Average Error: 0.3 → 0.3
Time: 9.9s
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 r840938 = x;
        double r840939 = 0.5;
        double r840940 = r840938 * r840939;
        double r840941 = y;
        double r840942 = r840940 - r840941;
        double r840943 = z;
        double r840944 = 2.0;
        double r840945 = r840943 * r840944;
        double r840946 = sqrt(r840945);
        double r840947 = r840942 * r840946;
        double r840948 = t;
        double r840949 = r840948 * r840948;
        double r840950 = r840949 / r840944;
        double r840951 = exp(r840950);
        double r840952 = r840947 * r840951;
        return r840952;
}
↓
double f(double x, double y, double z, double t) {
        double r840953 = x;
        double r840954 = 0.5;
        double r840955 = r840953 * r840954;
        double r840956 = y;
        double r840957 = r840955 - r840956;
        double r840958 = z;
        double r840959 = 2.0;
        double r840960 = r840958 * r840959;
        double r840961 = sqrt(r840960);
        double r840962 = r840957 * r840961;
        double r840963 = t;
        double r840964 = r840963 * r840963;
        double r840965 = r840964 / r840959;
        double r840966 = exp(r840965);
        double r840967 = r840962 * r840966;
        return r840967;
}

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 2019354 
(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))))