Average Error: 0.3 → 0.3
Time: 9.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)
double f(double x, double y, double z, double t) {
        double r699402 = x;
        double r699403 = 0.5;
        double r699404 = r699402 * r699403;
        double r699405 = y;
        double r699406 = r699404 - r699405;
        double r699407 = z;
        double r699408 = 2.0;
        double r699409 = r699407 * r699408;
        double r699410 = sqrt(r699409);
        double r699411 = r699406 * r699410;
        double r699412 = t;
        double r699413 = r699412 * r699412;
        double r699414 = r699413 / r699408;
        double r699415 = exp(r699414);
        double r699416 = r699411 * r699415;
        return r699416;
}
↓
double f(double x, double y, double z, double t) {
        double r699417 = x;
        double r699418 = 0.5;
        double r699419 = r699417 * r699418;
        double r699420 = y;
        double r699421 = r699419 - r699420;
        double r699422 = z;
        double r699423 = 2.0;
        double r699424 = r699422 * r699423;
        double r699425 = sqrt(r699424);
        double r699426 = t;
        double r699427 = r699426 * r699426;
        double r699428 = r699427 / r699423;
        double r699429 = exp(r699428);
        double r699430 = r699425 * r699429;
        double r699431 = r699421 * r699430;
        return r699431;
}

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 associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020100 
(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))))