Details

sample864.0ms

Algorithm

intervals

Results

750.0ms

3295×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	31	103
1	90	103
2	401	65
3	2023	51
done	5001	49

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize90.0ms

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)

rewrite146.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 222

Calls

4 calls:

46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
49.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(sqrt PI)

series121.0ms

Counts

4 → 10

Calls

4 calls:

37.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify1.8s

Counts

232 → 232

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	150	3287
1	407	2964
2	1497	2446
done	5000	2298

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.5b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1197×	`add-exp-log`
666×	`prod-exp`
409×	`div-exp`
205×	`add-cbrt-cube`
144×	`pow-exp`
106×	`cbrt-unprod`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
57×	`cbrt-undiv`
48×	`pow-to-exp`
39×	`associate-r`
32×	`pow1`
27×	`associate-l`
26×	`swap-sqr`
19×	`frac-times` `associate-*l/`
17×	`associate-*r/`
12×	`pow-prod-down`
9×	`div-inv`
8×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 384

Calls

4 calls:

1.1s	(* (* (* (* (pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 1) (/ 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)))
47.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series187.0ms

Counts

4 → 10

Calls

4 calls:

78.0ms	(* (* (* (* (pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 1) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
56.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
45.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify3.2s

Counts

394 → 394

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	490	12306
1	1138	9359
2	3396	4431
done	5001	3990

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

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

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

145×	`add-exp-log` `add-cbrt-cube`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
66×	`prod-exp` `cbrt-unprod`
65×	`pow1`
45×	`cbrt-undiv` `div-exp`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
23×	`pow-plus` `pow-prod-up`
19×	`frac-times` `associate-*l/`
9×	`associate-*r/` `div-inv`
8×	`pow-prod-down` `unswap-sqr`
6×	`pow2` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 257

Calls

4 calls:

227.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series170.0ms

Counts

4 → 10

Calls

4 calls:

80.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
47.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
42.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify2.3s

Counts

267 → 267

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	249	4933
1	642	4349
2	2081	2558
done	5000	2223

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize107.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fabs x))
0.6b	(cbrt (fabs x))
0.6b	(cbrt (fabs x))
1.0b	(sqrt PI)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt (fabs x))
1.0ms	(cbrt (fabs x))
1.0ms	(cbrt (fabs x))
2.0ms	(sqrt PI)

series519.0ms

Counts

4 → 10

Calls

4 calls:

174.0ms	(cbrt (fabs x))
175.0ms	(cbrt (fabs x))
170.0ms	(cbrt (fabs x))
0.0ms	(sqrt PI)

simplify2.1s

Counts

64 → 64

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	73	413
1	160	391
2	595	342
3	3316	315
done	5000	312

prune664.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

regimes446.0ms

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	100
1	59	100
done	59	100

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.5s

4356×

body

valid