Details

sample346.0ms

Algorithm

intervals

Results

286.0ms

3743×

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize29.0ms

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)

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:

10.0ms	(* (/ 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)

series68.0ms

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)

simplify76.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (55.0ms)

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

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

2333×	`add-exp-log`
1322×	`prod-exp`
1117×	`add-cbrt-cube`
809×	`div-exp`
618×	`cbrt-unprod`
361×	`cbrt-undiv`
131×	`frac-times` `associate-*l/`
105×	`times-frac`
93×	`add-sqr-sqrt`
71×	`pow1`
68×	`add-cube-cbrt` `*-un-lft-identity`
64×	`pow-to-exp` `pow-exp`
39×	`associate-r`
34×	`pow-plus` `pow-prod-up`
33×	`associate-*r/`
27×	`associate-l`
26×	`swap-sqr`
17×	`pow-prod-down`
16×	`pow3` `unpow2`
9×	`div-inv`
8×	`unswap-sqr`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `pow-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 633

Calls

4 calls:

47.0ms	(* (* (* (* (* (/ (* 1.0 1.0) (pow (fabs x) 2)) (/ 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)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series117.0ms

Counts

4 → 10

Calls

4 calls:

69.0ms	(* (* (* (* (* (/ (* 1.0 1.0) (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify154.0ms

Algorithm

egg-herbie

Counts

643 → 643

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	3694	14187
1	5001	9841

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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)

rewrite74.0ms

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

series105.0ms

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)))
31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify138.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	1312	4435
1	4819	2405
2	5002	2358

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

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)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

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

series505.0ms

Counts

4 → 10

Calls

4 calls:

100.0ms	(cbrt (fabs x))
298.0ms	(cbrt (fabs x))
106.0ms	(cbrt (fabs x))
0.0ms	(sqrt PI)

simplify45.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	51	196
1	100	181
2	235	175
3	990	173
4	5001	173

prune342.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes208.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	54
1	54	54

end0.0ms

sample6.4s

Algorithm

intervals

Results

5.5s

73630×

body

valid