Average Error: 0.3 → 0.3
Time: 12.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\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 r745601 = x;
        double r745602 = 0.5;
        double r745603 = r745601 * r745602;
        double r745604 = y;
        double r745605 = r745603 - r745604;
        double r745606 = z;
        double r745607 = 2.0;
        double r745608 = r745606 * r745607;
        double r745609 = sqrt(r745608);
        double r745610 = r745605 * r745609;
        double r745611 = t;
        double r745612 = r745611 * r745611;
        double r745613 = r745612 / r745607;
        double r745614 = exp(r745613);
        double r745615 = r745610 * r745614;
        return r745615;
}
↓
double f(double x, double y, double z, double t) {
        double r745616 = x;
        double r745617 = 0.5;
        double r745618 = r745616 * r745617;
        double r745619 = y;
        double r745620 = r745618 - r745619;
        double r745621 = z;
        double r745622 = 2.0;
        double r745623 = r745621 * r745622;
        double r745624 = sqrt(r745623);
        double r745625 = r745620 * r745624;
        double r745626 = t;
        double r745627 = r745626 * r745626;
        double r745628 = r745627 / r745622;
        double r745629 = exp(r745628);
        double r745630 = r745625 * r745629;
        return r745630;
}

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 2020035 +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))))