Average Error: 0.3 → 0.5
Time: 23.9s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[e^{\frac{t \cdot t}{2}} \cdot \left(\sqrt{2} \cdot \left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\right)\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
e^{\frac{t \cdot t}{2}} \cdot \left(\sqrt{2} \cdot \left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r31428857 = x;
        double r31428858 = 0.5;
        double r31428859 = r31428857 * r31428858;
        double r31428860 = y;
        double r31428861 = r31428859 - r31428860;
        double r31428862 = z;
        double r31428863 = 2.0;
        double r31428864 = r31428862 * r31428863;
        double r31428865 = sqrt(r31428864);
        double r31428866 = r31428861 * r31428865;
        double r31428867 = t;
        double r31428868 = r31428867 * r31428867;
        double r31428869 = r31428868 / r31428863;
        double r31428870 = exp(r31428869);
        double r31428871 = r31428866 * r31428870;
        return r31428871;
}
↓
double f(double x, double y, double z, double t) {
        double r31428872 = t;
        double r31428873 = r31428872 * r31428872;
        double r31428874 = 2.0;
        double r31428875 = r31428873 / r31428874;
        double r31428876 = exp(r31428875);
        double r31428877 = sqrt(r31428874);
        double r31428878 = z;
        double r31428879 = sqrt(r31428878);
        double r31428880 = x;
        double r31428881 = 0.5;
        double r31428882 = r31428880 * r31428881;
        double r31428883 = y;
        double r31428884 = r31428882 - r31428883;
        double r31428885 = r31428879 * r31428884;
        double r31428886 = r31428877 * r31428885;
        double r31428887 = r31428876 * r31428886;
        return r31428887;
}

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
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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 sqrt-prod0.5

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

  4. Applied associate-*r*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019170 +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))))