Details

sample51.0ms

Algorithm

intervals

Results

20.0ms	48×	body	2560	valid
10.0ms	46×	body	1280	valid
7.0ms	48×	body	640	valid
4.0ms	36×	body	320	valid
3.0ms	70×	body	80	valid
1.0ms	8×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 34.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
15.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
75×	`times-frac`
55×	`add-cube-cbrt`
18×	`swap-sqr` `associate-r` `associate-l`
17×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r*`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
6×	`*-commutative` `unswap-sqr`
5×	`associate-/l*`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`

Counts

2 → 142

Calls

2 calls:

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

series64.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- 1.0 (cos x))
45.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify73.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	545	1225
1	2348	1087
2	5001	1068

prune203.0ms

Filtered

148 candidates to 82 candidates (44.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	135	13	148
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	13	149

Merged error: 0.2b

Counts

149 → 13

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 1/24 (pow x 2))
11.9b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 40

Calls

2 calls:

6.0ms	(* 1/24 (pow x 2))
1.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series72.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* 1/24 (pow x 2))
47.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify100.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	139	196
1	532	173
2	2581	173
3	5001	172

prune97.0ms

Filtered

46 candidates to 30 candidates (34.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	46	13	59

Merged error: 0.2b

Counts

59 → 13

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.5b	(- 1.0 (cos x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

137×	`add-sqr-sqrt`
125×	`*-un-lft-identity`
117×	`frac-times`
99×	`associate-/l*`
84×	`add-cube-cbrt`
75×	`associate-/r*`
46×	`times-frac`
27×	`add-exp-log`
26×	`clear-num`
25×	`frac-2neg`
22×	`associate-/l/`
19×	`associate-r` `distribute-lft-out--`
18×	`difference-of-squares`
17×	`add-cbrt-cube`
13×	`associate-r/` `associate-l*`
12×	`flip3--` `flip--`
9×	`div-exp` `prod-diff` `associate-*l/`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `add-log-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `fma-neg` `un-div-inv` `log1p-expm1-u` `div-inv`
2×	`rec-exp` `1-exp`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down` `*-commutative`

Counts

3 → 271

Calls

3 calls:

12.0ms	(/ (- 1.0 (cos x)) x)
20.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
4.0ms	(- 1.0 (cos x))

series109.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- 1.0 (cos x)) x)
42.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
19.0ms	(- 1.0 (cos x))

simplify51.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1122	2125
1	5001	1863

prune302.0ms

Filtered

280 candidates to 145 candidates (48.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	272	8	280
Fresh	8	3	11
Picked	1	0	1
Done	0	1	1
Total	281	12	293

Merged error: 0.2b

Counts

293 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 x) (/ (exp (log (- 1.0 (cos x)))) x))
0.2b	(exp (log (- 1.0 (cos x))))
0.4b	(log (- 1.0 (cos x)))
1.5b	(- 1.0 (cos x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

159×	`add-sqr-sqrt`
144×	`frac-times`
136×	`*-un-lft-identity`
132×	`associate-/l*`
100×	`add-cube-cbrt`
81×	`associate-/r*`
78×	`log-prod`
73×	`exp-sum`
45×	`times-frac`
36×	`add-exp-log`
28×	`associate-r` `clear-num`
27×	`frac-2neg`
24×	`log-div`
22×	`exp-diff`
20×	`associate-/l/`
16×	`associate-*r/` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
14×	`div-exp`
13×	`flip3--` `associate-l` `flip--`
12×	`prod-exp`
9×	`prod-diff` `associate-*l/` `unswap-sqr`
8×	`pow1`
7×	`add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `exp-prod` `cbrt-unprod` `log1p-expm1-u`
3×	`rec-exp` `fma-neg` `1-exp`
2×	`log-pow` `un-div-inv` `div-inv` `rem-exp-log`
1×	`sub-neg` `diff-log` `rem-log-exp` `pow-prod-down` `*-commutative`

Counts

4 → 316

Calls

4 calls:

25.0ms	(* (/ 1 x) (/ (exp (log (- 1.0 (cos x)))) x))
5.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series165.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ 1 x) (/ (exp (log (- 1.0 (cos x)))) x))
24.0ms	(exp (log (- 1.0 (cos x))))
78.0ms	(log (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify64.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1262	2659
1	5001	2300

prune479.0ms

Filtered

328 candidates to 154 candidates (53.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	325	3	328
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	327	13	340

Merged error: 0.2b

Counts

340 → 13

regimes58.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.7b

bsearch56.0ms

Steps

Iters	Range		Point
9	0.0004381094517774334	96283.49646244562	0.03411142251183559
6	-0.04448272872103196	-0.010589856477353462	-0.029536016732455837

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	18
1	36	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

748.0ms	1597×	body	2560	valid
280.0ms	1226×	body	1280	valid
228.0ms	1534×	body	640	valid
101.0ms	913×	body	320	valid
72.0ms	2240×	body	80	valid
37.0ms	490×	body	160	valid