Details

sample80.0ms

Algorithm

intervals

Results

36.0ms	57×	body	2560	valid
14.0ms	37×	body	1280	valid
11.0ms	45×	body	640	valid
6.0ms	32×	body	320	valid
3.0ms	66×	body	80	valid
2.0ms	19×	body	160	valid

simplify7.0ms

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 (0.0%)

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: 33.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (cos x))
16.9b	(/ (- 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))

series67.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
49.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify62.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

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

prune114.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	37	11	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	11	49

Merged error: 0.2b

Counts

49 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 1/24 (pow x 2))
0.3b	(* 1/720 (pow x 4))
12.0b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 1/24 (pow x 2))
5.0ms	(* 1/720 (pow x 4))
7.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series104.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 1/24 (pow x 2))
35.0ms	(* 1/720 (pow x 4))
45.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify39.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	268	347
1	1132	316
2	5001	310

prune133.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	75	11	86

Merged error: 0.2b

Counts

86 → 11

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))
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))

rewrite52.0ms

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)
27.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series171.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
41.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
22.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify106.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (81.0ms)

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

prune337.0ms

Filtered

218 candidates to 123 candidates (56.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	218	11	229

Merged error: 0.2b

Counts

229 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))
2.3b	(log (exp (- 1.0 (cos x))))

rewrite48.0ms

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:

30.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
18.0ms	(- 1.0 (cos x))
22.0ms	(- 1.0 (cos x))
18.0ms	(log (exp (- 1.0 (cos x))))

simplify67.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (49.0ms)

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

prune306.0ms

Filtered

157 candidates to 101 candidates (64.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	157	11	168

Merged error: 0.1b

Counts

168 → 11

regimes98.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.7b

bsearch87.0ms

Steps

Iters	Range		Point
9	8.159003009805276e-07	0.06291072096871789	0.02982085320761324
9	-5.855776674212404	-7.74497267090904e-05	-0.03566864611298506

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

740.0ms	1543×	body	2560	valid
312.0ms	1260×	body	1280	valid
247.0ms	1534×	body	640	valid
106.0ms	898×	body	320	valid
76.0ms	2274×	body	80	valid
44.0ms	491×	body	160	valid