Average Error: 0.3 → 0.3
Time: 25.6s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\sqrt[3]{t} \cdot \frac{t}{2}\right)}\]
\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^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\sqrt[3]{t} \cdot \frac{t}{2}\right)}
double f(double x, double y, double z, double t) {
        double r531309 = x;
        double r531310 = 0.5;
        double r531311 = r531309 * r531310;
        double r531312 = y;
        double r531313 = r531311 - r531312;
        double r531314 = z;
        double r531315 = 2.0;
        double r531316 = r531314 * r531315;
        double r531317 = sqrt(r531316);
        double r531318 = r531313 * r531317;
        double r531319 = t;
        double r531320 = r531319 * r531319;
        double r531321 = r531320 / r531315;
        double r531322 = exp(r531321);
        double r531323 = r531318 * r531322;
        return r531323;
}
↓
double f(double x, double y, double z, double t) {
        double r531324 = x;
        double r531325 = 0.5;
        double r531326 = r531324 * r531325;
        double r531327 = y;
        double r531328 = r531326 - r531327;
        double r531329 = z;
        double r531330 = 2.0;
        double r531331 = r531329 * r531330;
        double r531332 = sqrt(r531331);
        double r531333 = r531328 * r531332;
        double r531334 = t;
        double r531335 = cbrt(r531334);
        double r531336 = r531335 * r531335;
        double r531337 = exp(r531336);
        double r531338 = r531334 / r531330;
        double r531339 = r531335 * r531338;
        double r531340 = pow(r531337, r531339);
        double r531341 = r531333 * r531340;
        return r531341;
}

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 add-cube-cbrt0.3

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

  9. Applied exp-prod0.3

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

  10. Applied pow-pow0.3

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

  11. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\sqrt[3]{t} \cdot \frac{t}{2}\right)}\]

Reproduce

herbie shell --seed 2019304 
(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))))