Details

analyze1.9s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample134.0ms

Algorithm

intervals

Results

53.0ms	55×	body	1280	valid
30.0ms	47×	body	640	valid
17.0ms	117×	body	80	valid
10.0ms	22×	body	320	valid
5.0ms	15×	body	160	valid
4.0ms	24×	body	80	invalid
1.0ms	6×	body	80	nan

simplify462.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4951	26
1	4951	26

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 8.8b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
16.6b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac`
79×	`add-sqr-sqrt`
64×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
34×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down`
16×	`add-cbrt-cube`
9×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `neg-mul-1` `pow-exp` `associate-/r*`
2×	`neg-sub0` `pow-neg` `div-sub` `associate-r/` `distribute-frac-neg` `pow-prod-down` `-commutative` `associate-/l/` `pow-sub`
1×	`tan-quot` `pow-pow` `frac-2neg` `clear-num` `associate-/r/`

Counts

4 → 178

Calls

4 calls:

14.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
7.0ms	(* x (/ 1.0 (tan B)))
23.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
12.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series242.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
24.0ms	(* x (/ 1.0 (tan B)))
92.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
32.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4957	3681
1	4957	3681

prune519.0ms

Filtered

150 candidates to 190 candidates (-26.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	175	15	190
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	176	16	192

Merged error: 8.5b

Counts

192 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.3b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
16.6b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
68×	`add-sqr-sqrt`
58×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down` `associate-r`
16×	`add-cbrt-cube`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
8×	`div-exp` `associate-/l*`
7×	`pow1`
6×	`associate-/r*`
5×	`prod-exp`
4×	`cbrt-undiv` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `neg-mul-1` `associate-l` `pow-exp` `cbrt-unprod`
2×	`neg-sub0` `pow-neg` `frac-2neg` `div-sub` `distribute-frac-neg` `clear-num` `associate-/l/` `pow-sub`
1×	`tan-quot` `pow-pow` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative`

Counts

4 → 167

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
14.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
10.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
10.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series226.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (* x 1.0) (tan B))
92.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
88.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
22.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4952	3595
1	4952	3595

prune447.0ms

Filtered

141 candidates to 179 candidates (-27.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	179	16	195

Merged error: 8.5b

Counts

195 → 16

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
0.5b	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
16.6b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
43×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`pow-neg` `associate-*r/` `distribute-frac-neg` `div-exp` `unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `neg-mul-1` `div-sub` `pow-exp` `associate-/r*` `div-inv` `associate-/l/` `pow-sub` `sqr-pow`
2×	`un-div-inv` `*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 137

Calls

4 calls:

7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
12.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
10.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

series204.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* x (/ 1.0 (tan B)))
68.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
92.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
22.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4958	2360
1	4958	2360

prune331.0ms

Filtered

111 candidates to 149 candidates (-34.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	2	12	14
Picked	0	1	1
Done	0	1	1
Total	149	16	165

Merged error: 8.5b

Counts

165 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
0.5b	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
16.6b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

187×	`times-frac`
115×	`add-sqr-sqrt`
110×	`add-cube-cbrt` `*-un-lft-identity`
39×	`unpow-prod-down`
28×	`associate-/l*`
22×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`associate-r`
13×	`pow-unpow` `sqr-pow`
9×	`div-exp`
8×	`div-inv`
7×	`pow1`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`associate-l`
2×	`tan-quot` `pow-to-exp` `frac-2neg` `pow-exp` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`pow-pow` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/`

Counts

4 → 208

Calls

4 calls:

3.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
13.0ms	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
8.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

series145.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (tan B))
22.0ms	(* x (/ 1.0 (tan B)))
92.0ms	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
21.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4972	5017
1	4972	5017

prune479.0ms

Filtered

177 candidates to 220 candidates (-24.3%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	207	13	220
Fresh	10	3	13
Picked	1	0	1
Done	0	2	2
Total	218	18	236

Merged error: 8.4b

Counts

236 → 18

regimes505.0ms

Accuracy

0% (0.3b remaining)

Error of 10.9b against oracle of 10.6b and baseline of 10.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	26
1	63	26

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1658×	body	1280	valid
842.0ms	1404×	body	640	valid
544.0ms	3935×	body	80	valid
296.0ms	694×	body	320	valid
89.0ms	309×	body	160	valid
89.0ms	610×	body	80	invalid
16.0ms	152×	body	80	nan
1.0ms	1×	body	1280	invalid

Details

analyze1.9s

sample134.0ms

simplify462.0ms

prune16.0ms

localize25.0ms

rewrite64.0ms

series242.0ms

simplify77.0ms

prune519.0ms

localize25.0ms

rewrite45.0ms

series226.0ms

simplify69.0ms

prune447.0ms

localize23.0ms

rewrite44.0ms

series204.0ms

simplify63.0ms

prune331.0ms

localize22.0ms

rewrite43.0ms

series145.0ms

simplify70.0ms

prune479.0ms

regimes505.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling