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

# Try it out

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# 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

$\leadsto \frac{\frac{e^{{\left(\frac{x - m}{s}\right)}^{2} \cdot \left(-0.5\right)}}{\color{blue}{1 \cdot \sqrt{2 \cdot \pi}}}}{s}$

$\leadsto \frac{\frac{\color{blue}{\sqrt{e^{{\left(\frac{x - m}{s}\right)}^{2} \cdot \left(-0.5\right)}} \cdot \sqrt{e^{{\left(\frac{x - m}{s}\right)}^{2} \cdot \left(-0.5\right)}}}}{1 \cdot \sqrt{2 \cdot \pi}}}{s}$
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))