Details

Time bar (total: 12.8s)

sample78.0ms

Algorithm
intervals
Results
25.0ms48×body1280valid
15.0ms34×body640valid
14.0ms131×body80valid
9.0ms28×body320valid
3.0ms15×body160valid

simplify187.0ms

Counts
1 → 1
Iterations
IterNodes
done168
15168
14165
13136
12114
1199
1089
969
853
742
632
526
423
322
219
115
07

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))
4.4b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
60×times-frac
57×add-sqr-sqrt
25×add-cube-cbrt
20×distribute-lft-out
18×distribute-lft-out--
14×difference-of-squares
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×difference-of-sqr-1 add-log-exp
4×associate-/r/
3×pow1 insert-posit16
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp flip-+ div-inv flip-- associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 117
Calls
3 calls:
16.0ms
(/ x (+ x 1))
20.0ms
(/ (+ x 1) (- x 1))
67.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series197.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(/ x (+ x 1))
41.0ms
(/ (+ x 1) (- x 1))
116.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.2s

Counts
126 → 126
Iterations
IterNodes
done2000
32000
21074
1399
0180

prune968.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
0.3b
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
21.4b
(- (/ x (+ x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1)))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
34×cbrt-prod *-un-lft-identity
16×cbrt-div
14×times-frac add-cube-cbrt
11×pow1
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out difference-of-squares
7×associate-*r* associate-*l*
6×add-exp-log add-log-exp
4×frac-times add-cbrt-cube insert-posit16 unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 sub-neg pow-plus flip3-- diff-log prod-exp *-commutative frac-sub cbrt-unprod flip-- distribute-lft-out--
Counts
4 → 107
Calls
4 calls:
2.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))
23.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
72.0ms
(- (/ x (+ x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1)))))

series226.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(cbrt (+ x 1))
35.0ms
(cbrt (+ x 1))
48.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
96.0ms
(- (/ x (+ x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1)))))

simplify1.3s

Counts
119 → 119
Iterations
IterNodes
done2004
32004
21200
1447
0189

prune992.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cbrt (+ x 1)))
0.3b
(cbrt (cbrt (+ x 1)))
0.3b
(cbrt (cbrt (+ x 1)))
23.3b
(- (/ x (+ x 1)) (/ (* (* (cbrt (cbrt (+ x 1))) (cbrt (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (/ (- x 1) (cbrt (+ x 1)))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod
18×*-un-lft-identity
15×add-sqr-sqrt
12×cbrt-div
10×add-cube-cbrt
6×add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ pow1/3 flip-+ distribute-lft-out
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log frac-sub flip-- distribute-lft-out--
Counts
4 → 71
Calls
4 calls:
6.0ms
(cbrt (cbrt (+ x 1)))
3.0ms
(cbrt (cbrt (+ x 1)))
3.0ms
(cbrt (cbrt (+ x 1)))
72.0ms
(- (/ x (+ x 1)) (/ (* (* (cbrt (cbrt (+ x 1))) (cbrt (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (/ (- x 1) (cbrt (+ x 1)))))

series255.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(cbrt (cbrt (+ x 1)))
46.0ms
(cbrt (cbrt (+ x 1)))
55.0ms
(cbrt (cbrt (+ x 1)))
115.0ms
(- (/ x (+ x 1)) (/ (* (* (cbrt (cbrt (+ x 1))) (cbrt (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (/ (- x 1) (cbrt (+ x 1)))))

simplify994.0ms

Counts
83 → 83
Iterations
IterNodes
done2000
32000
2872
1294
0129

prune780.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x 1) (- x 1))
0.0b
(* (+ x 1) (+ x 1))
0.0b
(/ (- (* x (- x 1)) (* (+ x 1) (+ x 1))) (* (+ x 1) (- x 1)))
19.2b
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
46×associate-*r/
36×flip3-+ flip-+
32×frac-sub
31×*-un-lft-identity
28×frac-times
24×flip3-- flip--
20×add-sqr-sqrt
18×associate-/l/
14×associate-*l/
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
11×associate-*r*
8×associate-*l* associate-/r/
7×distribute-lft-out
6×distribute-rgt-in distribute-lft-in swap-sqr add-log-exp
5×sub-neg
4×associate--l+ insert-posit16
3×times-frac prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv div-exp pow-prod-down *-commutative associate--r+ difference-of-squares unswap-sqr
1×pow2 clear-num associate-/r* frac-2neg pow-plus diff-log difference-of-sqr-1 div-sub pow-sqr pow-prod-up div-inv distribute-lft-out--
Counts
4 → 161
Calls
4 calls:
23.0ms
(* (+ x 1) (- x 1))
23.0ms
(* (+ x 1) (+ x 1))
56.0ms
(/ (- (* x (- x 1)) (* (+ x 1) (+ x 1))) (* (+ x 1) (- x 1)))
33.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))

series244.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (+ x 1) (- x 1))
21.0ms
(* (+ x 1) (+ x 1))
82.0ms
(/ (- (* x (- x 1)) (* (+ x 1) (+ x 1))) (* (+ x 1) (- x 1)))
49.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))

simplify1.2s

Counts
173 → 173
Iterations
IterNodes
done2005
22005
1898
0248

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch86.0ms

Steps
ItersRangePoint
10
186.95626557948964
3373396396890550.5
180005.41283506868
4
-6466188478224.698
-4073810451523.4326
-6041717527243.163

simplify7.0ms

Iterations
IterNodes
done50
250
141
023

end0.0ms

sample2.1s

Algorithm
intervals
Results
713.0ms1698×body1280valid
707.0ms1267×body640valid
362.0ms4118×body80valid
119.0ms626×body320valid
39.0ms291×body160valid