Average Error: 0.3 → 0.3
Time: 25.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}
double f(double x, double y, double z, double t) {
        double r27923358 = x;
        double r27923359 = 0.5;
        double r27923360 = r27923358 * r27923359;
        double r27923361 = y;
        double r27923362 = r27923360 - r27923361;
        double r27923363 = z;
        double r27923364 = 2.0;
        double r27923365 = r27923363 * r27923364;
        double r27923366 = sqrt(r27923365);
        double r27923367 = r27923362 * r27923366;
        double r27923368 = t;
        double r27923369 = r27923368 * r27923368;
        double r27923370 = r27923369 / r27923364;
        double r27923371 = exp(r27923370);
        double r27923372 = r27923367 * r27923371;
        return r27923372;
}
↓
double f(double x, double y, double z, double t) {
        double r27923373 = x;
        double r27923374 = 0.5;
        double r27923375 = r27923373 * r27923374;
        double r27923376 = y;
        double r27923377 = r27923375 - r27923376;
        double r27923378 = z;
        double r27923379 = 2.0;
        double r27923380 = r27923378 * r27923379;
        double r27923381 = sqrt(r27923380);
        double r27923382 = r27923377 * r27923381;
        double r27923383 = t;
        double r27923384 = exp(r27923383);
        double r27923385 = r27923383 / r27923379;
        double r27923386 = pow(r27923384, r27923385);
        double r27923387 = r27923382 * r27923386;
        return r27923387;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019158 +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))))