Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	51×	body	2560	valid
9.0ms	45×	body	1280	valid
7.0ms	51×	body	640	valid
2.0ms	25×	body	320	valid
2.0ms	63×	body	80	valid
1.0ms	21×	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: 32.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

3.2b	(- 1.0 (cos x))
16.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 126

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
11.0ms	(/ (- 1.0 (cos x)) (* x x))

series68.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- 1.0 (cos x))
50.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify56.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	487	1050
1	1961	1000
2	5002	981

prune177.0ms

Filtered

132 candidates to 73 candidates (55.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	121	11	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	11	133

Merged error: 0.2b

Counts

133 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.6b	(* 1/24 (pow x 2))
11.4b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
15×	`associate-r`
13×	`add-exp-log`
11×	`associate-l` `unswap-sqr`
9×	`add-cube-cbrt` `unpow-prod-down`
8×	`add-log-exp`
7×	`pow1` `add-cbrt-cube`
6×	`prod-exp` `distribute-lft-out--`
5×	`difference-of-squares` `sqr-pow`
4×	`distribute-lft-out`
3×	`unpow2`
2×	`pow-to-exp` `diff-log` `pow-prod-down` `pow-exp` `associate--l+` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `flip3--` `sum-log` `flip--`

Counts

3 → 80

Calls

3 calls:

6.0ms	(* 1/720 (pow x 4))
6.0ms	(* 1/24 (pow x 2))
21.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* 1/720 (pow x 4))
24.0ms	(* 1/24 (pow x 2))
47.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify40.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	292	472
1	1147	437
2	5002	433

prune137.0ms

Filtered

89 candidates to 50 candidates (56.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	89	11	100

Merged error: 0.2b

Counts

100 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.2b	(- 1.0 (cos x))
6.1b	(/ (- 1.0 (cos x)) (* (cbrt x) x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
80×	`times-frac`
47×	`add-cube-cbrt`
36×	`associate-l`
30×	`cbrt-prod`
18×	`associate-r` `distribute-lft-out--` `difference-of-squares`
16×	`associate-/r*`
12×	`unswap-sqr`
11×	`add-cbrt-cube`
9×	`add-exp-log`
6×	`*-commutative` `add-log-exp`
5×	`associate-/l*`
4×	`pow1`
3×	`cbrt-undiv`
2×	`flip3--` `pow1/3` `div-exp` `flip--` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `div-inv`

Counts

4 → 155

Calls

4 calls:

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

series640.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
176.0ms	(cbrt x)
19.0ms	(- 1.0 (cos x))
263.0ms	(/ (- 1.0 (cos x)) (* (cbrt x) x))

simplify66.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	617	1421
1	2291	1335
2	5001	1328

prune322.0ms

Filtered

167 candidates to 119 candidates (71.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	166	12	178

Merged error: 0.2b

Counts

178 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.2b	(- 1.0 (cos x))
3.3b	(log (exp (- 1.0 (cos x))))
6.1b	(/ (log (exp (- 1.0 (cos x)))) (* (cbrt x) x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

159×	`add-sqr-sqrt`
144×	`times-frac`
119×	`*-un-lft-identity`
108×	`log-pow`
90×	`exp-prod`
81×	`add-cube-cbrt`
60×	`associate-l`
43×	`cbrt-prod`
30×	`associate-r`
22×	`pow1`
20×	`unswap-sqr`
19×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/r*`
11×	`add-cbrt-cube`
10×	`add-exp-log` `*-commutative`
9×	`associate-/l*`
6×	`add-log-exp`
5×	`log-prod`
3×	`cbrt-undiv`
2×	`sub-neg` `log-div` `exp-diff` `div-exp` `rem-log-exp` `exp-sum` `cbrt-unprod`
1×	`flip3--` `frac-2neg` `pow1/3` `diff-log` `div-sub` `prod-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 231

Calls

4 calls:

1.0ms	(cbrt x)
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))
16.0ms	(/ (log (exp (- 1.0 (cos x)))) (* (cbrt x) x))

series482.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt x)
18.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))
264.0ms	(/ (log (exp (- 1.0 (cos x)))) (* (cbrt x) x))

simplify84.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	769	2418
1	2728	2137
2	5001	2134

prune403.0ms

Filtered

243 candidates to 149 candidates (61.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	240	3	243
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	243	12	255

Merged error: 0.2b

Counts

255 → 12

regimes62.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.9b

bsearch68.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	0.03316890245008123
7	-0.05767290693153419	-0.00024695944164034034	-0.03185288092824355

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

722.0ms	1553×	body	2560	valid
310.0ms	1341×	body	1280	valid
221.0ms	1477×	body	640	valid
101.0ms	936×	body	320	valid
73.0ms	2205×	body	80	valid
35.0ms	488×	body	160	valid