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

sample175.0ms

Algorithm

intervals

Results

42.0ms	45×	body	1280	valid
26.0ms	43×	body	640	valid
24.0ms	143×	body	80	valid
7.0ms	17×	body	320	valid
2.0ms	8×	body	160	valid

simplify446.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

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: 10.1b

Counts

2 → 2

localize37.0ms

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)))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
15.4b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite52.0ms

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:

7.0ms	(* 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))
12.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series264.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* x (/ 1.0 (tan B)))
100.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
96.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
41.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4957	3681
1	4957	3681

prune487.0ms

Filtered

150 candidates to 190 candidates (-26.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	179	11	190
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	180	12	192

Merged error: 9.8b

Counts

192 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
15.4b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite44.0ms

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:

4.0ms	(/ (* 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))

series242.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (* x 1.0) (tan B))
99.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
93.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
26.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4952	3595
1	4952	3595

prune408.0ms

Filtered

140 candidates to 179 candidates (-27.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	179	12	191

Merged error: 9.8b

Counts

191 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
0.6b	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
15.4b	(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))

series220.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* x (/ 1.0 (tan B)))
73.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
99.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
23.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4958	2360
1	4958	2360

prune304.0ms

Filtered

111 candidates to 149 candidates (-34.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	149	12	161

Merged error: 9.8b

Counts

161 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.2b	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
15.4b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac`
79×	`add-sqr-sqrt`
64×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow-unpow`
28×	`associate-r`
25×	`add-exp-log` `unpow-prod-down`
16×	`associate-l` `add-cbrt-cube`
9×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`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` `distribute-frac-neg` `pow-prod-down` `*-commutative` `associate-/l/` `pow-sub`
1×	`pow-pow` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 177

Calls

4 calls:

6.0ms	(* (/ x (sin B)) (cos 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))

series234.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (/ x (sin B)) (cos B))
99.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
94.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
23.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4949	3698
1	4949	3698

prune377.0ms

Filtered

149 candidates to 189 candidates (-26.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	187	14	201

Merged error: 9.8b

Counts

201 → 14

regimes432.0ms

Accuracy

0% (0.3b remaining)

Error of 10.4b against oracle of 10.1b and baseline of 10.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	26
1	63	26

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.5s	1675×	body	1280	valid
766.0ms	1348×	body	640	valid
505.0ms	3933×	body	80	valid
283.0ms	717×	body	320	valid
85.0ms	327×	body	160	valid

Details

analyze1.9s

sample175.0ms

simplify446.0ms

prune16.0ms

localize37.0ms

rewrite52.0ms

series264.0ms

simplify76.0ms

prune487.0ms

localize25.0ms

rewrite44.0ms

series242.0ms

simplify71.0ms

prune408.0ms

localize25.0ms

rewrite44.0ms

series220.0ms

simplify62.0ms

prune304.0ms

localize26.0ms

rewrite49.0ms

series234.0ms

simplify72.0ms

prune377.0ms

regimes432.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample4.8s

Profiling