} \cdot \frac{\sqrt{t + a}}{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

  5. Simplified3.0

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

  6. Final simplification3.0

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

Reproduce

herbie shell --seed 2019129 
(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)))))))))))