Average Error: 0.3 → 0.3
Time: 11.2s
Precision: binary64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt[3]{{\left({\left(e^{t}\right)}^{t}\right)}^{1.5}} \]
\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 \sqrt{z \cdot 2}\right) \cdot \sqrt[3]{{\left({\left(e^{t}\right)}^{t}\right)}^{1.5}}

(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
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (cbrt (pow (pow (exp t) t) 1.5))))
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 (((x * 0.5) - y) * sqrt(z * 2.0)) * cbrt(pow(pow(exp(t), t), 1.5));
}

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. Applied pow1/2_binary640.3

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

  4. Applied pow-pow_binary640.3

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

  5. Applied add-cbrt-cube_binary640.3

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

  6. Simplified0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt[3]{\color{blue}{{\left({\left(e^{t}\right)}^{t}\right)}^{1.5}}} \]

  7. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt[3]{{\left({\left(e^{t}\right)}^{t}\right)}^{1.5}} \]

Reproduce

herbie shell --seed 2022077 
(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))))