Details

sample384.0ms

Algorithm

intervals

Results

318.0ms

4192×

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

prune16.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

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)

rewrite48.0ms

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)))
1.0ms	(sqrt PI)

series70.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(* (/ 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)

simplify72.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	426	1781
1	2077	1524
2	5002	1377

prune1.1s

Filtered

224 candidates to 146 candidates (65.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 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

236×	`add-exp-log`
112×	`prod-exp`
94×	`div-exp`
93×	`add-sqr-sqrt` `add-cbrt-cube`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
38×	`cbrt-unprod`
29×	`cbrt-undiv`
27×	`associate-l`
26×	`swap-sqr`
24×	`pow1`
14×	`1-exp`
12×	`pow-to-exp` `pow-exp`
9×	`div-inv`
8×	`unswap-sqr`
7×	`frac-times` `associate-*l/`
5×	`associate-*r/` `pow-prod-down`
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 → 236

Calls

4 calls:

18.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series180.0ms

Counts

4 → 10

Calls

4 calls:

132.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify44.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1007	2431
1	5002	1951

prune1.2s

Filtered

246 candidates to 131 candidates (53.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

128×	`add-sqr-sqrt`
126×	`times-frac`
117×	`add-exp-log`
89×	`add-cube-cbrt` `*-un-lft-identity`
73×	`add-cbrt-cube`
66×	`associate-r`
46×	`prod-exp` `sqrt-prod`
45×	`div-exp`
36×	`associate-l`
26×	`swap-sqr` `cbrt-unprod`
25×	`cbrt-undiv`
21×	`pow1`
13×	`unswap-sqr`
10×	`div-inv`
4×	`pow-to-exp` `pow-exp` `add-log-exp`
3×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 242

Calls

4 calls:

28.0ms	(* (/ (* 1.0 (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (sqrt (fabs x))) (/ (sqrt 1.0) (sqrt (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)

series178.0ms

Counts

4 → 10

Calls

4 calls:

125.0ms	(* (/ (* 1.0 (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (sqrt (fabs x))) (/ (sqrt 1.0) (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)

simplify56.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1063	2942
1	5001	2471

prune1.4s

Filtered

252 candidates to 140 candidates (55.6%)

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

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)

rewrite50.0ms

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:

14.0ms	(* (* (/ 1.0 (fabs x)) (/ 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)))
5.0ms	(sqrt PI)

series89.0ms

Counts

4 → 10

Calls

4 calls:

37.0ms	(* (* (/ 1.0 (fabs x)) (/ 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)

simplify77.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	539	1768
1	2794	1324
2	5002	1206

prune1.3s

Filtered

219 candidates to 128 candidates (58.4%)

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 0.2b

regimes390.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	76
1	65	76

end0.0ms

sample1.1s

Algorithm

intervals

Results

904.0ms

11944×

body

valid