Details

Time bar (total: 8.1s)

sample59.0ms

Algorithm
intervals
Results
20.0ms59×body2560valid
11.0ms44×body1280valid
7.0ms126×body80valid
3.0ms16×body640valid
1.0msbody320valid
0.0msbody160valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11310
21610
31810
done1810

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 47.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- (sqrt (+ (* ti ti) 1.0)) 1.0) ti)
1.1b
(- (sqrt (+ (* ti ti) 1.0)) 1.0)
15.4b
(sqrt (+ (* ti ti) 1.0))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
25×*-un-lft-identity
18×times-frac
15×add-cube-cbrt
10×difference-of-squares
sqrt-prod
associate-/l*
add-cbrt-cube add-exp-log distribute-lft-out-- add-log-exp
pow1
associate-/r*
flip3-- sqrt-div flip-- associate-/l/
cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log div-sub div-exp flip-+ div-inv
Counts
3 → 72
Calls
3 calls:
179.0ms
(/ (- (sqrt (+ (* ti ti) 1.0)) 1.0) ti)
120.0ms
(- (sqrt (+ (* ti ti) 1.0)) 1.0)
18.0ms
(sqrt (+ (* ti ti) 1.0))

series355.0ms

Counts
3 → 9
Calls
3 calls:
163.0ms
(/ (- (sqrt (+ (* ti ti) 1.0)) 1.0) ti)
95.0ms
(- (sqrt (+ (* ti ti) 1.0)) 1.0)
96.0ms
(sqrt (+ (* ti ti) 1.0))

simplify1.4s

Counts
81 → 81
Iterations

Useful iterations: 2 (405.0ms)

IterNodesCost
01501285
13641207
215261131
done50021131

prune382.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 30.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1 (/ 1.0 ti))
0.0b
(- (- (/ 0.5 (* ti ti))) (+ 1 (/ 1.0 ti)))
0.2b
(/ 0.5 (* ti ti))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
15×add-log-exp
add-cbrt-cube add-exp-log
add-sqr-sqrt
add-cube-cbrt
diff-log distribute-lft-out--
pow1 sum-log times-frac distribute-lft-out associate-/l*
cbrt-undiv distribute-rgt-neg-in flip3-+ div-exp neg-log frac-sub flip-+ distribute-neg-frac
associate--l- neg-sub0 +-commutative clear-num associate-/r* sub-neg frac-2neg flip3-- prod-exp cbrt-unprod div-inv flip-- associate--r+ difference-of-squares
Counts
3 → 57
Calls
3 calls:
20.0ms
(+ 1 (/ 1.0 ti))
145.0ms
(- (- (/ 0.5 (* ti ti))) (+ 1 (/ 1.0 ti)))
15.0ms
(/ 0.5 (* ti ti))

series160.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(+ 1 (/ 1.0 ti))
46.0ms
(- (- (/ 0.5 (* ti ti))) (+ 1 (/ 1.0 ti)))
53.0ms
(/ 0.5 (* ti ti))

simplify1.9s

Counts
66 → 66
Iterations

Useful iterations: 2 (556.0ms)

IterNodesCost
0111844
1354789
22068710
done5001710

prune212.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.3b

regimes111.0ms

Accuracy

97.7% (0.4b remaining)

Error of 29.7b against oracle of 29.2b and baseline of 47.2b

bsearch187.0ms

Steps
ItersRangePoint
11
1.7728331387692633e-95
2.3657522157937943e-74
1.2622765090667187e-77
9
-3.4298688938742986e+159
-8.648518336606113e+153
-1.3418761783167835e+154

simplify12.0ms

Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02545
13545
24244
done4244

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.2s1259×body1280valid
762.0ms1583×body2560valid
380.0ms4099×body80valid
124.0ms592×body640valid
49.0ms307×body320valid
17.0ms158×body160valid
1.0msbody5120valid