Average Error: 0.3 → 0.3
Time: 23.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t + t}\right)}^{\left(\frac{\frac{t}{2}}{2}\right)}\]
\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 {\left(e^{t + t}\right)}^{\left(\frac{\frac{t}{2}}{2}\right)}
double f(double x, double y, double z, double t) {
        double r659587 = x;
        double r659588 = 0.5;
        double r659589 = r659587 * r659588;
        double r659590 = y;
        double r659591 = r659589 - r659590;
        double r659592 = z;
        double r659593 = 2.0;
        double r659594 = r659592 * r659593;
        double r659595 = sqrt(r659594);
        double r659596 = r659591 * r659595;
        double r659597 = t;
        double r659598 = r659597 * r659597;
        double r659599 = r659598 / r659593;
        double r659600 = exp(r659599);
        double r659601 = r659596 * r659600;
        return r659601;
}
↓
double f(double x, double y, double z, double t) {
        double r659602 = x;
        double r659603 = 0.5;
        double r659604 = r659602 * r659603;
        double r659605 = y;
        double r659606 = r659604 - r659605;
        double r659607 = z;
        double r659608 = 2.0;
        double r659609 = r659607 * r659608;
        double r659610 = sqrt(r659609);
        double r659611 = r659606 * r659610;
        double r659612 = t;
        double r659613 = r659612 + r659612;
        double r659614 = exp(r659613);
        double r659615 = r659612 / r659608;
        double r659616 = 2.0;
        double r659617 = r659615 / r659616;
        double r659618 = pow(r659614, r659617);
        double r659619 = r659611 * r659618;
        return r659619;
}

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 *-un-lft-identity0.3

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

  4. Applied times-frac0.3

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

  5. Applied exp-prod0.3

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

  6. Simplified0.3

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

  8. Applied sqr-pow0.3

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

  10. Applied pow-prod-down0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019326 
(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))))