Average Error: 0.3 → 0.3
Time: 24.4s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}
double f(double x, double y, double z, double t) {
        double r26887457 = x;
        double r26887458 = 0.5;
        double r26887459 = r26887457 * r26887458;
        double r26887460 = y;
        double r26887461 = r26887459 - r26887460;
        double r26887462 = z;
        double r26887463 = 2.0;
        double r26887464 = r26887462 * r26887463;
        double r26887465 = sqrt(r26887464);
        double r26887466 = r26887461 * r26887465;
        double r26887467 = t;
        double r26887468 = r26887467 * r26887467;
        double r26887469 = r26887468 / r26887463;
        double r26887470 = exp(r26887469);
        double r26887471 = r26887466 * r26887470;
        return r26887471;
}
↓
double f(double x, double y, double z, double t) {
        double r26887472 = t;
        double r26887473 = exp(r26887472);
        double r26887474 = 2.0;
        double r26887475 = r26887472 / r26887474;
        double r26887476 = pow(r26887473, r26887475);
        double r26887477 = sqrt(r26887476);
        double r26887478 = x;
        double r26887479 = 0.5;
        double r26887480 = r26887478 * r26887479;
        double r26887481 = y;
        double r26887482 = r26887480 - r26887481;
        double r26887483 = z;
        double r26887484 = r26887483 * r26887474;
        double r26887485 = sqrt(r26887484);
        double r26887486 = r26887482 * r26887485;
        double r26887487 = r26887477 * r26887486;
        double r26887488 = r26887487 * r26887477;
        return r26887488;
}

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-sqr-sqrt0.3

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

  9. Applied associate-*r*0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019171 
(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 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))