Average Error: 0.3 → 0.3
Time: 8.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\right)\]
\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 {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\right)
double f(double x, double y, double z, double t) {
        double r813964 = x;
        double r813965 = 0.5;
        double r813966 = r813964 * r813965;
        double r813967 = y;
        double r813968 = r813966 - r813967;
        double r813969 = z;
        double r813970 = 2.0;
        double r813971 = r813969 * r813970;
        double r813972 = sqrt(r813971);
        double r813973 = r813968 * r813972;
        double r813974 = t;
        double r813975 = r813974 * r813974;
        double r813976 = r813975 / r813970;
        double r813977 = exp(r813976);
        double r813978 = r813973 * r813977;
        return r813978;
}
↓
double f(double x, double y, double z, double t) {
        double r813979 = x;
        double r813980 = 0.5;
        double r813981 = r813979 * r813980;
        double r813982 = y;
        double r813983 = r813981 - r813982;
        double r813984 = z;
        double r813985 = 2.0;
        double r813986 = r813984 * r813985;
        double r813987 = sqrt(r813986);
        double r813988 = t;
        double r813989 = exp(r813988);
        double r813990 = r813988 / r813985;
        double r813991 = pow(r813989, r813990);
        double r813992 = r813987 * r813991;
        double r813993 = r813983 * r813992;
        return r813993;
}

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 *-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 associate-*l*0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 +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))))