Average Error: 0.3 → 0.3
Time: 24.3s
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 r38829468 = x;
        double r38829469 = 0.5;
        double r38829470 = r38829468 * r38829469;
        double r38829471 = y;
        double r38829472 = r38829470 - r38829471;
        double r38829473 = z;
        double r38829474 = 2.0;
        double r38829475 = r38829473 * r38829474;
        double r38829476 = sqrt(r38829475);
        double r38829477 = r38829472 * r38829476;
        double r38829478 = t;
        double r38829479 = r38829478 * r38829478;
        double r38829480 = r38829479 / r38829474;
        double r38829481 = exp(r38829480);
        double r38829482 = r38829477 * r38829481;
        return r38829482;
}
↓
double f(double x, double y, double z, double t) {
        double r38829483 = t;
        double r38829484 = exp(r38829483);
        double r38829485 = 2.0;
        double r38829486 = r38829483 / r38829485;
        double r38829487 = pow(r38829484, r38829486);
        double r38829488 = sqrt(r38829487);
        double r38829489 = x;
        double r38829490 = 0.5;
        double r38829491 = r38829489 * r38829490;
        double r38829492 = y;
        double r38829493 = r38829491 - r38829492;
        double r38829494 = z;
        double r38829495 = r38829494 * r38829485;
        double r38829496 = sqrt(r38829495);
        double r38829497 = r38829493 * r38829496;
        double r38829498 = r38829488 * r38829497;
        double r38829499 = cbrt(r38829483);
        double r38829500 = r38829499 * r38829499;
        double r38829501 = exp(r38829500);
        double r38829502 = r38829486 * r38829499;
        double r38829503 = pow(r38829501, r38829502);
        double r38829504 = sqrt(r38829503);
        double r38829505 = r38829498 * r38829504;
        return r38829505;
}

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 
(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))))