Details

sample440.0ms

Algorithm

intervals

Results

376.0ms

3723×

body

valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

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: 1.1b

Counts

2 → 2

localize35.0ms

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)

rewrite44.0ms

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:

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

series77.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify76.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (58.0ms)

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

prune1.0s

Filtered

224 candidates to 146 candidates (65.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	207	17	224
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	208	18	226

Merged error: 0.5b

Counts

226 → 18

localize34.0ms

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)

rewrite61.0ms

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:

24.0ms	(* (* (* (/ 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)

series104.0ms

Counts

4 → 10

Calls

4 calls:

58.0ms	(* (* (* (/ 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)

simplify50.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	956	2876
1	5002	2096

prune1.0s

Filtered

257 candidates to 133 candidates (51.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	246	11	257
Fresh	10	7	17
Picked	1	0	1
Done	0	0	0
Total	257	18	275

Merged error: 0.3b

Counts

275 → 18

localize31.0ms

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)

rewrite79.0ms

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:

28.0ms	(* (* (* (* (/ 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)))
15.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series107.0ms

Counts

4 → 10

Calls

4 calls:

55.0ms	(* (* (* (* (/ 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)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify130.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (98.0ms)

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

prune1.1s

Filtered

342 candidates to 134 candidates (39.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	341	19	360

Merged error: 0.3b

Counts

360 → 19

localize35.0ms

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)

rewrite77.0ms

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:

28.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series102.0ms

Counts

4 → 10

Calls

4 calls:

50.0ms	(* (* (* (* (/ 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)))
30.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify63.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1384	4475
1	5002	2461

prune934.0ms

Filtered

342 candidates to 135 candidates (39.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	1	16	17
Picked	1	0	1
Done	0	1	1
Total	343	18	361

Merged error: 0.2b

Counts

361 → 18

regimes284.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	50
1	47	50

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.3s

13463×

body

valid

Details

sample440.0ms

simplify68.0ms

prune14.0ms

localize35.0ms

rewrite44.0ms

series77.0ms

simplify76.0ms

prune1.0s

localize34.0ms

rewrite61.0ms

series104.0ms

simplify50.0ms

prune1.0s

localize31.0ms

rewrite79.0ms

series107.0ms

simplify130.0ms

prune1.1s

localize35.0ms

rewrite77.0ms

series102.0ms

simplify63.0ms

prune934.0ms

regimes284.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.5s

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