Average Error: 0.0 → 0.0
Time: 8.6s
Precision: 64
Internal Precision: 320
\[\frac{e^{\left(x \cdot x\right) \cdot \left(-0.5\right)}}{\sqrt{2 \cdot \pi}}\]
\[e^{\left(-0.5\right) \cdot \left(x \cdot x\right)} \cdot \frac{1}{\sqrt{\pi \cdot 2}}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{e^{\left(x \cdot x\right) \cdot \left(-0.5\right)}}{\sqrt{2 \cdot \pi}}\]
  2. Using strategy rm
  3. Applied div-inv0.0

    \[\leadsto \color{blue}{e^{\left(x \cdot x\right) \cdot \left(-0.5\right)} \cdot \frac{1}{\sqrt{2 \cdot \pi}}}\]
  4. Final simplification0.0

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

Runtime

Time bar (total: 8.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "exp(x*x*(-0.5))/sqrt(2*PI)"
  (/ (exp (* (* x x) (- 0.5))) (sqrt (* 2 PI))))