Details

sample153.0ms

Algorithm

intervals

Results

56.0ms	63×	body	1280	valid
33.0ms	45×	body	640	valid
21.0ms	152×	body	80	valid
7.0ms	62×	body	80	nan
6.0ms	16×	body	320	valid
3.0ms	10×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	80	26
3	147	26
4	330	26
5	882	26
6	3255	26
done	5000	26

prune21.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.2b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
5.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

4.0ms	(/ F (sin B))
8.0ms	(* x (/ 1.0 (tan B)))
15.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
14.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series152.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ F (sin B))
31.0ms	(* x (/ 1.0 (tan B)))
66.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
42.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify572.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (218.0ms)

Iter	Nodes	Cost
0	323	2810
1	827	2627
2	2452	2471
done	5000	2471

prune418.0ms

Filtered

126 candidates to 166 candidates (-31.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	152	14	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	14	167

Merged error: 2.9b

Counts

167 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
0.9b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

12.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
8.0ms	(* x (/ 1.0 (tan B)))
12.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
11.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series152.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
29.0ms	(* x (/ 1.0 (tan B)))
63.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify548.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (205.0ms)

Iter	Nodes	Cost
0	307	2682
1	787	2496
2	2367	2293
done	5001	2293

prune361.0ms

Filtered

108 candidates to 145 candidates (-34.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	138	7	145
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	144	15	159

Merged error: 1.2b

Counts

159 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
0.9b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
13.0ms	(* 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))
11.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (* x 1.0) (tan B))
36.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
64.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
28.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify542.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (194.0ms)

Iter	Nodes	Cost
0	292	2584
1	744	2408
2	2309	2205
done	5000	2205

prune323.0ms

Filtered

102 candidates to 134 candidates (-31.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	135	14	149

Merged error: 1.2b

Counts

149 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
17.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite44.0ms

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-r` `prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `associate-l` `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:

5.0ms	(/ (* x 1.0) (tan B))
12.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
14.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series237.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (* x 1.0) (tan B))
75.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
111.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify776.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (190.0ms)

Iter	Nodes	Cost
0	266	2188
1	663	2063
2	2323	1842
done	5000	1842

prune207.0ms

Filtered

83 candidates to 109 candidates (-31.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 1.1b

Counts

123 → 15

regimes372.0ms

Accuracy

95.6% (0.4b remaining)

Error of 1.4b against oracle of 0.9b and baseline of 10.3b

bsearch179.0ms

Steps

Iters	Range		Point
10	1.470553665056455e+141	2.9691984191834726e+158	1.3731501411501404e+154
10	-3.6631665912156965e+144	-4.423171497057879e+133	-3.60794749827767e+144

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	104
1	66	104
2	69	104
3	70	104
done	70	104

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	1709×	body	1280	valid
789.0ms	1417×	body	640	valid
625.0ms	4771×	body	80	valid
263.0ms	686×	body	320	valid
179.0ms	1650×	body	80	nan
90.0ms	337×	body	160	valid

Details

sample153.0ms

simplify1.1s

prune21.0ms

localize24.0ms

rewrite48.0ms

series152.0ms

simplify572.0ms

prune418.0ms

localize21.0ms

rewrite51.0ms

series152.0ms

simplify548.0ms

prune361.0ms

localize21.0ms

rewrite46.0ms

series154.0ms

simplify542.0ms

prune323.0ms

localize20.0ms

rewrite44.0ms

series237.0ms

simplify776.0ms

prune207.0ms

regimes372.0ms

bsearch179.0ms

simplify9.0ms

end0.0ms

sample3.8s

Profiling