Average Error: 0.3 → 0.3
Time: 25.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}
double f(double x, double y, double z, double t) {
        double r50688966 = x;
        double r50688967 = 0.5;
        double r50688968 = r50688966 * r50688967;
        double r50688969 = y;
        double r50688970 = r50688968 - r50688969;
        double r50688971 = z;
        double r50688972 = 2.0;
        double r50688973 = r50688971 * r50688972;
        double r50688974 = sqrt(r50688973);
        double r50688975 = r50688970 * r50688974;
        double r50688976 = t;
        double r50688977 = r50688976 * r50688976;
        double r50688978 = r50688977 / r50688972;
        double r50688979 = exp(r50688978);
        double r50688980 = r50688975 * r50688979;
        return r50688980;
}
↓
double f(double x, double y, double z, double t) {
        double r50688981 = x;
        double r50688982 = 0.5;
        double r50688983 = r50688981 * r50688982;
        double r50688984 = y;
        double r50688985 = r50688983 - r50688984;
        double r50688986 = z;
        double r50688987 = 2.0;
        double r50688988 = r50688986 * r50688987;
        double r50688989 = sqrt(r50688988);
        double r50688990 = r50688985 * r50688989;
        double r50688991 = t;
        double r50688992 = r50688991 * r50688991;
        double r50688993 = r50688992 / r50688987;
        double r50688994 = exp(r50688993);
        double r50688995 = sqrt(r50688994);
        double r50688996 = r50688990 * r50688995;
        double r50688997 = r50688996 * r50688995;
        return r50688997;
}

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 add-sqr-sqrt0.3

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

  4. Applied associate-*r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))