Average Error: 0.3 → 0.3
Time: 22.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)
double f(double x, double y, double z, double t) {
        double r522924 = x;
        double r522925 = 0.5;
        double r522926 = r522924 * r522925;
        double r522927 = y;
        double r522928 = r522926 - r522927;
        double r522929 = z;
        double r522930 = 2.0;
        double r522931 = r522929 * r522930;
        double r522932 = sqrt(r522931);
        double r522933 = r522928 * r522932;
        double r522934 = t;
        double r522935 = r522934 * r522934;
        double r522936 = r522935 / r522930;
        double r522937 = exp(r522936);
        double r522938 = r522933 * r522937;
        return r522938;
}
↓
double f(double x, double y, double z, double t) {
        double r522939 = x;
        double r522940 = 0.5;
        double r522941 = r522939 * r522940;
        double r522942 = y;
        double r522943 = r522941 - r522942;
        double r522944 = z;
        double r522945 = 2.0;
        double r522946 = r522944 * r522945;
        double r522947 = sqrt(r522946);
        double r522948 = t;
        double r522949 = r522948 * r522948;
        double r522950 = r522949 / r522945;
        double r522951 = exp(r522950);
        double r522952 = r522947 * r522951;
        double r522953 = r522943 * r522952;
        return r522953;
}

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 associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"
  :precision binary64

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2))) (pow (exp 1) (/ (* t t) 2)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2))) (exp (/ (* t t) 2))))