Details

sample34.0ms

Algorithm

intervals

Results

15.0ms	81×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	183×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	11×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

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: 39.6b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.3b	(- (exp x) 1.0)

rewrite12.0ms

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	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2717	309
3	5001	309

prune104.0ms

Filtered

58 candidates to 43 candidates (74.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Merged error: 0.1b

Counts

59 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x 1/6) 1/2)
0.0b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)
2.1b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

4.0ms	(+ (* x 1/6) 1/2)
8.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
4.0ms	(* x 1/6)
10.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

series161.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x 1/6) 1/2)
66.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
14.0ms	(* x 1/6)
49.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	384	620
1	2008	562
2	5002	562

prune162.0ms

Filtered

101 candidates to 70 candidates (69.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	100	5	105

Merged error: 0.1b

Counts

105 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.9b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2))
1.5b	(/ (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)) (cbrt x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

486×	`times-frac`
253×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
195×	`cbrt-prod`
150×	`unpow-prod-down`
40×	`associate-/l*`
25×	`unpow2` `sqr-pow`
19×	`add-exp-log`
17×	`associate-/r*`
10×	`div-exp`
9×	`add-cbrt-cube` `div-inv`
4×	`pow1` `cbrt-undiv` `add-log-exp`
3×	`associate-/l/`
2×	`pow-to-exp` `frac-2neg` `pow1/3` `pow-exp` `clear-num`
1×	`flip3-+` `flip-+`

Counts

4 → 367

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
13.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2))
19.0ms	(/ (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)) (cbrt x))

series512.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt x)
177.0ms	(cbrt x)
94.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2))
66.0ms	(/ (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)) (cbrt x))

simplify95.0ms

Algorithm

egg-herbie

Counts

379 → 379

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1217	7067
1	5001	6478

prune1.1s

Filtered

379 candidates to 289 candidates (76.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	378	1	379
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	379	5	384

Merged error: 0.1b

Counts

384 → 5

localize35.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2))
12.5b	(cbrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)))
12.5b	(cbrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)))
12.5b	(cbrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

150×	`cbrt-prod`
132×	`times-frac`
91×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
78×	`unpow-prod-down`
13×	`unpow2` `sqr-pow`
11×	`associate-/r*`
9×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`pow1` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-exp` `associate-/l*`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip-+`

Counts

4 → 201

Calls

4 calls:

14.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2))
9.0ms	(cbrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)))
10.0ms	(cbrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)))
13.0ms	(cbrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2))
178.0ms	(cbrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)))
177.0ms	(cbrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)))
179.0ms	(cbrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) (pow (cbrt x) 2)))

simplify86.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	502	3783
1	1907	3567
2	5001	3503

prune787.0ms

Filtered

213 candidates to 146 candidates (68.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	213	5	218

Merged error: 0.1b

Counts

218 → 5

Details

sample34.0ms

simplify6.0ms

prune2.0ms

localize4.0ms

rewrite12.0ms

series59.0ms

simplify76.0ms

prune104.0ms

localize8.0ms

rewrite27.0ms

series161.0ms

simplify65.0ms

prune162.0ms

localize12.0ms

rewrite61.0ms

series512.0ms

simplify95.0ms

prune1.1s

localize35.0ms

rewrite55.0ms

series631.0ms

simplify86.0ms

prune787.0ms

regimes51.0ms

bsearch3.0ms

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