Details

sample53.0ms

Algorithm

intervals

Results

20.0ms	41×	body	2560	valid
10.0ms	39×	body	1280	valid
7.0ms	43×	body	640	valid
4.0ms	31×	body	320	valid
3.0ms	79×	body	80	valid
2.0ms	23×	body	160	valid

simplify7.0ms

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: 27.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.8b	(- 1.0 (cos x))
12.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

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))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
48.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify34.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (28.0ms)

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

prune128.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(/ (sqrt (- 1.0 (cos x))) x)
2.8b	(- 1.0 (cos x))
2.8b	(- 1.0 (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
48×	`times-frac`
40×	`sqrt-prod`
18×	`prod-diff`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`fma-neg` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 158

Calls

4 calls:

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

series213.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify182.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 3 (163.0ms)

Iter	Nodes	Cost
0	301	1368
1	936	1148
2	4953	1118
3	5001	1112

prune301.0ms

Filtered

170 candidates to 110 candidates (64.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	170	9	179

Merged error: 0.1b

Counts

179 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
2.8b	(- 1.0 (cos x))
2.8b	(- 1.0 (cos x))
2.8b	(- 1.0 (cos x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`cbrt-prod`
27×	`prod-diff`
12×	`cbrt-div`
11×	`pow1`
10×	`swap-sqr` `add-log-exp`
9×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log` `pow1/3`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 142

Calls

4 calls:

10.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series198.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify168.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	283	1323
1	928	1020
2	4905	923
3	5001	914

prune288.0ms

Filtered

154 candidates to 93 candidates (60.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	153	10	163

Merged error: 0.0b

Counts

163 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (sqrt (cbrt (- 1.0 (cos x)))) 4)
2.2b	(log (pow (exp 1) (pow (sqrt (cbrt (- 1.0 (cos x)))) 4)))
2.8b	(- 1.0 (cos x))
2.8b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`prod-diff`
14×	`unpow-prod-down`
8×	`sqrt-prod` `add-log-exp`
7×	`log-prod`
6×	`pow1` `add-exp-log` `fma-neg`
5×	`cbrt-prod`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow` `rem-log-exp` `distribute-lft-out--` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `pow-exp` `flip--` `sqr-pow`
1×	`pow1/2` `pow1/3` `log-pow` `sqrt-pow2`

Counts

4 → 107

Calls

4 calls:

9.0ms	(pow (sqrt (cbrt (- 1.0 (cos x)))) 4)
3.0ms	(log (pow (exp 1) (pow (sqrt (cbrt (- 1.0 (cos x)))) 4)))
5.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series536.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(pow (sqrt (cbrt (- 1.0 (cos x)))) 4)
341.0ms	(log (pow (exp 1) (pow (sqrt (cbrt (- 1.0 (cos x)))) 4)))
19.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify52.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	361	1013
1	1252	721
2	5001	693

prune323.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	119	10	129

Merged error: 0.0b

Counts

129 → 10

regimes90.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch72.0ms

Steps

Iters	Range		Point
10	0.00022027325057658872	62623256.830634765	0.03061966180240735
9	-17.831791951177678	-3.7534567552478157e-06	-0.027340075628349603

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

sample1.9s

Algorithm

intervals

Results

934.0ms	1622×	body	2560	valid
311.0ms	1231×	body	1280	valid
244.0ms	1482×	body	640	valid
120.0ms	979×	body	320	valid
85.0ms	2213×	body	80	valid
39.0ms	473×	body	160	valid

Details

sample53.0ms

simplify7.0ms

prune2.0ms

localize6.0ms

rewrite13.0ms

series66.0ms

simplify34.0ms

prune128.0ms

localize11.0ms

rewrite26.0ms

series213.0ms

simplify182.0ms

prune301.0ms

localize10.0ms

rewrite31.0ms

series198.0ms

simplify168.0ms

prune288.0ms

localize21.0ms

rewrite24.0ms

series536.0ms

simplify52.0ms

prune323.0ms

regimes90.0ms

bsearch72.0ms

simplify1.0ms

end0.0ms

sample1.9s

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