Details

sample146.0ms

Algorithm

intervals

Results

80.0ms	57×	body	2560	valid
35.0ms	79×	body	1280	valid
16.0ms	67×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	13×	body	80	valid

simplify5.0ms

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

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: 29.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.0b	(- 1.0 (cos x))

rewrite17.0ms

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:

12.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series12.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

simplify78.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

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

prune131.0ms

Filtered

42 candidates to 58 candidates (-38.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	42	16	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	16	59

Merged error: 0.3b

Counts

59 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ (cos x) 1.0))
0.3b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.8b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

6.0ms	(* (cos x) (+ (cos x) 1.0))
4.0ms	(+ (cos x) 1.0)
2.0ms	(pow (cos x) 3)
13.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series19.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (cos x) (+ (cos x) 1.0))
2.0ms	(+ (cos x) 1.0)
5.0ms	(pow (cos x) 3)
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	353	593
1	1734	555
2	5001	535

prune194.0ms

Filtered

61 candidates to 104 candidates (-70.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	101	19	120

Merged error: 0.2b

Counts

120 → 19

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ (cos x) 1.0))
0.3b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.8b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

6.0ms	(* (cos x) (+ (cos x) 1.0))
4.0ms	(+ (cos x) 1.0)
2.0ms	(pow (cos x) 3)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series19.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (cos x) (+ (cos x) 1.0))
2.0ms	(+ (cos x) 1.0)
5.0ms	(pow (cos x) 3)
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	353	593
1	1734	555
2	5001	535

prune186.0ms

Filtered

61 candidates to 104 candidates (-70.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	104	19	123

Merged error: 0.2b

Counts

123 → 19

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x)))) (sin x))
0.3b	(* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x))))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`sqrt-prod`
24×	`sqrt-div`
19×	`pow1`
14×	`add-cube-cbrt` `flip3--` `flip--`
12×	`swap-sqr`
11×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `associate-/l/` `distribute-lft-out--` `add-log-exp`
6×	`difference-of-squares`
5×	`pow-prod-up`
4×	`associate-r/` `associate-l/` `unswap-sqr`
3×	`times-frac` `pow-prod-down` `associate-/r*` `pow-sqr`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `prod-exp` `cbrt-unprod`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `rem-square-sqrt` `-commutative` `div-inv` `associate-/l`

Counts

4 → 122

Calls

4 calls:

11.0ms	(/ (* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x)))) (sin x))
11.0ms	(* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series17.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	304	852
1	1300	750
2	5001	734

prune131.0ms

Filtered

75 candidates to 134 candidates (-78.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	2	15	17
Picked	1	0	1
Done	0	1	1
Total	135	18	153

Merged error: 0.2b

Counts

153 → 18

regimes211.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.7b

bsearch26.0ms

Steps

Iters	Range		Point
9	1.7854326419021657e-07	0.0364262917160445	0.023324099176157787
4	-0.030191044061917315	-0.017383324682467557	-0.021785978219153415

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	20
1	43	20

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.2s	1662×	body	2560	valid
1.3s	2815×	body	1280	valid
441.0ms	1796×	body	640	valid
146.0ms	897×	body	320	valid
57.0ms	477×	body	160	valid
26.0ms	6×	body	5120	valid
24.0ms	347×	body	80	valid

Details

sample146.0ms

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite17.0ms

series12.0ms

simplify78.0ms

prune131.0ms

localize15.0ms

rewrite28.0ms

series19.0ms

simplify67.0ms

prune194.0ms

localize17.0ms

rewrite25.0ms

series19.0ms

simplify67.0ms

prune186.0ms

localize10.0ms

rewrite34.0ms

series17.0ms

simplify51.0ms

prune131.0ms

regimes211.0ms

bsearch26.0ms

simplify1.0ms

end0.0ms

sample4.4s

Profiling