Average Error: 4.0 → 2.8
Time: 28.4s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}\]
\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}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3797020 = x;
        double r3797021 = y;
        double r3797022 = 2.0;
        double r3797023 = z;
        double r3797024 = t;
        double r3797025 = a;
        double r3797026 = r3797024 + r3797025;
        double r3797027 = sqrt(r3797026);
        double r3797028 = r3797023 * r3797027;
        double r3797029 = r3797028 / r3797024;
        double r3797030 = b;
        double r3797031 = c;
        double r3797032 = r3797030 - r3797031;
        double r3797033 = 5.0;
        double r3797034 = 6.0;
        double r3797035 = r3797033 / r3797034;
        double r3797036 = r3797025 + r3797035;
        double r3797037 = 3.0;
        double r3797038 = r3797024 * r3797037;
        double r3797039 = r3797022 / r3797038;
        double r3797040 = r3797036 - r3797039;
        double r3797041 = r3797032 * r3797040;
        double r3797042 = r3797029 - r3797041;
        double r3797043 = r3797022 * r3797042;
        double r3797044 = exp(r3797043);
        double r3797045 = r3797021 * r3797044;
        double r3797046 = r3797020 + r3797045;
        double r3797047 = r3797020 / r3797046;
        return r3797047;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3797048 = x;
        double r3797049 = y;
        double r3797050 = a;
        double r3797051 = t;
        double r3797052 = r3797050 + r3797051;
        double r3797053 = sqrt(r3797052);
        double r3797054 = cbrt(r3797051);
        double r3797055 = r3797053 / r3797054;
        double r3797056 = z;
        double r3797057 = r3797054 * r3797054;
        double r3797058 = r3797056 / r3797057;
        double r3797059 = r3797055 * r3797058;
        double r3797060 = 5.0;
        double r3797061 = 6.0;
        double r3797062 = r3797060 / r3797061;
        double r3797063 = r3797050 + r3797062;
        double r3797064 = 2.0;
        double r3797065 = 3.0;
        double r3797066 = r3797051 * r3797065;
        double r3797067 = r3797064 / r3797066;
        double r3797068 = r3797063 - r3797067;
        double r3797069 = b;
        double r3797070 = c;
        double r3797071 = r3797069 - r3797070;
        double r3797072 = r3797068 * r3797071;
        double r3797073 = r3797059 - r3797072;
        double r3797074 = r3797073 * r3797064;
        double r3797075 = exp(r3797074);
        double r3797076 = r3797049 * r3797075;
        double r3797077 = r3797048 + r3797076;
        double r3797078 = r3797048 / r3797077;
        return r3797078;
}

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 4.0

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

  3. Applied add-cube-cbrt4.0

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

  4. Applied times-frac2.8

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

  5. Final simplification2.8

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

Reproduce

herbie shell --seed 2019172 
(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)))))))))))