Details

sample405.0ms

Algorithm

intervals

Results

342.0ms

3305×

body

valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

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

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `times-frac`
63×	`add-cube-cbrt` `*-un-lft-identity`
26×	`unpow-prod-down` `cube-prod`
22×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `div-exp`
4×	`pow-exp` `prod-exp` `cbrt-unprod` `add-log-exp` `rem-cube-cbrt` `unswap-sqr`
3×	`sqrt-prod`
2×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `sqr-pow`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 172

Calls

4 calls:

11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series92.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms	(pow (/ 1.0 (fabs x)) 3)
37.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify132.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	584	1144
1	3655	959
2	5001	912

prune834.0ms

Filtered

182 candidates to 100 candidates (54.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	163	19	182
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	164	20	184

Merged error: 0.4b

Counts

184 → 20

localize29.0ms

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)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
98×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
13×	`unpow-prod-down` `cube-prod`
10×	`div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

14.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series84.0ms

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)))
33.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify114.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	535	1298
1	3321	1112
2	5001	972

prune838.0ms

Filtered

203 candidates to 119 candidates (58.6%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	194	9	203
Fresh	5	14	19
Picked	1	0	1
Done	0	0	0
Total	200	23	223

Merged error: 0.3b

Counts

223 → 23

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-sqr-sqrt`
158×	`times-frac`
85×	`add-cube-cbrt` `*-un-lft-identity`
67×	`add-exp-log`
53×	`associate-r`
41×	`unpow-prod-down` `associate-l`
31×	`add-cbrt-cube`
29×	`div-exp` `unswap-sqr`
27×	`cube-prod`
20×	`prod-exp`
17×	`sqr-pow`
15×	`pow1`
13×	`swap-sqr`
10×	`pow-exp`
9×	`cbrt-undiv` `pow-to-exp`
8×	`cbrt-unprod` `div-inv` `unpow2`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `rem-cube-cbrt`
1×	`cube-div` `pow2` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 251

Calls

4 calls:

32.0ms	(* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series108.0ms

Counts

4 → 10

Calls

4 calls:

54.0ms	(* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify50.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1131	2131
1	5002	1843

prune1.1s

Filtered

261 candidates to 156 candidates (59.8%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	248	13	261
Fresh	13	9	22
Picked	1	0	1
Done	0	0	0
Total	262	22	284

Merged error: 0.2b

Counts

284 → 22

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
0.4b	(* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt`
121×	`add-exp-log`
118×	`times-frac`
58×	`add-cube-cbrt` `*-un-lft-identity`
49×	`div-exp` `prod-exp`
43×	`associate-r`
41×	`unpow-prod-down`
37×	`add-cbrt-cube`
29×	`associate-l`
27×	`cube-prod`
26×	`frac-times`
25×	`unswap-sqr`
18×	`pow-exp`
17×	`pow-to-exp` `sqr-pow`
16×	`associate-*r/`
14×	`associate-*l/`
13×	`pow1` `cbrt-unprod`
12×	`frac-add`
9×	`cbrt-undiv`
8×	`unpow2`
4×	`cube-mult` `flip3-+` `unpow3` `pow-prod-down` `flip-+` `div-inv` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`*-commutative` `rem-cube-cbrt`
1×	`cube-div` `distribute-rgt-in` `rem-sqrt-square` `pow-pow` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 245

Calls

4 calls:

20.0ms	(* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
29.0ms	(* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series204.0ms

Counts

4 → 10

Calls

4 calls:

119.0ms	(* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
53.0ms	(* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3)))
32.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify62.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1430	3138
1	5001	2782

prune922.0ms

Filtered

255 candidates to 150 candidates (58.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	248	7	255
Fresh	9	12	21
Picked	1	0	1
Done	0	0	0
Total	258	19	277

Merged error: 0.2b

Counts

277 → 19

regimes394.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	32
1	44	32

end0.0ms

sample10.1s

Algorithm

intervals

Results

9.0s

89134×

body

valid

Details

sample405.0ms

simplify69.0ms

prune14.0ms

localize26.0ms

rewrite30.0ms

series92.0ms

simplify132.0ms

prune834.0ms

localize29.0ms

rewrite42.0ms

series84.0ms

simplify114.0ms

prune838.0ms

localize35.0ms

rewrite62.0ms

series108.0ms

simplify50.0ms

prune1.1s

localize35.0ms

rewrite73.0ms

series204.0ms

simplify62.0ms

prune922.0ms

regimes394.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample10.1s

Profiling