Average Error: 0.3 → 0.5
Time: 8.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z} \cdot \left(\sqrt{2} \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\right)\right)\]
\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 \left(\sqrt{2} \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\right)\right)
double f(double x, double y, double z, double t) {
        double r939927 = x;
        double r939928 = 0.5;
        double r939929 = r939927 * r939928;
        double r939930 = y;
        double r939931 = r939929 - r939930;
        double r939932 = z;
        double r939933 = 2.0;
        double r939934 = r939932 * r939933;
        double r939935 = sqrt(r939934);
        double r939936 = r939931 * r939935;
        double r939937 = t;
        double r939938 = r939937 * r939937;
        double r939939 = r939938 / r939933;
        double r939940 = exp(r939939);
        double r939941 = r939936 * r939940;
        return r939941;
}
↓
double f(double x, double y, double z, double t) {
        double r939942 = x;
        double r939943 = 0.5;
        double r939944 = r939942 * r939943;
        double r939945 = y;
        double r939946 = r939944 - r939945;
        double r939947 = z;
        double r939948 = sqrt(r939947);
        double r939949 = 2.0;
        double r939950 = sqrt(r939949);
        double r939951 = exp(1.0);
        double r939952 = t;
        double r939953 = r939952 * r939952;
        double r939954 = r939953 / r939949;
        double r939955 = pow(r939951, r939954);
        double r939956 = r939950 * r939955;
        double r939957 = r939948 * r939956;
        double r939958 = r939946 * r939957;
        return r939958;
}

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

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

  4. Applied exp-prod0.3

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

  5. Simplified0.3

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

  7. Applied associate-*l*0.3

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

  9. Applied sqrt-prod0.5

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

  10. Applied associate-*l*0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2020083 +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))))