Details

analyze508.0ms

Algorithm: search

sample144.0ms

Algorithm

intervals

Results

70.0ms	52×	body	2560	valid
43.0ms	86×	body	1280	valid
16.0ms	64×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	15×	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: 31.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.8b	(- 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))
3.0ms	(- 1.0 (cos x))

series10.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify77.0ms

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

prune125.0ms

Filtered

42 candidates to 58 candidates (-38.1%)

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: 0.3b

Counts

59 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/240 (pow x 5)) (* 1/2 x))
0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b	(* 1/240 (pow x 5))
0.5b	(* 1/24 (pow x 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

4.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
8.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series25.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
6.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
4.0ms	(* 1/240 (pow x 5))
4.0ms	(* 1/24 (pow x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	355	458
1	1538	429
2	5002	428

prune165.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	92	13	105

Merged error: 0.3b

Counts

105 → 13

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
2.8b	(- 1.0 (cos x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`flip3--` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

3.0ms	(/ 1 (sin x))
10.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms	(- 1.0 (cos x))

series16.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/ 1 (sin x))
9.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms	(- 1.0 (cos x))

simplify41.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	320	546
1	1393	480
2	5001	454

prune121.0ms

Filtered

57 candidates to 96 candidates (-68.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	93	16	109

Merged error: 0.3b

Counts

109 → 16

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
0.2b	(log (- 1.0 (cos x)))
0.3b	(exp (log (- 1.0 (cos x))))
2.8b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`log-prod`
16×	`add-cube-cbrt`
13×	`times-frac` `associate-r` `exp-sum`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1` `log-div` `associate-l`
6×	`exp-diff` `add-log-exp` `unswap-sqr`
5×	`flip3--` `flip--`
4×	`exp-prod` `prod-exp` `distribute-lft-out--` `difference-of-squares`
2×	`frac-times` `div-exp` `associate-*l/` `log-pow` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 97

Calls

4 calls:

12.0ms	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
3.0ms	(log (- 1.0 (cos x)))
4.0ms	(exp (log (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series26.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
13.0ms	(log (- 1.0 (cos x)))
3.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

simplify45.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	381	701
1	1383	625
2	5001	609

prune125.0ms

Filtered

72 candidates to 109 candidates (-51.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	101	8	109
Fresh	9	5	14
Picked	1	0	1
Done	0	1	1
Total	111	14	125

Merged error: 0.3b

Counts

125 → 14

regimes177.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.1b

bsearch48.0ms

Steps

Iters	Range		Point
8	0.02157265737145759	486.56193610373157	0.022015772071504337
9	-2214.7112569607552	-0.0007921003653238374	-0.022861107563872385

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	13
1	34	13

end0.0ms

analyze505.0ms

Algorithm: search

sample4.5s

Algorithm

intervals

Results

2.3s	1570×	body	2560	valid
1.3s	2711×	body	1280	valid
484.0ms	1913×	body	640	valid
179.0ms	920×	body	320	valid
68.0ms	522×	body	160	valid
38.0ms	8×	body	5120	valid
27.0ms	356×	body	80	valid

Details

analyze508.0ms

sample144.0ms

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series10.0ms

simplify77.0ms

prune125.0ms

localize10.0ms

rewrite25.0ms

series25.0ms

simplify52.0ms

prune165.0ms

localize8.0ms

rewrite19.0ms

series16.0ms

simplify41.0ms

prune121.0ms

localize12.0ms

rewrite27.0ms

series26.0ms

simplify45.0ms

prune125.0ms

regimes177.0ms

bsearch48.0ms

simplify1.0ms

end0.0ms

analyze505.0ms

sample4.5s

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