Average Error: 0.3 → 0.5
Time: 8.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z} \cdot \left(\sqrt{2} \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\right)\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z} \cdot \left(\sqrt{2} \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\right)\right)
double f(double x, double y, double z, double t) {
        double r932315 = x;
        double r932316 = 0.5;
        double r932317 = r932315 * r932316;
        double r932318 = y;
        double r932319 = r932317 - r932318;
        double r932320 = z;
        double r932321 = 2.0;
        double r932322 = r932320 * r932321;
        double r932323 = sqrt(r932322);
        double r932324 = r932319 * r932323;
        double r932325 = t;
        double r932326 = r932325 * r932325;
        double r932327 = r932326 / r932321;
        double r932328 = exp(r932327);
        double r932329 = r932324 * r932328;
        return r932329;
}
↓
double f(double x, double y, double z, double t) {
        double r932330 = x;
        double r932331 = 0.5;
        double r932332 = r932330 * r932331;
        double r932333 = y;
        double r932334 = r932332 - r932333;
        double r932335 = z;
        double r932336 = sqrt(r932335);
        double r932337 = 2.0;
        double r932338 = sqrt(r932337);
        double r932339 = exp(1.0);
        double r932340 = t;
        double r932341 = r932340 * r932340;
        double r932342 = r932341 / r932337;
        double r932343 = pow(r932339, r932342);
        double r932344 = r932338 * r932343;
        double r932345 = r932336 * r932344;
        double r932346 = r932334 * r932345;
        return r932346;
}

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
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\color{blue}{1 \cdot \frac{t \cdot t}{2}}}\]

  4. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}}\]

  5. Simplified0.3

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

  7. Applied associate-*l*0.3

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

  9. Applied sqrt-prod0.5

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

  10. Applied associate-*l*0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2020083 
(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))))