Average Error: 0.3 → 0.3
Time: 8.5s
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 r699218 = x;
        double r699219 = 0.5;
        double r699220 = r699218 * r699219;
        double r699221 = y;
        double r699222 = r699220 - r699221;
        double r699223 = z;
        double r699224 = 2.0;
        double r699225 = r699223 * r699224;
        double r699226 = sqrt(r699225);
        double r699227 = r699222 * r699226;
        double r699228 = t;
        double r699229 = r699228 * r699228;
        double r699230 = r699229 / r699224;
        double r699231 = exp(r699230);
        double r699232 = r699227 * r699231;
        return r699232;
}
↓
double f(double x, double y, double z, double t) {
        double r699233 = x;
        double r699234 = 0.5;
        double r699235 = r699233 * r699234;
        double r699236 = y;
        double r699237 = r699235 - r699236;
        double r699238 = z;
        double r699239 = 2.0;
        double r699240 = r699238 * r699239;
        double r699241 = sqrt(r699240);
        double r699242 = r699237 * r699241;
        double r699243 = t;
        double r699244 = r699243 * r699243;
        double r699245 = r699244 / r699239;
        double r699246 = exp(r699245);
        double r699247 = r699242 * r699246;
        return r699247;
}

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 2020027 
(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))))