Average Error: 0.3 → 0.3
Time: 26.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}}
double f(double x, double y, double z, double t) {
        double r23206440 = x;
        double r23206441 = 0.5;
        double r23206442 = r23206440 * r23206441;
        double r23206443 = y;
        double r23206444 = r23206442 - r23206443;
        double r23206445 = z;
        double r23206446 = 2.0;
        double r23206447 = r23206445 * r23206446;
        double r23206448 = sqrt(r23206447);
        double r23206449 = r23206444 * r23206448;
        double r23206450 = t;
        double r23206451 = r23206450 * r23206450;
        double r23206452 = r23206451 / r23206446;
        double r23206453 = exp(r23206452);
        double r23206454 = r23206449 * r23206453;
        return r23206454;
}
↓
double f(double x, double y, double z, double t) {
        double r23206455 = t;
        double r23206456 = exp(r23206455);
        double r23206457 = 2.0;
        double r23206458 = r23206455 / r23206457;
        double r23206459 = pow(r23206456, r23206458);
        double r23206460 = sqrt(r23206459);
        double r23206461 = x;
        double r23206462 = 0.5;
        double r23206463 = r23206461 * r23206462;
        double r23206464 = y;
        double r23206465 = r23206463 - r23206464;
        double r23206466 = z;
        double r23206467 = r23206466 * r23206457;
        double r23206468 = sqrt(r23206467);
        double r23206469 = r23206465 * r23206468;
        double r23206470 = r23206460 * r23206469;
        double r23206471 = cbrt(r23206455);
        double r23206472 = r23206471 * r23206471;
        double r23206473 = exp(r23206472);
        double r23206474 = r23206458 * r23206471;
        double r23206475 = pow(r23206473, r23206474);
        double r23206476 = sqrt(r23206475);
        double r23206477 = r23206470 * r23206476;
        return r23206477;
}

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
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2.0}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2.0}}}\]

  4. Applied times-frac0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2.0}}}\]

  5. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \color{blue}{{\left(e^{\frac{t}{1}}\right)}^{\left(\frac{t}{2.0}\right)}}\]

  6. Simplified0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\color{blue}{\left(e^{t}\right)}}^{\left(\frac{t}{2.0}\right)}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \color{blue}{\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right)}\]

  9. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right) \cdot \sqrt{{\left(e^{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\right)}^{\left(\frac{t}{2.0}\right)}}\]

  12. Applied exp-prod0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right) \cdot \sqrt{{\color{blue}{\left({\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\sqrt[3]{t}\right)}\right)}}^{\left(\frac{t}{2.0}\right)}}\]

  13. Applied pow-pow0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right) \cdot \sqrt{\color{blue}{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\sqrt[3]{t} \cdot \frac{t}{2.0}\right)}}}\]

  14. Final simplification0.3

    \[\leadsto \left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))