Average Error: 0.3 → 0.3
Time: 9.7s
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 r1066448 = x;
        double r1066449 = 0.5;
        double r1066450 = r1066448 * r1066449;
        double r1066451 = y;
        double r1066452 = r1066450 - r1066451;
        double r1066453 = z;
        double r1066454 = 2.0;
        double r1066455 = r1066453 * r1066454;
        double r1066456 = sqrt(r1066455);
        double r1066457 = r1066452 * r1066456;
        double r1066458 = t;
        double r1066459 = r1066458 * r1066458;
        double r1066460 = r1066459 / r1066454;
        double r1066461 = exp(r1066460);
        double r1066462 = r1066457 * r1066461;
        return r1066462;
}
↓
double f(double x, double y, double z, double t) {
        double r1066463 = x;
        double r1066464 = 0.5;
        double r1066465 = r1066463 * r1066464;
        double r1066466 = y;
        double r1066467 = r1066465 - r1066466;
        double r1066468 = z;
        double r1066469 = 2.0;
        double r1066470 = r1066468 * r1066469;
        double r1066471 = sqrt(r1066470);
        double r1066472 = r1066467 * r1066471;
        double r1066473 = t;
        double r1066474 = r1066473 * r1066473;
        double r1066475 = r1066474 / r1066469;
        double r1066476 = exp(r1066475);
        double r1066477 = r1066472 * r1066476;
        return r1066477;
}

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 2019353 
(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))))