Details

sample92.0ms

Algorithm

intervals

Results

25.0ms	56×	body	2560	valid
10.0ms	41×	body	1280	valid
6.0ms	41×	body	640	valid
4.0ms	33×	body	320	valid
3.0ms	64×	body	80	valid
2.0ms	21×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
16.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
6.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify58.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune89.0ms

Filtered

48 candidates to 34 candidates (29.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	8	49

Merged error: 0.1b

Counts

49 → 8

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.7b	(- 1.0 (cos x))
1.7b	(- 1.0 (cos x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

6.0ms	(/ (sqrt (- 1.0 (cos x))) x)
26.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series20.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
6.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

simplify90.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	667	2403
1	3340	2087
2	5001	1922

prune275.0ms

Filtered

218 candidates to 123 candidates (43.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	215	11	226

Merged error: 0.1b

Counts

226 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
1.7b	(- 1.0 (cos x))
1.7b	(- 1.0 (cos x))
1.8b	(log (exp (- 1.0 (cos x))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
72×	`times-frac`
61×	`*-un-lft-identity`
48×	`sqrt-prod`
43×	`add-cube-cbrt`
40×	`associate-r`
28×	`associate-l`
24×	`log-pow`
20×	`exp-prod`
16×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
8×	`add-log-exp`
5×	`log-prod`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
3×	`sub-neg`
2×	`flip3--` `diff-log` `exp-sum` `flip--` `div-inv`
1×	`frac-times` `log-div` `exp-diff` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 145

Calls

4 calls:

29.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
5.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series14.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
3.0ms	(log (exp (- 1.0 (cos x))))

simplify62.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	603	1575
1	2567	1213
2	5001	1120

prune242.0ms

Filtered

157 candidates to 100 candidates (36.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	157	11	168

Merged error: 0.1b

Counts

168 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
1.5b	(- (pow 1.0 3) (pow (cos x) 3))
1.7b	(- 1.0 (cos x))
1.8b	(log (exp (- 1.0 (cos x))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
18×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`pow1` `log-pow`
5×	`add-exp-log` `log-prod` `exp-prod` `add-cbrt-cube`
3×	`sub-neg` `pow-unpow`
2×	`flip3--` `diff-log` `exp-sum` `flip--`
1×	`difference-cubes` `cube-mult` `pow-to-exp` `log-div` `pow-pow` `exp-diff` `unpow3` `rem-log-exp` `pow-exp` `rem-cube-cbrt`

Counts

4 → 91

Calls

4 calls:

2.0ms	(pow (cos x) 3)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (cos x) 3)
10.0ms	(- (pow 1.0 3) (pow (cos x) 3))
3.0ms	(- 1.0 (cos x))
3.0ms	(log (exp (- 1.0 (cos x))))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	297	548
1	1060	518
2	5001	498

prune189.0ms

Filtered

103 candidates to 61 candidates (40.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	1	8	9
Picked	1	0	1
Done	1	0	1
Total	102	12	114

Merged error: 0.1b

Counts

114 → 12

regimes88.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.1b

bsearch38.0ms

Steps

Iters	Range		Point
10	1.8861453929162526e-07	127140.91663662092	0.027844290097912085
10	-81569296.22560106	-6.097158829196934e-11	-0.030108524197303543

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	51
1	60	51

end0.0ms

sample1.7s

Algorithm

intervals

Results

753.0ms	1584×	body	2560	valid
319.0ms	1269×	body	1280	valid
237.0ms	1478×	body	640	valid
105.0ms	893×	body	320	valid
84.0ms	2285×	body	80	valid
48.0ms	491×	body	160	valid

Details

sample92.0ms

simplify6.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series9.0ms

simplify58.0ms

prune89.0ms

localize7.0ms

rewrite51.0ms

series20.0ms

simplify90.0ms

prune275.0ms

localize12.0ms

rewrite49.0ms

series14.0ms

simplify62.0ms

prune242.0ms

localize22.0ms

rewrite24.0ms

series21.0ms

simplify42.0ms

prune189.0ms

regimes88.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample1.7s

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