Average Error: 0.3 → 0.3
Time: 19.4s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}
double f(double x, double y, double z, double t) {
        double r13794047 = x;
        double r13794048 = 0.5;
        double r13794049 = r13794047 * r13794048;
        double r13794050 = y;
        double r13794051 = r13794049 - r13794050;
        double r13794052 = z;
        double r13794053 = 2.0;
        double r13794054 = r13794052 * r13794053;
        double r13794055 = sqrt(r13794054);
        double r13794056 = r13794051 * r13794055;
        double r13794057 = t;
        double r13794058 = r13794057 * r13794057;
        double r13794059 = r13794058 / r13794053;
        double r13794060 = exp(r13794059);
        double r13794061 = r13794056 * r13794060;
        return r13794061;
}
↓
double f(double x, double y, double z, double t) {
        double r13794062 = x;
        double r13794063 = 0.5;
        double r13794064 = r13794062 * r13794063;
        double r13794065 = y;
        double r13794066 = r13794064 - r13794065;
        double r13794067 = z;
        double r13794068 = 2.0;
        double r13794069 = r13794067 * r13794068;
        double r13794070 = sqrt(r13794069);
        double r13794071 = r13794066 * r13794070;
        double r13794072 = t;
        double r13794073 = exp(r13794072);
        double r13794074 = r13794072 / r13794068;
        double r13794075 = pow(r13794073, r13794074);
        double r13794076 = r13794071 * r13794075;
        return r13794076;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2.0}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2.0}}}\]

  4. Applied times-frac0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2.0}}}\]

  5. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \color{blue}{{\left(e^{\frac{t}{1}}\right)}^{\left(\frac{t}{2.0}\right)}}\]

  6. Simplified0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\color{blue}{\left(e^{t}\right)}}^{\left(\frac{t}{2.0}\right)}\]

  7. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))