Details

sample52.0ms

Algorithm

intervals

Results

19.0ms	45×	body	2560	valid
11.0ms	46×	body	1280	valid
8.0ms	48×	body	640	valid
4.0ms	38×	body	320	valid
3.0ms	65×	body	80	valid
1.0ms	14×	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 (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: 32.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
13.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
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` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

4.0ms	(- 1.0 (cos x))
13.0ms	(/ (- 1.0 (cos x)) (* x x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify33.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317

prune115.0ms

Filtered

64 candidates to 43 candidates (67.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	9	65

Merged error: 0.1b

Counts

65 → 9

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 1/24 (pow x 2))
12.2b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

9.0ms	(* 1/24 (pow x 2))
1.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series65.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* 1/24 (pow x 2))
42.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify105.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	139	194
1	532	171
2	2601	171
3	5001	170

prune92.0ms

Filtered

45 candidates to 30 candidates (66.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	45	9	54

Merged error: 0.1b

Counts

54 → 9

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.8b	(- 1.0 (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

8.0ms	(/ (/ (- 1.0 (cos x)) x) x)
6.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series109.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (/ (- 1.0 (cos x)) x) x)
46.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify60.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	592	1453
1	2212	1292
2	5001	1283

prune237.0ms

Filtered

174 candidates to 114 candidates (65.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	169	5	174
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	172	11	183

Merged error: 0.1b

Counts

183 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (log (exp (- 1.0 (cos x)))) x)
0.2b	(exp (- 1.0 (cos x)))
1.8b	(- 1.0 (cos x))
1.9b	(log (exp (- 1.0 (cos x))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
30×	`exp-prod` `log-pow`
27×	`times-frac` `prod-diff`
22×	`exp-sum`
14×	`log-prod`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `exp-diff` `fma-neg` `associate-/r*`
2×	`log-div` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 141

Calls

4 calls:

9.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
5.0ms	(exp (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
6.0ms	(log (exp (- 1.0 (cos x))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
44.0ms	(exp (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify50.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	393	1192
1	1234	873
2	5001	725

prune200.0ms

Filtered

153 candidates to 95 candidates (62.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	153	11	164

Merged error: 0.1b

Counts

164 → 11

regimes98.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.5b

bsearch77.0ms

Steps

Iters	Range		Point
10	8.416769919470913e-17	1.2368608357549227	0.03505810655614032
11	-55383.34621353126	-7.66540900750845e-16	-0.029675694574374373

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	15
1	27	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

744.0ms	1563×	body	2560	valid
394.0ms	1457×	body	640	valid
297.0ms	1204×	body	1280	valid
107.0ms	942×	body	320	valid
85.0ms	2315×	body	80	valid
51.0ms	519×	body	160	valid