Average Error: 0.3 → 0.3
Time: 12.0s
Precision: binary64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{2 \cdot \frac{t \cdot t}{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{2 \cdot \frac{t \cdot t}{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (x * 0.5)) - y)) * ((double) sqrt(((double) (z * 2.0)))))) * ((double) exp((((double) (t * t)) / 2.0)))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (((double) (x * 0.5)) - y)) * ((double) sqrt(((double) (z * 2.0)))))) * ((double) pow(((double) exp(((double) (2.0 * (((double) (t * t)) / 2.0))))), 0.3333333333333333)))) * ((double) cbrt(((double) exp((((double) (t * t)) / 2.0)))))));
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.3

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

  4. Applied associate-*r*0.3

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

  6. Applied pow1/30.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\sqrt[3]{e^{\frac{t \cdot t}{2}}} \cdot \color{blue}{{\left(e^{\frac{t \cdot t}{2}}\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\]

  7. Applied pow1/30.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\color{blue}{{\left(e^{\frac{t \cdot t}{2}}\right)}^{\frac{1}{3}}} \cdot {\left(e^{\frac{t \cdot t}{2}}\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\]

  8. Applied pow-prod-down0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{{\left(e^{\frac{t \cdot t}{2}} \cdot e^{\frac{t \cdot t}{2}}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\]

  9. Simplified0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\color{blue}{\left(e^{2 \cdot \frac{t \cdot t}{2}}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\]

  10. Final simplification0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{2 \cdot \frac{t \cdot t}{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{e^{\frac{t \cdot t}{2}}}\]

Reproduce

herbie shell --seed 2020182 
(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 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

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