Average Error: 0.3 → 0.3
Time: 25.9s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}
double f(double x, double y, double z, double t) {
        double r31595904 = x;
        double r31595905 = 0.5;
        double r31595906 = r31595904 * r31595905;
        double r31595907 = y;
        double r31595908 = r31595906 - r31595907;
        double r31595909 = z;
        double r31595910 = 2.0;
        double r31595911 = r31595909 * r31595910;
        double r31595912 = sqrt(r31595911);
        double r31595913 = r31595908 * r31595912;
        double r31595914 = t;
        double r31595915 = r31595914 * r31595914;
        double r31595916 = r31595915 / r31595910;
        double r31595917 = exp(r31595916);
        double r31595918 = r31595913 * r31595917;
        return r31595918;
}
↓
double f(double x, double y, double z, double t) {
        double r31595919 = t;
        double r31595920 = r31595919 * r31595919;
        double r31595921 = 2.0;
        double r31595922 = r31595920 / r31595921;
        double r31595923 = exp(r31595922);
        double r31595924 = sqrt(r31595923);
        double r31595925 = x;
        double r31595926 = 0.5;
        double r31595927 = r31595925 * r31595926;
        double r31595928 = y;
        double r31595929 = r31595927 - r31595928;
        double r31595930 = z;
        double r31595931 = r31595930 * r31595921;
        double r31595932 = sqrt(r31595931);
        double r31595933 = r31595929 * r31595932;
        double r31595934 = r31595924 * r31595933;
        double r31595935 = r31595934 * r31595924;
        return r31595935;
}

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
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

Derivation

  1. Initial program 0.3

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

  3. Applied add-sqr-sqrt0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{\left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right)}\]

  4. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}}\]

  5. Final simplification0.3

    \[\leadsto \left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\]

Reproduce

herbie shell --seed 2019172 +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 1.0) (/ (* t t) 2.0)))

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