Average Error: 0.3 → 0.3
Time: 12.2s
Precision: binary64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[{\left(\sqrt{\sqrt{e^{t}}}\right)}^{t} \cdot \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(\sqrt{\sqrt{e^{t}}}\right)}^{t}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
{\left(\sqrt{\sqrt{e^{t}}}\right)}^{t} \cdot \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(\sqrt{\sqrt{e^{t}}}\right)}^{t}\right)
(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
 (*
  (pow (sqrt (sqrt (exp t))) t)
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (sqrt (sqrt (exp t))) t))))
double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt(z * 2.0)) * exp((t * t) / 2.0);
}
↓
double code(double x, double y, double z, double t) {
	return pow(sqrt(sqrt(exp(t))), t) * ((((x * 0.5) - y) * sqrt(z * 2.0)) * pow(sqrt(sqrt(exp(t))), t));
}

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. Simplified0.3

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

  4. Applied add-sqr-sqrt_binary64_212420.3

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

  5. Applied unpow-prod-down_binary64_212990.3

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

  6. Applied associate-*r*_binary64_211600.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2021043 
(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))))