Average Error: 0.3 → 0.3
Time: 21.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 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}}
double f(double x, double y, double z, double t) {
        double r609923 = x;
        double r609924 = 0.5;
        double r609925 = r609923 * r609924;
        double r609926 = y;
        double r609927 = r609925 - r609926;
        double r609928 = z;
        double r609929 = 2.0;
        double r609930 = r609928 * r609929;
        double r609931 = sqrt(r609930);
        double r609932 = r609927 * r609931;
        double r609933 = t;
        double r609934 = r609933 * r609933;
        double r609935 = r609934 / r609929;
        double r609936 = exp(r609935);
        double r609937 = r609932 * r609936;
        return r609937;
}
↓
double f(double x, double y, double z, double t) {
        double r609938 = x;
        double r609939 = 0.5;
        double r609940 = r609938 * r609939;
        double r609941 = y;
        double r609942 = r609940 - r609941;
        double r609943 = z;
        double r609944 = 2.0;
        double r609945 = r609943 * r609944;
        double r609946 = sqrt(r609945);
        double r609947 = r609942 * r609946;
        double r609948 = t;
        double r609949 = r609948 * r609948;
        double r609950 = r609949 / r609944;
        double r609951 = exp(r609950);
        double r609952 = r609947 * r609951;
        return r609952;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019303 +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))))