Average Error: 0.3 → 0.3
Time: 23.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\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}}}
double f(double x, double y, double z, double t) {
        double r528954 = x;
        double r528955 = 0.5;
        double r528956 = r528954 * r528955;
        double r528957 = y;
        double r528958 = r528956 - r528957;
        double r528959 = z;
        double r528960 = 2.0;
        double r528961 = r528959 * r528960;
        double r528962 = sqrt(r528961);
        double r528963 = r528958 * r528962;
        double r528964 = t;
        double r528965 = r528964 * r528964;
        double r528966 = r528965 / r528960;
        double r528967 = exp(r528966);
        double r528968 = r528963 * r528967;
        return r528968;
}
↓
double f(double x, double y, double z, double t) {
        double r528969 = x;
        double r528970 = 0.5;
        double r528971 = r528969 * r528970;
        double r528972 = y;
        double r528973 = r528971 - r528972;
        double r528974 = z;
        double r528975 = 2.0;
        double r528976 = r528974 * r528975;
        double r528977 = sqrt(r528976);
        double r528978 = r528973 * r528977;
        double r528979 = t;
        double r528980 = r528979 * r528979;
        double r528981 = r528980 / r528975;
        double r528982 = exp(r528981);
        double r528983 = sqrt(r528982);
        double r528984 = r528978 * r528983;
        double r528985 = r528984 * r528983;
        return r528985;
}

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

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

Reproduce

herbie shell --seed 2019208 
(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))))