Details

sample143.0ms

Algorithm

intervals

Results

69.0ms	57×	body	2560	valid
44.0ms	93×	body	1280	valid
14.0ms	58×	body	640	valid
5.0ms	28×	body	320	valid
3.0ms	1×	body	5120	valid
1.0ms	10×	body	160	valid
1.0ms	9×	body	80	valid

simplify6.0ms

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: 33.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(- 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))

series59.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
24.0ms	(- 1.0 (cos x))

simplify80.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune165.0ms

Filtered

58 candidates to 42 candidates (72.4%)

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: 0.1b

Counts

59 → 16

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`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×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

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))

series144.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
46.0ms	(* 1/240 (pow x 5))
40.0ms	(* 1/24 (pow x 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	301	375
1	1301	346
2	5002	346

prune165.0ms

Filtered

78 candidates to 49 candidates (62.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	78	16	94

Merged error: 0.1b

Counts

94 → 16

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.4b	(- 1.0 (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

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

series150.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
18.0ms	(exp (log (- 1.0 (cos x))))
77.0ms	(log (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify91.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	289	829
1	791	761
2	2667	734
3	5001	708

prune222.0ms

Filtered

110 candidates to 69 candidates (62.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	111	15	126

Merged error: 0.1b

Counts

126 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(pow E (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.4b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

8.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
5.0ms	(pow E (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series509.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
204.0ms	(pow E (log (- 1.0 (cos x))))
75.0ms	(log (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify55.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	410	1229
1	1449	1100
2	5001	1062

prune280.0ms

Filtered

136 candidates to 96 candidates (70.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	135	16	151

Merged error: 0.1b

Counts

151 → 16

regimes162.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.0b

bsearch102.0ms

Steps

Iters	Range		Point
10	0.0002141056345597589	3206628.0142593775	0.02033085351791419
11	-4.816760182774211e+16	-0.0014803844373699059	-0.0247351870379494

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	30
1	52	30
2	52	30

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.0s	1562×	body	2560	valid
1.3s	2834×	body	1280	valid
447.0ms	1861×	body	640	valid
160.0ms	961×	body	320	valid
65.0ms	452×	body	160	valid
22.0ms	326×	body	80	valid
11.0ms	4×	body	5120	valid