Average Error: 0.3 → 0.3
Time: 13.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{t \cdot t}{2}} \cdot \sqrt{z \cdot 2}\right)\]
\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(e^{\frac{t \cdot t}{2}} \cdot \sqrt{z \cdot 2}\right)
double f(double x, double y, double z, double t) {
        double r929992 = x;
        double r929993 = 0.5;
        double r929994 = r929992 * r929993;
        double r929995 = y;
        double r929996 = r929994 - r929995;
        double r929997 = z;
        double r929998 = 2.0;
        double r929999 = r929997 * r929998;
        double r930000 = sqrt(r929999);
        double r930001 = r929996 * r930000;
        double r930002 = t;
        double r930003 = r930002 * r930002;
        double r930004 = r930003 / r929998;
        double r930005 = exp(r930004);
        double r930006 = r930001 * r930005;
        return r930006;
}
↓
double f(double x, double y, double z, double t) {
        double r930007 = x;
        double r930008 = 0.5;
        double r930009 = r930007 * r930008;
        double r930010 = y;
        double r930011 = r930009 - r930010;
        double r930012 = t;
        double r930013 = r930012 * r930012;
        double r930014 = 2.0;
        double r930015 = r930013 / r930014;
        double r930016 = exp(r930015);
        double r930017 = z;
        double r930018 = r930017 * r930014;
        double r930019 = sqrt(r930018);
        double r930020 = r930016 * r930019;
        double r930021 = r930011 * r930020;
        return r930021;
}

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. Simplified0.3

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

  5. Final simplification0.3

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

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))))