Details

analyze227.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample59.0ms

Algorithm

intervals

Results

24.0ms	47×	body	2560	valid
11.0ms	43×	body	1280	valid
8.0ms	45×	body	640	valid
4.0ms	32×	body	320	valid
3.0ms	76×	body	80	valid
1.0ms	13×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	907	8
1	907	8

prune3.0ms

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: 30.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
14.1b	(/ (- 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 → 41

Calls

2 calls:

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
11.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify41.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4992	437
1	4992	437

prune108.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	36	11	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	11	48

Merged error: 0.1b

Counts

48 → 11

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite24.0ms

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 → 146

Calls

3 calls:

9.0ms	(/ (/ (- 1.0 (cos x)) x) x)
6.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series14.0ms

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))

simplify67.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5738	1984

prune186.0ms

Filtered

101 candidates to 155 candidates (-53.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	156	10	166

Merged error: 0.1b

Counts

166 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (+ 1.0 (cos x)))
0.3b	(* (cos x) (cos x))
0.4b	(+ 1.0 (cos x))
1.5b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`times-frac`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`distribute-lft-out` `difference-of-squares`
4×	`associate-/r` `associate-/l`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`sqr-cos-a` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `associate--r+` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

8.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (+ 1.0 (cos x)))
4.0ms	(* (cos x) (cos x))
4.0ms	(+ 1.0 (cos x))
4.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series21.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (+ 1.0 (cos x)))
3.0ms	(* (cos x) (cos x))
2.0ms	(+ 1.0 (cos x))
5.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5259	1078

prune173.0ms

Filtered

75 candidates to 105 candidates (-40.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 0.1b

Counts

115 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (+ (* 1.0 1.0) -1/2) (* 1/2 (cos (* 2 x)))) (+ 1.0 (cos x))) x)
0.2b	(/ (- (+ (* 1.0 1.0) -1/2) (* 1/2 (cos (* 2 x)))) (+ 1.0 (cos x)))
0.4b	(+ 1.0 (cos x))
1.4b	(- (+ (* 1.0 1.0) -1/2) (* 1/2 (cos (* 2 x))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
98×	`*-un-lft-identity`
64×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `flip--`
1×	`+-commutative` `sub-neg` `associate--l+`

Counts

4 → 152

Calls

4 calls:

13.0ms	(/ (/ (- (+ (* 1.0 1.0) -1/2) (* 1/2 (cos (* 2 x)))) (+ 1.0 (cos x))) x)
11.0ms	(/ (- (+ (* 1.0 1.0) -1/2) (* 1/2 (cos (* 2 x)))) (+ 1.0 (cos x)))
3.0ms	(+ 1.0 (cos x))
8.0ms	(- (+ (* 1.0 1.0) -1/2) (* 1/2 (cos (* 2 x))))

series32.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (/ (- (+ (* 1.0 1.0) -1/2) (* 1/2 (cos (* 2 x)))) (+ 1.0 (cos x))) x)
12.0ms	(/ (- (+ (* 1.0 1.0) -1/2) (* 1/2 (cos (* 2 x)))) (+ 1.0 (cos x)))
2.0ms	(+ 1.0 (cos x))
5.0ms	(- (+ (* 1.0 1.0) -1/2) (* 1/2 (cos (* 2 x))))

simplify53.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4979	4217
1	4979	4217

prune358.0ms

Filtered

124 candidates to 164 candidates (-32.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	164	12	176

Merged error: 0.1b

Counts

176 → 12

regimes82.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch26.0ms

Steps

Iters	Range		Point
7	0.023626374086077477	2.868360553754522	0.03374736963733248
8	-0.08011432297497073	-5.504442004899442e-05	-0.02026115641790327

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	164	52
1	164	52

end0.0ms

sample1.8s

Algorithm

intervals

Results

832.0ms	1606×	body	2560	valid
338.0ms	1230×	body	1280	valid
244.0ms	1458×	body	640	valid
119.0ms	992×	body	320	valid
84.0ms	2229×	body	80	valid
46.0ms	485×	body	160	valid

Details

analyze227.0ms

sample59.0ms

simplify45.0ms

prune3.0ms

localize6.0ms

rewrite11.0ms

series14.0ms

simplify41.0ms

prune108.0ms

localize6.0ms

rewrite24.0ms

series14.0ms

simplify67.0ms

prune186.0ms

localize10.0ms

rewrite22.0ms

series21.0ms

simplify48.0ms

prune173.0ms

localize14.0ms

rewrite40.0ms

series32.0ms

simplify53.0ms

prune358.0ms

regimes82.0ms

bsearch26.0ms

simplify3.0ms

end0.0ms

sample1.8s

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