Average Error: 0.3 → 0.3
Time: 24.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\sqrt{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\]
\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^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}
double f(double x, double y, double z, double t) {
        double r25889379 = x;
        double r25889380 = 0.5;
        double r25889381 = r25889379 * r25889380;
        double r25889382 = y;
        double r25889383 = r25889381 - r25889382;
        double r25889384 = z;
        double r25889385 = 2.0;
        double r25889386 = r25889384 * r25889385;
        double r25889387 = sqrt(r25889386);
        double r25889388 = r25889383 * r25889387;
        double r25889389 = t;
        double r25889390 = r25889389 * r25889389;
        double r25889391 = r25889390 / r25889385;
        double r25889392 = exp(r25889391);
        double r25889393 = r25889388 * r25889392;
        return r25889393;
}
↓
double f(double x, double y, double z, double t) {
        double r25889394 = t;
        double r25889395 = cbrt(r25889394);
        double r25889396 = r25889395 * r25889395;
        double r25889397 = exp(r25889396);
        double r25889398 = 2.0;
        double r25889399 = r25889394 / r25889398;
        double r25889400 = r25889399 * r25889395;
        double r25889401 = pow(r25889397, r25889400);
        double r25889402 = sqrt(r25889401);
        double r25889403 = x;
        double r25889404 = 0.5;
        double r25889405 = r25889403 * r25889404;
        double r25889406 = y;
        double r25889407 = r25889405 - r25889406;
        double r25889408 = z;
        double r25889409 = r25889408 * r25889398;
        double r25889410 = sqrt(r25889409);
        double r25889411 = r25889407 * r25889410;
        double r25889412 = r25889402 * r25889411;
        double r25889413 = exp(r25889394);
        double r25889414 = pow(r25889413, r25889399);
        double r25889415 = sqrt(r25889414);
        double r25889416 = r25889412 * r25889415;
        return r25889416;
}

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

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

  12. Applied exp-prod0.3

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

  13. Applied pow-pow0.3

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

  14. Final simplification0.3

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

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))))