Average Error: 0.3 → 0.5
Time: 10.7s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \left(\left(\sqrt{z} \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot e^{\frac{t \cdot t}{2}}\]
\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 \left(\left(\sqrt{z} \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot e^{\frac{t \cdot t}{2}}
double f(double x, double y, double z, double t) {
        double r799278 = x;
        double r799279 = 0.5;
        double r799280 = r799278 * r799279;
        double r799281 = y;
        double r799282 = r799280 - r799281;
        double r799283 = z;
        double r799284 = 2.0;
        double r799285 = r799283 * r799284;
        double r799286 = sqrt(r799285);
        double r799287 = r799282 * r799286;
        double r799288 = t;
        double r799289 = r799288 * r799288;
        double r799290 = r799289 / r799284;
        double r799291 = exp(r799290);
        double r799292 = r799287 * r799291;
        return r799292;
}
↓
double f(double x, double y, double z, double t) {
        double r799293 = x;
        double r799294 = 0.5;
        double r799295 = r799293 * r799294;
        double r799296 = y;
        double r799297 = r799295 - r799296;
        double r799298 = z;
        double r799299 = sqrt(r799298);
        double r799300 = 2.0;
        double r799301 = sqrt(r799300);
        double r799302 = cbrt(r799301);
        double r799303 = r799302 * r799302;
        double r799304 = r799299 * r799303;
        double r799305 = r799304 * r799302;
        double r799306 = r799297 * r799305;
        double r799307 = t;
        double r799308 = r799307 * r799307;
        double r799309 = r799308 / r799300;
        double r799310 = exp(r799309);
        double r799311 = r799306 * r799310;
        return r799311;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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 associate-*l*0.5

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

  8. Applied add-cube-cbrt0.5

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \sqrt[3]{\sqrt{2}}\right)}\right)\right) \cdot e^{\frac{t \cdot t}{2}}\]

  9. Applied associate-*r*0.5

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\left(\sqrt{z} \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right)}\right) \cdot e^{\frac{t \cdot t}{2}}\]

  10. Final simplification0.5

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \left(\left(\sqrt{z} \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot e^{\frac{t \cdot t}{2}}\]

Reproduce

herbie shell --seed 2019322 
(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))))