Average Error: 0.3 → 0.5
Time: 23.4s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[e^{\frac{t \cdot t}{2}} \cdot \left(\sqrt{2} \cdot \left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\right)\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
e^{\frac{t \cdot t}{2}} \cdot \left(\sqrt{2} \cdot \left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r37594210 = x;
        double r37594211 = 0.5;
        double r37594212 = r37594210 * r37594211;
        double r37594213 = y;
        double r37594214 = r37594212 - r37594213;
        double r37594215 = z;
        double r37594216 = 2.0;
        double r37594217 = r37594215 * r37594216;
        double r37594218 = sqrt(r37594217);
        double r37594219 = r37594214 * r37594218;
        double r37594220 = t;
        double r37594221 = r37594220 * r37594220;
        double r37594222 = r37594221 / r37594216;
        double r37594223 = exp(r37594222);
        double r37594224 = r37594219 * r37594223;
        return r37594224;
}
↓
double f(double x, double y, double z, double t) {
        double r37594225 = t;
        double r37594226 = r37594225 * r37594225;
        double r37594227 = 2.0;
        double r37594228 = r37594226 / r37594227;
        double r37594229 = exp(r37594228);
        double r37594230 = sqrt(r37594227);
        double r37594231 = z;
        double r37594232 = sqrt(r37594231);
        double r37594233 = x;
        double r37594234 = 0.5;
        double r37594235 = r37594233 * r37594234;
        double r37594236 = y;
        double r37594237 = r37594235 - r37594236;
        double r37594238 = r37594232 * r37594237;
        double r37594239 = r37594230 * r37594238;
        double r37594240 = r37594229 * r37594239;
        return r37594240;
}

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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))