Average Error: 0.3 → 0.3
Time: 23.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt{e^{\frac{t \cdot t}{2}}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}
double f(double x, double y, double z, double t) {
        double r37096634 = x;
        double r37096635 = 0.5;
        double r37096636 = r37096634 * r37096635;
        double r37096637 = y;
        double r37096638 = r37096636 - r37096637;
        double r37096639 = z;
        double r37096640 = 2.0;
        double r37096641 = r37096639 * r37096640;
        double r37096642 = sqrt(r37096641);
        double r37096643 = r37096638 * r37096642;
        double r37096644 = t;
        double r37096645 = r37096644 * r37096644;
        double r37096646 = r37096645 / r37096640;
        double r37096647 = exp(r37096646);
        double r37096648 = r37096643 * r37096647;
        return r37096648;
}
↓
double f(double x, double y, double z, double t) {
        double r37096649 = t;
        double r37096650 = r37096649 * r37096649;
        double r37096651 = 2.0;
        double r37096652 = r37096650 / r37096651;
        double r37096653 = exp(r37096652);
        double r37096654 = sqrt(r37096653);
        double r37096655 = x;
        double r37096656 = 0.5;
        double r37096657 = r37096655 * r37096656;
        double r37096658 = y;
        double r37096659 = r37096657 - r37096658;
        double r37096660 = z;
        double r37096661 = r37096660 * r37096651;
        double r37096662 = sqrt(r37096661);
        double r37096663 = r37096659 * r37096662;
        double r37096664 = r37096654 * r37096663;
        double r37096665 = r37096664 * r37096654;
        return r37096665;
}

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

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

Reproduce

herbie shell --seed 2019174 
(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))))