Details

sample337.0ms

Algorithm

intervals

Results

283.0ms

2983×

body

valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

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

prune17.0ms

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)

rewrite46.0ms

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

series69.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify77.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (55.0ms)

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

prune990.0ms

Filtered

224 candidates to 146 candidates (65.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	209	15	224
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	210	16	226

Merged error: 0.5b

Counts

226 → 16

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

241×	`add-exp-log`
145×	`add-cbrt-cube`
114×	`prod-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
85×	`div-exp`
68×	`add-cube-cbrt` `*-un-lft-identity`
66×	`cbrt-unprod`
45×	`cbrt-undiv`
39×	`associate-r`
28×	`pow1`
27×	`associate-l`
26×	`swap-sqr`
19×	`frac-times` `associate-*l/`
9×	`associate-*r/` `div-inv`
8×	`pow-to-exp` `pow-prod-down` `pow-exp` `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 → 247

Calls

4 calls:

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

series102.0ms

Counts

4 → 10

Calls

4 calls:

56.0ms	(* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 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)

simplify48.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	956	2876
1	5002	2096

prune1.0s

Filtered

257 candidates to 133 candidates (51.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	246	11	257
Fresh	7	8	15
Picked	1	0	1
Done	0	0	0
Total	254	19	273

Merged error: 0.3b

Counts

273 → 19

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (/ 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)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`pow3` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 332

Calls

4 calls:

27.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series100.0ms

Counts

4 → 10

Calls

4 calls:

54.0ms	(* (* (* (* (/ 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)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify132.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	1306	4435
1	4803	2405
2	5001	2358

prune1.2s

Filtered

342 candidates to 134 candidates (39.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	340	2	342
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	342	19	361

Merged error: 0.3b

Counts

361 → 19

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (cbrt (/ 1.0 (fabs x))) (cbrt (/ 1.0 (fabs x))))
0.7b	(pow (cbrt (/ 1.0 (fabs x))) 3)
1.0b	(sqrt PI)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

119×	`add-sqr-sqrt`
100×	`times-frac`
90×	`cbrt-prod`
82×	`add-cube-cbrt` `*-un-lft-identity`
29×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
19×	`add-exp-log`
16×	`unpow-prod-down` `cube-prod` `add-cbrt-cube`
13×	`unswap-sqr`
10×	`div-inv`
7×	`pow1/3`
5×	`cbrt-div` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `sqrt-prod` `pow-sqr` `pow-prod-up`
2×	`pow2` `frac-times` `pow-pow` `pow-plus` `associate-r/` `associate-l/` `*-commutative`
1×	`cube-div` `cube-mult` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 209

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
15.0ms	(* (cbrt (/ 1.0 (fabs x))) (cbrt (/ 1.0 (fabs x))))
5.0ms	(pow (cbrt (/ 1.0 (fabs x))) 3)
1.0ms	(sqrt PI)

series426.0ms

Counts

4 → 10

Calls

4 calls:

22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
195.0ms	(* (cbrt (/ 1.0 (fabs x))) (cbrt (/ 1.0 (fabs x))))
208.0ms	(pow (cbrt (/ 1.0 (fabs x))) 3)
0.0ms	(sqrt PI)

simplify47.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	755	1746
1	5001	1504

prune1.1s

Filtered

219 candidates to 137 candidates (62.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	219	19	238

Merged error: 0.3b

Counts

238 → 19

regimes310.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	61
1	57	61

end0.0ms

sample515.0ms

Algorithm

intervals

Results

441.0ms

4739×

body

valid

Details

sample337.0ms

simplify67.0ms

prune17.0ms

localize28.0ms

rewrite46.0ms

series69.0ms

simplify77.0ms

prune990.0ms

localize33.0ms

rewrite59.0ms

series102.0ms

simplify48.0ms

prune1.0s

localize30.0ms

rewrite83.0ms

series100.0ms

simplify132.0ms

prune1.2s

localize38.0ms

rewrite42.0ms

series426.0ms

simplify47.0ms

prune1.1s

regimes310.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample515.0ms

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