Details

sample1.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 76.989746%

Results

26.0ms	41×	body	2560	valid
11.0ms	39×	body	1280	valid
10.0ms	59×	body	640	valid
4.0ms	31×	body	320	valid
2.0ms	66×	body	80	valid
2.0ms	20×	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

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: 32.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

3.0b	(- 1.0 (cos x))
12.1b	(/ (- 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

prune86.0ms

Filtered

34 candidates to 48 candidates (-41.2%)

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

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
11.8b	(- (+ (* 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	(* 1/720 (pow x 4))
5.0ms	(* 1/24 (pow x 2))
7.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series11.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* 1/720 (pow x 4))
3.0ms	(* 1/24 (pow x 2))
5.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify38.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	268	345
1	1132	313
2	5001	307

prune125.0ms

Filtered

46 candidates to 75 candidates (-63.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 0.1b

Counts

83 → 8

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.2b	(/ (- 1.0 (cos x)) x)
3.0b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

10.0ms	(/ (/ (- 1.0 (cos x)) x) x)
5.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series13.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ (/ (- 1.0 (cos x)) x) x)
5.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

simplify50.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186

prune168.0ms

Filtered

104 candidates to 156 candidates (-50.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	148	8	156
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	152	12	164

Merged error: 0.1b

Counts

164 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.3b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
2.8b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

23.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
2.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series39.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
5.0ms	(pow (cos x) 3)
2.0ms	(+ (cos x) 1.0)
8.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify102.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	617	2953
1	2699	2889
2	5002	2810

prune286.0ms

Filtered

105 candidates to 201 candidates (-91.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	202	11	213

Merged error: 0.1b

Counts

213 → 11

regimes136.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.9b

bsearch39.0ms

Steps

Iters	Range		Point
10	0.00026739590391061516	71489105.79069951	0.03083767509773662
9	-0.05425976550749722	-1.2696857363672504e-08	-0.034761080653484655

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	10
1	29	10

end0.0ms

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 76.989746%

Results

860.0ms	1583×	body	2560	valid
363.0ms	1229×	body	1280	valid
283.0ms	1521×	body	640	valid
131.0ms	929×	body	320	valid
93.0ms	2264×	body	80	valid
48.0ms	474×	body	160	valid

Details

sample1.0s

simplify6.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series9.0ms

simplify58.0ms

prune86.0ms

localize9.0ms

rewrite18.0ms

series11.0ms

simplify38.0ms

prune125.0ms

localize6.0ms

rewrite25.0ms

series13.0ms

simplify50.0ms

prune168.0ms

localize14.0ms

rewrite49.0ms

series39.0ms

simplify102.0ms

prune286.0ms

regimes136.0ms

bsearch39.0ms

simplify1.0ms

end0.0ms

sample2.9s

Profiling