Average Error: 0.3 → 0.5
Time: 7.9s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}
double f(double x, double y, double z, double t) {
        double r931206 = x;
        double r931207 = 0.5;
        double r931208 = r931206 * r931207;
        double r931209 = y;
        double r931210 = r931208 - r931209;
        double r931211 = z;
        double r931212 = 2.0;
        double r931213 = r931211 * r931212;
        double r931214 = sqrt(r931213);
        double r931215 = r931210 * r931214;
        double r931216 = t;
        double r931217 = r931216 * r931216;
        double r931218 = r931217 / r931212;
        double r931219 = exp(r931218);
        double r931220 = r931215 * r931219;
        return r931220;
}
↓
double f(double x, double y, double z, double t) {
        double r931221 = x;
        double r931222 = 0.5;
        double r931223 = r931221 * r931222;
        double r931224 = y;
        double r931225 = r931223 - r931224;
        double r931226 = z;
        double r931227 = sqrt(r931226);
        double r931228 = r931225 * r931227;
        double r931229 = 2.0;
        double r931230 = sqrt(r931229);
        double r931231 = r931228 * r931230;
        double r931232 = exp(1.0);
        double r931233 = t;
        double r931234 = r931233 * r931233;
        double r931235 = r931234 / r931229;
        double r931236 = pow(r931232, r931235);
        double r931237 = r931231 * r931236;
        return r931237;
}

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
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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 sqrt-prod0.5

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

  4. Applied associate-*r*0.5

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

  6. Applied *-un-lft-identity0.5

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot e^{\color{blue}{1 \cdot \frac{t \cdot t}{2}}}\]

  7. Applied exp-prod0.5

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \sqrt{2}\right) \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}}\]

  8. Simplified0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2020089 
(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))))