Details

sample153.0ms

Algorithm

intervals

Results

57.0ms	63×	body	1280	valid
25.0ms	45×	body	640	valid
20.0ms	152×	body	80	valid
7.0ms	62×	body	80	nan
7.0ms	16×	body	320	valid
3.0ms	10×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	80	26
3	147	26
4	330	26
5	894	26
6	3284	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)))

rewrite50.0ms

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)))
17.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ F (sin B))
32.0ms	(* x (/ 1.0 (tan B)))
67.0ms	(* (/ 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)))

simplify638.0ms

Counts

166 → 166

Iterations

Useful iterations: done (627.0ms)

Iter	Nodes	Cost
0	323	2810
1	827	2653
2	2581	2489
done	5000	2477

prune421.0ms

Filtered

129 candidates to 166 candidates (-28.7%)

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

localize22.0ms

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)))

rewrite52.0ms

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)))
13.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
28.0ms	(* x (/ 1.0 (tan B)))
69.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify633.0ms

Counts

145 → 145

Iterations

Useful iterations: done (628.0ms)

Iter	Nodes	Cost
0	307	2682
1	787	2520
2	2520	2313
done	5001	2298

prune381.0ms

Filtered

112 candidates to 145 candidates (-29.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	137	8	145
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	142	17	159

Merged error: 2.1b

Counts

159 → 17

localize22.0ms

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))
12.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
13.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* x 1.0) (tan B))
38.0ms	(* 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)))

simplify583.0ms

Counts

134 → 134

Iterations

Useful iterations: done (578.0ms)

Iter	Nodes	Cost
0	292	2584
1	744	2431
2	2396	2221
done	5000	2208

prune333.0ms

Filtered

104 candidates to 134 candidates (-28.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	137	14	151

Merged error: 1.2b

Counts

151 → 14

localize21.0ms

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))

rewrite43.0ms

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)))
12.0ms	(/ 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))

series236.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (* x 1.0) (tan B))
67.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
112.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
28.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify639.0ms

Counts

109 → 109

Iterations

Useful iterations: done (630.0ms)

Iter	Nodes	Cost
0	266	2188
1	663	2079
2	2490	1862
done	5001	1844

prune433.0ms

Filtered

85 candidates to 109 candidates (-28.2%)

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

regimes373.0ms

Accuracy

95.7% (0.4b remaining)

Error of 1.3b against oracle of 0.9b and baseline of 10.3b

bsearch185.0ms

Steps

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

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	104
1	69	104
2	72	104
3	73	104
done	73	104

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	1709×	body	1280	valid
783.0ms	1417×	body	640	valid
637.0ms	4771×	body	80	valid
267.0ms	686×	body	320	valid
187.0ms	1650×	body	80	nan
91.0ms	337×	body	160	valid

Details

sample153.0ms

simplify1.2s

prune21.0ms

localize24.0ms

rewrite50.0ms

series153.0ms

simplify638.0ms

prune421.0ms

localize22.0ms

rewrite52.0ms

series158.0ms

simplify633.0ms

prune381.0ms

localize22.0ms

rewrite46.0ms

series157.0ms

simplify583.0ms

prune333.0ms

localize21.0ms

rewrite43.0ms

series236.0ms

simplify639.0ms

prune433.0ms

regimes373.0ms

bsearch185.0ms

simplify10.0ms

end0.0ms

sample3.9s

Profiling