Average Error: 0.3 → 0.3
Time: 10.5s
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 r885622 = x;
        double r885623 = 0.5;
        double r885624 = r885622 * r885623;
        double r885625 = y;
        double r885626 = r885624 - r885625;
        double r885627 = z;
        double r885628 = 2.0;
        double r885629 = r885627 * r885628;
        double r885630 = sqrt(r885629);
        double r885631 = r885626 * r885630;
        double r885632 = t;
        double r885633 = r885632 * r885632;
        double r885634 = r885633 / r885628;
        double r885635 = exp(r885634);
        double r885636 = r885631 * r885635;
        return r885636;
}
↓
double f(double x, double y, double z, double t) {
        double r885637 = x;
        double r885638 = 0.5;
        double r885639 = r885637 * r885638;
        double r885640 = y;
        double r885641 = r885639 - r885640;
        double r885642 = z;
        double r885643 = 2.0;
        double r885644 = r885642 * r885643;
        double r885645 = sqrt(r885644);
        double r885646 = r885641 * r885645;
        double r885647 = t;
        double r885648 = r885647 * r885647;
        double r885649 = r885648 / r885643;
        double r885650 = exp(r885649);
        double r885651 = r885646 * r885650;
        return r885651;
}

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 2019353 +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))))