Average Error: 0.3 → 0.5
Time: 9.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z} \cdot \sqrt{2}\right)\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z} \cdot \sqrt{2}\right)\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}
double f(double x, double y, double z, double t) {
        double r704856 = x;
        double r704857 = 0.5;
        double r704858 = r704856 * r704857;
        double r704859 = y;
        double r704860 = r704858 - r704859;
        double r704861 = z;
        double r704862 = 2.0;
        double r704863 = r704861 * r704862;
        double r704864 = sqrt(r704863);
        double r704865 = r704860 * r704864;
        double r704866 = t;
        double r704867 = r704866 * r704866;
        double r704868 = r704867 / r704862;
        double r704869 = exp(r704868);
        double r704870 = r704865 * r704869;
        return r704870;
}
↓
double f(double x, double y, double z, double t) {
        double r704871 = x;
        double r704872 = 0.5;
        double r704873 = r704871 * r704872;
        double r704874 = y;
        double r704875 = r704873 - r704874;
        double r704876 = z;
        double r704877 = sqrt(r704876);
        double r704878 = 2.0;
        double r704879 = sqrt(r704878);
        double r704880 = r704877 * r704879;
        double r704881 = r704875 * r704880;
        double r704882 = t;
        double r704883 = exp(r704882);
        double r704884 = r704882 / r704878;
        double r704885 = pow(r704883, r704884);
        double r704886 = r704881 * r704885;
        return r704886;
}

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 *-un-lft-identity0.3

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

  4. Applied times-frac0.3

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

  5. Applied exp-prod0.3

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

  6. Simplified0.3

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

  8. Applied sqrt-prod0.5

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

  9. Applied associate-*r*0.5

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

  11. Applied associate-*l*0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(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))))