Details

sample347.0ms

Algorithm

intervals

Results

252.0ms	55×	body	1280	valid
24.0ms	38×	body	640	valid
24.0ms	163×	body	80	valid
10.0ms	23×	body	320	valid
6.0ms	13×	body	160	valid
5.0ms	49×	body	80	nan

simplify473.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5149	26

prune33.0ms

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: 11.4b

Counts

2 → 2

localize26.0ms

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)))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
16.5b	(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`
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)))
9.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
11.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series246.0ms

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)))
89.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
40.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5156	3695

prune541.0ms

Filtered

150 candidates to 190 candidates (-26.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	173	17	190
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	174	18	192

Merged error: 11.0b

Counts

192 → 18

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
0.3b	(* x (/ 1.0 (tan B)))
0.6b	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
16.5b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

rewrite41.0ms

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:

9.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
9.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
9.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

series205.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
23.0ms	(* x (/ 1.0 (tan B)))
93.0ms	(/ (* 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))

simplify40.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4999	2373
1	4999	2373

prune346.0ms

Filtered

111 candidates to 149 candidates (-34.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	6	11	17
Picked	0	1	1
Done	0	0	0
Total	152	15	167

Merged error: 1.2b

Counts

167 → 15

localize22.0ms

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))) (/ 1.0 2.0)) (sin B)))
0.3b	(* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B))
16.4b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
17×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
10×	`associate-l`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/`

Counts

4 → 108

Calls

4 calls:

7.0ms	(* x (/ 1.0 (tan B)))
9.0ms	(/ F (* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B)))
9.0ms	(* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B))
7.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

series199.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* x (/ 1.0 (tan B)))
91.0ms	(/ F (* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B)))
61.0ms	(* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B))
23.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

simplify33.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5310	1951

prune290.0ms

Filtered

92 candidates to 120 candidates (-30.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	8	5	13
Picked	1	0	1
Done	0	1	1
Total	121	14	135

Merged error: 1.0b

Counts

135 → 14

localize22.0ms

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))) (/ 1.0 2.0)) (sin B)))
0.3b	(* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B))
16.4b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`pow-unpow`
7×	`unpow-prod-down` `associate-l` `prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `associate-r` `pow-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 97

Calls

4 calls:

4.0ms	(/ (* x 1.0) (tan B))
9.0ms	(/ F (* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B)))
9.0ms	(* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B))
7.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

series196.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* x 1.0) (tan B))
90.0ms	(/ F (* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B)))
63.0ms	(* (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))

simplify62.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4967	1853
1	4967	1853

prune185.0ms

Filtered

81 candidates to 109 candidates (-34.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	112	11	123

Merged error: 1.0b

Counts

123 → 11

regimes457.0ms

Accuracy

95.7% (0.4b remaining)

Error of 1.4b against oracle of 1.0b and baseline of 10.6b

bsearch171.0ms

Steps

Iters	Range		Point
8	2.635807861600005e+143	2.0536164315686213e+146	2.015855220819964e+146
9	-5.131065402717253e+158	-1.6251532931763321e+153	-1.329634943152444e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	118
1	75	118

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	1634×	body	1280	valid
863.0ms	1421×	body	640	valid
678.0ms	4845×	body	80	valid
285.0ms	672×	body	320	valid
164.0ms	1617×	body	80	nan
100.0ms	355×	body	160	valid

Details

sample347.0ms

simplify473.0ms

prune33.0ms

localize26.0ms

rewrite49.0ms

series246.0ms

simplify62.0ms

prune541.0ms

localize23.0ms

rewrite41.0ms

series205.0ms

simplify40.0ms

prune346.0ms

localize22.0ms

rewrite35.0ms

series199.0ms

simplify33.0ms

prune290.0ms

localize22.0ms

rewrite32.0ms

series196.0ms

simplify62.0ms

prune185.0ms

regimes457.0ms

bsearch171.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling