Average Error: 0.3 → 0.3
Time: 7.4s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\]
\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^{t}\right)}^{\left(\frac{t}{2}\right)}
double f(double x, double y, double z, double t) {
        double r807322 = x;
        double r807323 = 0.5;
        double r807324 = r807322 * r807323;
        double r807325 = y;
        double r807326 = r807324 - r807325;
        double r807327 = z;
        double r807328 = 2.0;
        double r807329 = r807327 * r807328;
        double r807330 = sqrt(r807329);
        double r807331 = r807326 * r807330;
        double r807332 = t;
        double r807333 = r807332 * r807332;
        double r807334 = r807333 / r807328;
        double r807335 = exp(r807334);
        double r807336 = r807331 * r807335;
        return r807336;
}
↓
double f(double x, double y, double z, double t) {
        double r807337 = x;
        double r807338 = 0.5;
        double r807339 = r807337 * r807338;
        double r807340 = y;
        double r807341 = r807339 - r807340;
        double r807342 = z;
        double r807343 = 2.0;
        double r807344 = r807342 * r807343;
        double r807345 = sqrt(r807344);
        double r807346 = r807341 * r807345;
        double r807347 = t;
        double r807348 = exp(r807347);
        double r807349 = r807347 / r807343;
        double r807350 = pow(r807348, r807349);
        double r807351 = r807346 * r807350;
        return r807351;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

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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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(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))))