Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	241×	body	80	valid
2.0ms	11×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	9×	body	160	valid

simplify6.5s

Counts

1 → 1

Iterations

Useful iterations: 4 (50.0ms)

Iter	Nodes	Cost
0	11	245
1	22	245
2	50	245
3	103	245
4	195	220
5	406	220
6	989	220
7	2046	220
8	3757	220
done	5001	220

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.6b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.6b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

27.0ms	(/ (- t z) (- a t))
1.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series295.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- t z) (- a t))
235.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.2s

Counts

70 → 70

Iterations

Useful iterations: 3 (716.0ms)

Iter	Nodes	Cost
0	113	18350
1	263	17426
2	646	17346
3	2106	17296
done	5044	17296

prune503.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ t (- a t))
0.0b	(- (/ t (- a t)) (/ z (- a t)))
2.6b	(fma (- (/ t (- a t)) (/ z (- a t))) y (+ x y))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

694×	`*-un-lft-identity`
684×	`add-sqr-sqrt`
678×	`times-frac`
441×	`prod-diff`
402×	`add-cube-cbrt`
145×	`distribute-lft-out--`
139×	`difference-of-squares`
92×	`associate-/r/`
47×	`flip3--` `flip--`
46×	`div-inv`
21×	`fma-neg`
5×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `distribute-rgt-out--` `log1p-expm1-u` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub` `fma-udef` `sub-div`

Counts

3 → 542

Calls

3 calls:

18.0ms	(/ t (- a t))
121.0ms	(- (/ t (- a t)) (/ z (- a t)))
0.0ms	(fma (- (/ t (- a t)) (/ z (- a t))) y (+ x y))

series524.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ t (- a t))
143.0ms	(- (/ t (- a t)) (/ z (- a t)))
321.0ms	(fma (- (/ t (- a t)) (/ z (- a t))) y (+ x y))

simplify5.0s

Counts

551 → 551

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	553	431278
1	1228	376401
2	2901	335999
done	5001	292331

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
7.0b	(fma (- (/ (* (cbrt t) (cbrt t)) (/ (- a t) (cbrt t))) (/ z (- a t))) y (+ x y))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt t)
0.0ms	(fma (- (/ (* (cbrt t) (cbrt t)) (/ (- a t) (cbrt t))) (/ z (- a t))) y (+ x y))

series1.1s

Counts

4 → 12

Calls

4 calls:

246.0ms	(cbrt t)
241.0ms	(cbrt t)
211.0ms	(cbrt t)
389.0ms	(fma (- (/ (* (cbrt t) (cbrt t)) (/ (- a t) (cbrt t))) (/ z (- a t))) y (+ x y))

simplify3.5s

Counts

61 → 61

Iterations

Useful iterations: 3 (177.0ms)

Iter	Nodes	Cost
0	50	14073
1	89	13047
2	194	12930
3	530	10800
4	2586	10800
done	5036	10800

prune495.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

localize104.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt (cbrt t))
6.3b	(fma (- (/ (* (* (cbrt (* (cbrt t) (cbrt t))) (cbrt (cbrt t))) (cbrt t)) (/ (- a t) (cbrt t))) (/ z (- a t))) y (+ x y))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt (cbrt t))
0.0ms	(fma (- (/ (* (* (cbrt (* (cbrt t) (cbrt t))) (cbrt (cbrt t))) (cbrt t)) (/ (- a t) (cbrt t))) (/ z (- a t))) y (+ x y))

series1.3s

Counts

4 → 12

Calls

4 calls:

273.0ms	(cbrt t)
301.0ms	(cbrt t)
375.0ms	(cbrt (cbrt t))
379.0ms	(fma (- (/ (* (* (cbrt (* (cbrt t) (cbrt t))) (cbrt (cbrt t))) (cbrt t)) (/ (- a t) (cbrt t))) (/ z (- a t))) y (+ x y))

simplify5.0s

Counts

64 → 64

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	72	19050
1	130	17995
2	298	17917
3	823	17387
4	3559	16987
done	5015	16987

prune688.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

regimes849.0ms

Accuracy

40.3% (4.8b remaining)

Error of 8.2b against oracle of 3.4b and baseline of 11.4b

bsearch51.0ms

Steps

Iters	Range		Point
8	1.1258900840831215e+123	6.879984775840782e+127	2.7163182851104776e+127
0	-1.4132096724829227e+117	-1.351671608157525e+117	-1.382440640320224e+117

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	777
1	26	777
done	26	777

end0.0ms

sample1.4s

Algorithm

intervals

Results

626.0ms	7309×	body	80	valid
168.0ms	463×	body	640	valid
93.0ms	257×	body	1280	valid
67.0ms	399×	body	320	valid
28.0ms	262×	body	160	valid
5.0ms	16×	body	2560	valid