Details

sample331.0ms

Algorithm

intervals

Results

274.0ms

3559×

body

valid

simplify67.0ms

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)

Merged error: 1.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite53.0ms

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:

13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
16.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(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)

simplify72.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (56.0ms)

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

prune1.1s

Filtered

224 candidates to 146 candidates (65.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize34.0ms

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)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite369.0ms

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:

314.0ms	(* (* (* (* (/ 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)))
16.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series105.0ms

Counts

4 → 10

Calls

4 calls:

51.0ms	(* (* (* (* (/ 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)

simplify62.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1387	4492
1	5001	2488

prune1.1s

Filtered

342 candidates to 135 candidates (39.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1.0 (fabs x)) (sqrt (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
163×	`add-sqr-sqrt`
138×	`add-cube-cbrt` `*-un-lft-identity`
45×	`sqrt-prod`
33×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
16×	`div-inv`
13×	`associate-/l*`
11×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`associate-/r*`
4×	`add-log-exp`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 259

Calls

4 calls:

7.0ms	(/ (/ 1.0 (fabs x)) (sqrt (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series122.0ms

Counts

4 → 10

Calls

4 calls:

69.0ms	(/ (/ 1.0 (fabs x)) (sqrt (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)

simplify120.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	793	2547
1	4350	2202
2	5001	2167

prune1.8s

Filtered

269 candidates to 175 candidates (65.1%)

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
1.0b	(sqrt PI)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-exp-log` `add-cbrt-cube`
130×	`pow1`
86×	`add-sqr-sqrt`
80×	`times-frac`
73×	`prod-exp` `cbrt-unprod`
61×	`add-cube-cbrt` `*-un-lft-identity`
48×	`cbrt-undiv` `div-exp`
38×	`pow-prod-up`
27×	`swap-sqr` `associate-r` `associate-l`
25×	`pow-prod-down`
24×	`pow-sqr`
20×	`pow-plus`
19×	`frac-times`
15×	`pow2`
13×	`associate-r/` `associate-l/`
9×	`unswap-sqr`
8×	`div-inv`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 267

Calls

4 calls:

13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
1.0ms	(sqrt PI)

series91.0ms

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)))
39.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
0.0ms	(sqrt PI)

simplify100.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	755	2197
1	3511	1420
2	5001	1339

prune922.0ms

Filtered

277 candidates to 123 candidates (44.4%)

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 0.4b

regimes411.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	60
1	54	60

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.6s

20839×

body

valid