Average Error: 0.3 → 0.5
Time: 27.3s
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 r41131294 = x;
        double r41131295 = 0.5;
        double r41131296 = r41131294 * r41131295;
        double r41131297 = y;
        double r41131298 = r41131296 - r41131297;
        double r41131299 = z;
        double r41131300 = 2.0;
        double r41131301 = r41131299 * r41131300;
        double r41131302 = sqrt(r41131301);
        double r41131303 = r41131298 * r41131302;
        double r41131304 = t;
        double r41131305 = r41131304 * r41131304;
        double r41131306 = r41131305 / r41131300;
        double r41131307 = exp(r41131306);
        double r41131308 = r41131303 * r41131307;
        return r41131308;
}
↓
double f(double x, double y, double z, double t) {
        double r41131309 = t;
        double r41131310 = r41131309 * r41131309;
        double r41131311 = 2.0;
        double r41131312 = r41131310 / r41131311;
        double r41131313 = exp(r41131312);
        double r41131314 = sqrt(r41131311);
        double r41131315 = z;
        double r41131316 = sqrt(r41131315);
        double r41131317 = x;
        double r41131318 = 0.5;
        double r41131319 = r41131317 * r41131318;
        double r41131320 = y;
        double r41131321 = r41131319 - r41131320;
        double r41131322 = r41131316 * r41131321;
        double r41131323 = r41131314 * r41131322;
        double r41131324 = r41131313 * r41131323;
        return r41131324;
}

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 2019170 
(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))))