Details

sample144.0ms

Algorithm

intervals

Results

77.0ms	59×	body	2560	valid
36.0ms	84×	body	1280	valid
16.0ms	59×	body	640	valid
5.0ms	31×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	13×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	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: 29.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.9b	(- 1.0 (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

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

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify82.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2640	373
3	5002	373

prune146.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	45	13	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	13	59

Merged error: 0.1b

Counts

59 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.5b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
0.9b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
9.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series132.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
44.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify92.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune272.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	122	15	137

Merged error: 0.1b

Counts

137 → 15

localize15.0ms

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)))
0.4b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
0.8b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite51.0ms

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:

21.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
3.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
14.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series223.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
28.0ms	(pow (cos x) 3)
10.0ms	(+ (cos x) 1.0)
51.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify101.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (74.0ms)

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

prune410.0ms

Filtered

201 candidates to 105 candidates (52.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	196	5	201
Fresh	5	8	13
Picked	1	0	1
Done	1	0	1
Total	203	13	216

Merged error: 0.1b

Counts

216 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (cos x) 2) (cos x))
0.2b	(pow (cos x) 2)
0.5b	(+ (cos x) 1.0)
0.8b	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`add-exp-log`
9×	`add-cube-cbrt`
8×	`associate-l` `add-log-exp`
7×	`unpow-prod-down`
6×	`pow1` `add-cbrt-cube`
5×	`unpow2`
4×	`unswap-sqr`
3×	`pow-unpow` `associate-r` `prod-exp` `sqr-pow`
2×	`pow-to-exp` `pow3` `pow-exp`
1×	`difference-cubes` `+-commutative` `sub-neg` `flip3--` `pow-pow` `flip3-+` `pow-plus` `diff-log` `sum-log` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (pow (cos x) 2) (cos x))
2.0ms	(pow (cos x) 2)
4.0ms	(+ (cos x) 1.0)
7.0ms	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (pow (cos x) 2) (cos x))
16.0ms	(pow (cos x) 2)
9.0ms	(+ (cos x) 1.0)
52.0ms	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	304	412
1	1236	342
2	5002	332

prune190.0ms

Filtered

85 candidates to 56 candidates (65.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	85	13	98

Merged error: 0.1b

Counts

98 → 13

regimes152.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.2b

bsearch82.0ms

Steps

Iters	Range		Point
10	1.4358440906352691e-08	58326792.95653587	0.021774379651084565
7	-0.42296476227477825	-0.006911778759371886	-0.0249538198256524

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	30
1	48	30

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1579×	body	2560	valid
1.2s	2782×	body	1280	valid
452.0ms	1906×	body	640	valid
179.0ms	933×	body	320	valid
60.0ms	418×	body	160	valid
26.0ms	382×	body	80	valid

Details

sample144.0ms

simplify7.0ms

prune2.0ms

localize8.0ms

rewrite11.0ms

series60.0ms

simplify82.0ms

prune146.0ms

localize10.0ms

rewrite29.0ms

series132.0ms

simplify92.0ms

prune272.0ms

localize15.0ms

rewrite51.0ms

series223.0ms

simplify101.0ms

prune410.0ms

localize16.0ms

rewrite21.0ms

series106.0ms

simplify51.0ms

prune190.0ms

regimes152.0ms

bsearch82.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling