Details

sample391.0ms

Algorithm

intervals

Results

330.0ms

3399×

body

valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36

prune14.0ms

Filtered

1 candidates to 1 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: 1.2b

Counts

2 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
120×	`times-frac`
89×	`add-cube-cbrt` `*-un-lft-identity`
40×	`add-exp-log` `add-cbrt-cube`
39×	`swap-sqr` `associate-r` `associate-l`
26×	`pow1`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `sqrt-prod` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 214

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series75.0ms

Counts

4 → 10

Calls

4 calls:

28.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify73.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	426	1780
1	2077	1524
2	5002	1377

prune967.0ms

Filtered

224 candidates to 146 candidates (65.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	213	11	224
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	214	12	226

Merged error: 0.6b

Counts

226 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

1357×	`add-exp-log`
781×	`add-cbrt-cube`
746×	`prod-exp`
473×	`div-exp`
426×	`cbrt-unprod`
249×	`cbrt-undiv`
131×	`frac-times` `associate-*l/`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
39×	`pow1` `associate-r`
33×	`associate-*r/`
32×	`pow-to-exp` `pow-exp`
27×	`associate-l`
26×	`swap-sqr`
17×	`pow-prod-down`
9×	`div-inv`
8×	`unswap-sqr`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 489

Calls

4 calls:

41.0ms	(* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series118.0ms

Counts

4 → 10

Calls

4 calls:

71.0ms	(* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify121.0ms

Algorithm

egg-herbie

Counts

499 → 499

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2775	10159
1	5001	7055

prune1.3s

Filtered

499 candidates to 146 candidates (29.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	488	11	499
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	497	14	511

Merged error: 0.2b

Counts

511 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
90×	`times-frac`
69×	`add-exp-log` `add-cbrt-cube`
68×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
38×	`pow1`
27×	`associate-l`
26×	`swap-sqr` `prod-exp` `cbrt-unprod`
21×	`cbrt-undiv` `div-exp`
10×	`unswap-sqr`
9×	`div-inv`
8×	`pow-plus` `pow-prod-up`
7×	`frac-times` `associate-*l/`
5×	`associate-*r/` `pow-prod-down`
4×	`pow2` `pow-sqr` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow3`

Counts

4 → 209

Calls

4 calls:

13.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series83.0ms

Counts

4 → 10

Calls

4 calls:

36.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify82.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	525	1756
1	2732	1311
2	5002	1193

prune822.0ms

Filtered

219 candidates to 128 candidates (58.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	219	14	233

Merged error: 0.2b

Counts

233 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) 1.0) 1.0) 1.0) 1.0) 1.0) (pow (fabs x) 5))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-exp-log`
98×	`prod-exp`
90×	`add-sqr-sqrt`
87×	`times-frac`
65×	`add-cube-cbrt` `*-un-lft-identity`
63×	`add-cbrt-cube`
44×	`div-exp`
28×	`cbrt-unprod`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
16×	`cbrt-undiv`
12×	`pow-to-exp` `pow-exp`
9×	`div-inv`
8×	`unswap-sqr`
7×	`associate-l/` `associate-/r`
6×	`unpow-prod-down`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/` `associate-/l*`

Counts

4 → 207

Calls

4 calls:

22.0ms	(/ (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) 1.0) 1.0) 1.0) 1.0) 1.0) (pow (fabs x) 5))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series115.0ms

Counts

4 → 10

Calls

4 calls:

69.0ms	(/ (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) 1.0) 1.0) 1.0) 1.0) 1.0) (pow (fabs x) 5))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify126.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	901	2100
1	4542	1740
2	5001	1727

prune932.0ms

Filtered

217 candidates to 127 candidates (58.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	213	4	217
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	217	14	231

Merged error: 0.2b

Counts

231 → 14

regimes229.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	44
1	43	44

end0.0ms

sample835.0ms

Algorithm

intervals

Results

729.0ms

7552×

body

valid