Average Error: 0.3 → 0.5
Time: 6.2s
Precision: binary64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt[3]{\sqrt{2}} \cdot \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right)\right) \cdot e^{\frac{t \cdot t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt[3]{\sqrt{2}} \cdot \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right)\right) \cdot e^{\frac{t \cdot t}{2}}
(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))
↓
(FPCore (x y z t)
 :precision binary64
 (*
  (*
   (cbrt (sqrt 2.0))
   (* (* (- (* x 0.5) y) (sqrt z)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))
  (exp (/ (* t t) 2.0))))
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) cbrt(((double) sqrt(2.0)))) * ((double) (((double) (((double) (((double) (x * 0.5)) - y)) * ((double) sqrt(z)))) * ((double) (((double) cbrt(((double) sqrt(2.0)))) * ((double) cbrt(((double) sqrt(2.0)))))))))) * ((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
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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-prod_binary640.5

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

  4. Applied associate-*r*_binary640.5

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

  6. Applied add-cube-cbrt_binary640.5

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

  7. Applied associate-*r*_binary640.5

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2020210 
(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))))