Average Error: 0.2 → 0.1
Time: 46.9s
Precision: 64
Internal Precision: 576
\[\frac{\frac{e^{{\left(\frac{x - m}{s}\right)}^{2} \cdot \left(-0.5\right)}}{\sqrt{2 \cdot \pi}}}{s}\]
\[\frac{\sqrt{e^{\left(-0.5\right) \cdot {\left(\frac{x - m}{s}\right)}^{2}}} \cdot \frac{\sqrt{e^{\left(-0.5\right) \cdot {\left(\frac{x - m}{s}\right)}^{2}}}}{\sqrt{2 \cdot \pi}}}{s}\]

Error

Bits error versus x

Bits error versus m

Bits error versus s

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{\frac{e^{{\left(\frac{x - m}{s}\right)}^{2} \cdot \left(-0.5\right)}}{\sqrt{2 \cdot \pi}}}{s}\]
  2. Using strategy rm
  3. Applied *-un-lft-identity0.2

    \[\leadsto \frac{\frac{e^{{\left(\frac{x - m}{s}\right)}^{2} \cdot \left(-0.5\right)}}{\color{blue}{1 \cdot \sqrt{2 \cdot \pi}}}}{s}\]
  4. Applied add-sqr-sqrt0.1

    \[\leadsto \frac{\frac{\color{blue}{\sqrt{e^{{\left(\frac{x - m}{s}\right)}^{2} \cdot \left(-0.5\right)}} \cdot \sqrt{e^{{\left(\frac{x - m}{s}\right)}^{2} \cdot \left(-0.5\right)}}}}{1 \cdot \sqrt{2 \cdot \pi}}}{s}\]
  5. Applied times-frac0.1

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

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

Runtime

Time bar (total: 46.9s)Debug log

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