Details

Time bar (total: 44.0s)

sample43.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
5.0ms256×pre80true

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01025
13125
216523
3102919
done500115

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* 2.0 2.0) (/ 1.0 (* i i)))
0.4b
(/ 1.0 (* i i))
0.9b
(/ (/ (/ 1 2.0) 2.0) (- (* 2.0 2.0) (/ 1.0 (* i i))))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
659×times-frac
349×add-sqr-sqrt
259×add-cube-cbrt *-un-lft-identity
90×difference-of-squares
46×associate-/l*
26×div-inv
23×add-exp-log
17×add-cbrt-cube
13×div-exp
8×cbrt-undiv
6×associate-/r*
5×add-log-exp
3×pow1
2×flip3-- frac-2neg clear-num associate-/r/ flip--
1×sub-neg rec-exp diff-log 1-exp prod-exp cbrt-unprod associate-/l/
Counts
3 → 319
Calls
3 calls:
29.0ms
(- (* 2.0 2.0) (/ 1.0 (* i i)))
18.0ms
(/ 1.0 (* i i))
110.0ms
(/ (/ (/ 1 2.0) 2.0) (- (* 2.0 2.0) (/ 1.0 (* i i))))

series251.0ms

Counts
3 → 9
Calls
3 calls:
93.0ms
(- (* 2.0 2.0) (/ 1.0 (* i i)))
50.0ms
(/ 1.0 (* i i))
108.0ms
(/ (/ (/ 1 2.0) 2.0) (- (* 2.0 2.0) (/ 1.0 (* i i))))

simplify1.2s

Counts
328 → 328
Iterations

Useful iterations: done (1.2s)

IterNodesCost
06389343
116038671
done50008327

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (sqrt (/ (/ 1 2.0) 2.0)) (+ 2.0 (/ (sqrt 1.0) i))) (/ (sqrt (/ (/ 1 2.0) 2.0)) (- 2.0 (/ (sqrt 1.0) i))))
0.0b
(- 2.0 (/ (sqrt 1.0) i))
0.1b
(/ (sqrt (/ (/ 1 2.0) 2.0)) (- 2.0 (/ (sqrt 1.0) i)))
0.1b
(/ (sqrt (/ (/ 1 2.0) 2.0)) (+ 2.0 (/ (sqrt 1.0) i)))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
2938×times-frac
2032×add-sqr-sqrt
1444×*-un-lft-identity
1196×sqrt-prod
1056×add-cube-cbrt
328×associate-*r*
282×difference-of-squares
190×associate-*l*
114×div-inv
94×distribute-lft-out--
93×distribute-lft-out
92×associate-/l*
49×unswap-sqr
20×add-exp-log add-cbrt-cube
11×associate-/r*
8×associate-/r/
6×pow1 cbrt-undiv div-exp add-log-exp
4×prod-exp cbrt-unprod
3×flip3-- flip--
2×frac-2neg flip3-+ sqrt-div clear-num flip-+ associate-/l/
1×frac-times sub-neg diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 1242
Calls
4 calls:
1.8s
(* (/ (sqrt (/ (/ 1 2.0) 2.0)) (+ 2.0 (/ (sqrt 1.0) i))) (/ (sqrt (/ (/ 1 2.0) 2.0)) (- 2.0 (/ (sqrt 1.0) i))))
29.0ms
(- 2.0 (/ (sqrt 1.0) i))
108.0ms
(/ (sqrt (/ (/ 1 2.0) 2.0)) (- 2.0 (/ (sqrt 1.0) i)))
106.0ms
(/ (sqrt (/ (/ 1 2.0) 2.0)) (+ 2.0 (/ (sqrt 1.0) i)))

series910.0ms

Counts
4 → 12
Calls
4 calls:
439.0ms
(* (/ (sqrt (/ (/ 1 2.0) 2.0)) (+ 2.0 (/ (sqrt 1.0) i))) (/ (sqrt (/ (/ 1 2.0) 2.0)) (- 2.0 (/ (sqrt 1.0) i))))
108.0ms
(- 2.0 (/ (sqrt 1.0) i))
182.0ms
(/ (sqrt (/ (/ 1 2.0) 2.0)) (- 2.0 (/ (sqrt 1.0) i)))
180.0ms
(/ (sqrt (/ (/ 1 2.0) 2.0)) (+ 2.0 (/ (sqrt 1.0) i)))

simplify3.4s

Counts
1254 → 1254
Iterations

Useful iterations: done (3.3s)

IterNodesCost
0134239096
1375636227
done500034309

prune6.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (/ (/ 1 2.0) 2.0)) (+ 2.0 (/ (sqrt 1.0) i)))
0.2b
(/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i)))
0.6b
(* (sqrt (sqrt (/ 1 2.0))) (/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i))))
1.0b
(sqrt (sqrt (/ 1 2.0)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
2725×times-frac
2015×add-sqr-sqrt
1841×sqrt-prod
1319×*-un-lft-identity
990×add-cube-cbrt
391×associate-*r*
333×difference-of-squares
111×distribute-lft-out--
101×associate-/l*
85×div-inv
47×distribute-lft-out
35×unswap-sqr
19×associate-*l*
13×add-exp-log add-cbrt-cube
11×associate-/r*
9×pow1
8×sqrt-pow1 sqrt-div
6×associate-/r/
4×rem-sqrt-square add-log-exp
3×cbrt-undiv div-exp
2×flip3-- frac-2neg pow1/2 prod-exp clear-num flip-- cbrt-unprod associate-/l/
1×frac-times pow-flip flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+ inv-pow
Counts
4 → 1206
Calls
4 calls:
108.0ms
(/ (sqrt (/ (/ 1 2.0) 2.0)) (+ 2.0 (/ (sqrt 1.0) i)))
122.0ms
(/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i)))
553.0ms
(* (sqrt (sqrt (/ 1 2.0))) (/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i))))
13.0ms
(sqrt (sqrt (/ 1 2.0)))

series835.0ms

Counts
4 → 10
Calls
4 calls:
190.0ms
(/ (sqrt (/ (/ 1 2.0) 2.0)) (+ 2.0 (/ (sqrt 1.0) i)))
378.0ms
(/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i)))
266.0ms
(* (sqrt (sqrt (/ 1 2.0))) (/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i))))
0.0ms
(sqrt (sqrt (/ 1 2.0)))

simplify3.9s

Counts
1216 → 1216
Iterations

Useful iterations: done (3.8s)

IterNodesCost
0152434696
1307831158
done500029734

prune6.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (sqrt (sqrt (/ 1 2.0)))) (/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i))))
0.2b
(/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i)))
1.0b
(sqrt (sqrt (/ 1 2.0)))
1.0b
(sqrt (sqrt (/ 1 2.0)))

rewrite972.0ms

Algorithm
rewrite-expression-head
Rules
2234×times-frac
1827×add-sqr-sqrt
1720×sqrt-prod
1009×*-un-lft-identity
772×add-cube-cbrt
391×associate-*r*
333×difference-of-squares
111×distribute-lft-out--
65×div-inv
55×associate-/l*
42×unswap-sqr
22×associate-*l*
16×sqrt-pow1
12×pow1
11×add-exp-log sqrt-div add-cbrt-cube
8×rem-sqrt-square
7×associate-/r*
4×pow1/2 associate-/r/ add-log-exp
2×cbrt-undiv flip3-- pow-flip div-exp prod-exp flip-- cbrt-unprod inv-pow
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1001
Calls
4 calls:
559.0ms
(* (sqrt (sqrt (sqrt (/ 1 2.0)))) (/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i))))
108.0ms
(/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i)))
10.0ms
(sqrt (sqrt (/ 1 2.0)))
21.0ms
(sqrt (sqrt (/ 1 2.0)))

series866.0ms

Counts
4 → 8
Calls
4 calls:
502.0ms
(* (sqrt (sqrt (sqrt (/ 1 2.0)))) (/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i))))
363.0ms
(/ (sqrt (/ (sqrt (/ 1 2.0)) 2.0)) (- 2.0 (/ (sqrt 1.0) i)))
0.0ms
(sqrt (sqrt (/ 1 2.0)))
0.0ms
(sqrt (sqrt (/ 1 2.0)))

simplify2.6s

Counts
1009 → 1009
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0110229004
1238926056
done500024915

prune6.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes58.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01934
12434
done2434

end0.0ms

sample1.1s

Algorithm
intervals
Results
725.0ms8000×body80valid
171.0ms8000×pre80true