Average Error: 0.3 → 0.3
Time: 9.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\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 r816996 = x;
        double r816997 = 0.5;
        double r816998 = r816996 * r816997;
        double r816999 = y;
        double r817000 = r816998 - r816999;
        double r817001 = z;
        double r817002 = 2.0;
        double r817003 = r817001 * r817002;
        double r817004 = sqrt(r817003);
        double r817005 = r817000 * r817004;
        double r817006 = t;
        double r817007 = r817006 * r817006;
        double r817008 = r817007 / r817002;
        double r817009 = exp(r817008);
        double r817010 = r817005 * r817009;
        return r817010;
}
↓
double f(double x, double y, double z, double t) {
        double r817011 = x;
        double r817012 = 0.5;
        double r817013 = r817011 * r817012;
        double r817014 = y;
        double r817015 = r817013 - r817014;
        double r817016 = z;
        double r817017 = 2.0;
        double r817018 = r817016 * r817017;
        double r817019 = sqrt(r817018);
        double r817020 = r817015 * r817019;
        double r817021 = t;
        double r817022 = r817021 * r817021;
        double r817023 = r817022 / r817017;
        double r817024 = exp(r817023);
        double r817025 = r817020 * r817024;
        return r817025;
}

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 2020021 +o rules:numerics
(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))))