Average Error: 0.3 → 0.3
Time: 14.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left({\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \sqrt{z \cdot 2}\right)\]
\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({\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \sqrt{z \cdot 2}\right)
double f(double x, double y, double z, double t) {
        double r903401 = x;
        double r903402 = 0.5;
        double r903403 = r903401 * r903402;
        double r903404 = y;
        double r903405 = r903403 - r903404;
        double r903406 = z;
        double r903407 = 2.0;
        double r903408 = r903406 * r903407;
        double r903409 = sqrt(r903408);
        double r903410 = r903405 * r903409;
        double r903411 = t;
        double r903412 = r903411 * r903411;
        double r903413 = r903412 / r903407;
        double r903414 = exp(r903413);
        double r903415 = r903410 * r903414;
        return r903415;
}
↓
double f(double x, double y, double z, double t) {
        double r903416 = x;
        double r903417 = 0.5;
        double r903418 = r903416 * r903417;
        double r903419 = y;
        double r903420 = r903418 - r903419;
        double r903421 = t;
        double r903422 = exp(r903421);
        double r903423 = 2.0;
        double r903424 = r903421 / r903423;
        double r903425 = pow(r903422, r903424);
        double r903426 = z;
        double r903427 = r903426 * r903423;
        double r903428 = sqrt(r903427);
        double r903429 = r903425 * r903428;
        double r903430 = r903420 * r903429;
        return r903430;
}

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 associate-*l*0.3

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(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))))