Average Error: 0.3 → 0.5
Time: 26.6s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left({\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \sqrt{z}\right) \cdot \left(\sqrt{2} \cdot \left(x \cdot 0.5 - y\right)\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left({\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \sqrt{z}\right) \cdot \left(\sqrt{2} \cdot \left(x \cdot 0.5 - y\right)\right)
double f(double x, double y, double z, double t) {
        double r636641 = x;
        double r636642 = 0.5;
        double r636643 = r636641 * r636642;
        double r636644 = y;
        double r636645 = r636643 - r636644;
        double r636646 = z;
        double r636647 = 2.0;
        double r636648 = r636646 * r636647;
        double r636649 = sqrt(r636648);
        double r636650 = r636645 * r636649;
        double r636651 = t;
        double r636652 = r636651 * r636651;
        double r636653 = r636652 / r636647;
        double r636654 = exp(r636653);
        double r636655 = r636650 * r636654;
        return r636655;
}
↓
double f(double x, double y, double z, double t) {
        double r636656 = t;
        double r636657 = exp(r636656);
        double r636658 = 2.0;
        double r636659 = r636656 / r636658;
        double r636660 = pow(r636657, r636659);
        double r636661 = z;
        double r636662 = sqrt(r636661);
        double r636663 = r636660 * r636662;
        double r636664 = sqrt(r636658);
        double r636665 = x;
        double r636666 = 0.5;
        double r636667 = r636665 * r636666;
        double r636668 = y;
        double r636669 = r636667 - r636668;
        double r636670 = r636664 * r636669;
        double r636671 = r636663 * r636670;
        return r636671;
}

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
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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. Simplified0.3

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

  4. Applied sqrt-prod0.5

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

  5. Applied associate-*r*0.5

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

  6. Simplified0.5

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

  8. Applied *-un-lft-identity0.5

    \[\leadsto \color{blue}{\left(1 \cdot \left(x \cdot 0.5 - y\right)\right)} \cdot \left(\left(\sqrt{z} \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\right) \cdot \sqrt{2}\right)\]

  9. Applied associate-*l*0.5

    \[\leadsto \color{blue}{1 \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \left(\left(\sqrt{z} \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\right) \cdot \sqrt{2}\right)\right)}\]

  10. Simplified0.5

    \[\leadsto 1 \cdot \color{blue}{\left(\left(\left(0.5 \cdot x - y\right) \cdot \sqrt{2}\right) \cdot \left({\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \sqrt{z}\right)\right)}\]

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2019195 
(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))))