Details

Time bar (total: 25.6s)

sample281.0ms

Algorithm
intervals
Results
99.0ms39×body2560valid
72.0ms64×body1280valid
26.0ms128×body80valid
14.0ms15×body640valid
6.0msbody160valid
6.0ms256×pre80true
5.0ms206×pre80false
5.0msbody320valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 4 (197.0ms)

IterNodesCost
02641
14841
29441
322336
457434
5254834
done500034

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.7b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b
(erf (/ a (sqrt 2.0)))
0.4b
(/ a (sqrt 2.0))
0.4b
(/ b (sqrt 2.0))
0.9b
(- (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow a 2.0)) 2.0))) (* a (erf (/ a (sqrt 2.0))))) (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow b 2.0)) 2.0))) (* a (erf (/ b (sqrt 2.0))))))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt *-un-lft-identity times-frac
34×add-cube-cbrt
24×sqrt-prod
16×add-log-exp
12×associate-/r*
add-cbrt-cube add-exp-log
associate-/l*
pow1 sum-log flip3-+ diff-log frac-sub flip-+
cbrt-undiv clear-num frac-2neg div-exp div-inv
sub-neg flip3-- associate--l+ flip-- associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 108
Calls
4 calls:
1.0ms
(erf (/ a (sqrt 2.0)))
11.0ms
(/ a (sqrt 2.0))
11.0ms
(/ b (sqrt 2.0))
1.9s
(- (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow a 2.0)) 2.0))) (* a (erf (/ a (sqrt 2.0))))) (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow b 2.0)) 2.0))) (* a (erf (/ b (sqrt 2.0))))))

series820.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(erf (/ a (sqrt 2.0)))
115.0ms
(/ a (sqrt 2.0))
113.0ms
(/ b (sqrt 2.0))
582.0ms
(- (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow a 2.0)) 2.0))) (* a (erf (/ a (sqrt 2.0))))) (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow b 2.0)) 2.0))) (* a (erf (/ b (sqrt 2.0))))))

simplify1.7s

Counts
120 → 120
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02383002
16062835
224052639
done50022627

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize110.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1 (sqrt (sqrt 2.0))) (/ b (sqrt (sqrt 2.0))))
0.4b
(/ a (sqrt 2.0))
0.9b
(- (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow a 2.0)) 2.0))) (* a (erf (/ a (sqrt 2.0))))) (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow b 2.0)) 2.0))) (* a (erf (* (/ 1 (sqrt (sqrt 2.0))) (/ b (sqrt (sqrt 2.0))))))))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
170×add-sqr-sqrt
147×sqrt-prod
144×times-frac
93×*-un-lft-identity
79×add-cube-cbrt
32×add-exp-log
31×associate-*r* associate-*l*
28×unswap-sqr
20×add-cbrt-cube
16×add-log-exp
15×associate-/r*
11×div-exp
pow1
prod-exp
cbrt-undiv associate-/l*
pow-flip
sum-log sqrt-pow1 flip3-+ diff-log frac-sub cbrt-unprod flip-+ div-inv
rec-exp 1-exp
clear-num frac-2neg pow1/2
frac-times sub-neg flip3-- pow-prod-down associate-*l/ associate--l+ associate-*r/ *-commutative flip-- associate--r+ distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 235
Calls
4 calls:
99.0ms
(* (/ 1 (sqrt (sqrt 2.0))) (/ b (sqrt (sqrt 2.0))))
12.0ms
(/ a (sqrt 2.0))
1.9s
(- (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow a 2.0)) 2.0))) (* a (erf (/ a (sqrt 2.0))))) (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow b 2.0)) 2.0))) (* a (erf (* (/ 1 (sqrt (sqrt 2.0))) (/ b (sqrt (sqrt 2.0))))))))
18.0ms
(/ 1 (sqrt (sqrt 2.0)))

series842.0ms

Counts
4 → 10
Calls
4 calls:
123.0ms
(* (/ 1 (sqrt (sqrt 2.0))) (/ b (sqrt (sqrt 2.0))))
115.0ms
(/ a (sqrt 2.0))
604.0ms
(- (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow a 2.0)) 2.0))) (* a (erf (/ a (sqrt 2.0))))) (+ (* (sqrt (/ 2.0 PI)) (exp (/ (- (pow b 2.0)) 2.0))) (* a (erf (* (/ 1 (sqrt (sqrt 2.0))) (/ b (sqrt (sqrt 2.0))))))))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify809.0ms

Counts
245 → 245
Iterations

Useful iterations: done (792.0ms)

IterNodesCost
03605531
110635057
done50014454

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes318.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 11.1b

bsearch298.0ms

Steps
ItersRangePoint
8
9.285203124246302e-07
0.020477744205211073
1.0371352189748177e-06

simplify16.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05195
17395
done7395

end0.0ms

sample10.3s

Algorithm
intervals
Results
3.0s1763×body1280valid
2.5s1304×body2560valid
1.5s4036×body80valid
858.0ms7988×pre80false
829.0ms278×body320valid
572.0ms476×body640valid
188.0ms8000×pre80true
73.0ms143×body160valid