Average Error: 4.1 → 2.9
Time: 19.9s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\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^{2 \cdot \left(\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)}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r70071 = x;
        double r70072 = y;
        double r70073 = 2.0;
        double r70074 = z;
        double r70075 = t;
        double r70076 = a;
        double r70077 = r70075 + r70076;
        double r70078 = sqrt(r70077);
        double r70079 = r70074 * r70078;
        double r70080 = r70079 / r70075;
        double r70081 = b;
        double r70082 = c;
        double r70083 = r70081 - r70082;
        double r70084 = 5.0;
        double r70085 = 6.0;
        double r70086 = r70084 / r70085;
        double r70087 = r70076 + r70086;
        double r70088 = 3.0;
        double r70089 = r70075 * r70088;
        double r70090 = r70073 / r70089;
        double r70091 = r70087 - r70090;
        double r70092 = r70083 * r70091;
        double r70093 = r70080 - r70092;
        double r70094 = r70073 * r70093;
        double r70095 = exp(r70094);
        double r70096 = r70072 * r70095;
        double r70097 = r70071 + r70096;
        double r70098 = r70071 / r70097;
        return r70098;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r70099 = x;
        double r70100 = y;
        double r70101 = 2.0;
        double r70102 = z;
        double r70103 = t;
        double r70104 = cbrt(r70103);
        double r70105 = r70104 * r70104;
        double r70106 = r70102 / r70105;
        double r70107 = a;
        double r70108 = r70103 + r70107;
        double r70109 = sqrt(r70108);
        double r70110 = r70109 / r70104;
        double r70111 = r70106 * r70110;
        double r70112 = b;
        double r70113 = c;
        double r70114 = r70112 - r70113;
        double r70115 = 5.0;
        double r70116 = 6.0;
        double r70117 = r70115 / r70116;
        double r70118 = r70107 + r70117;
        double r70119 = 3.0;
        double r70120 = r70103 * r70119;
        double r70121 = r70101 / r70120;
        double r70122 = r70118 - r70121;
        double r70123 = r70114 * r70122;
        double r70124 = r70111 - r70123;
        double r70125 = r70101 * r70124;
        double r70126 = exp(r70125);
        double r70127 = r70100 * r70126;
        double r70128 = r70099 + r70127;
        double r70129 = r70099 / r70128;
        return r70129;
}

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 4.1

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

  3. Applied add-cube-cbrt4.1

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

  4. Applied times-frac2.9

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

  5. Final simplification2.9

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

Reproduce

herbie shell --seed 2019297 
(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)))))))))))