Average Error: 0.3 → 0.3
Time: 28.2s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\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 e^{\frac{t \cdot t}{2}}
double f(double x, double y, double z, double t) {
        double r649439 = x;
        double r649440 = 0.5;
        double r649441 = r649439 * r649440;
        double r649442 = y;
        double r649443 = r649441 - r649442;
        double r649444 = z;
        double r649445 = 2.0;
        double r649446 = r649444 * r649445;
        double r649447 = sqrt(r649446);
        double r649448 = r649443 * r649447;
        double r649449 = t;
        double r649450 = r649449 * r649449;
        double r649451 = r649450 / r649445;
        double r649452 = exp(r649451);
        double r649453 = r649448 * r649452;
        return r649453;
}
↓
double f(double x, double y, double z, double t) {
        double r649454 = x;
        double r649455 = 0.5;
        double r649456 = r649454 * r649455;
        double r649457 = y;
        double r649458 = r649456 - r649457;
        double r649459 = z;
        double r649460 = 2.0;
        double r649461 = r649459 * r649460;
        double r649462 = sqrt(r649461);
        double r649463 = r649458 * r649462;
        double r649464 = t;
        double r649465 = r649464 * r649464;
        double r649466 = r649465 / r649460;
        double r649467 = exp(r649466);
        double r649468 = r649463 * r649467;
        return r649468;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019194 
(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))))