Details

sample495.0ms

Algorithm

intervals

Results

80.0ms	58×	body	1280	valid
26.0ms	40×	body	640	valid
23.0ms	156×	body	80	valid
8.0ms	18×	body	320	valid
4.0ms	38×	body	80	nan
2.0ms	8×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	15
1	91	14
2	169	14
3	378	14
4	1100	14
5	5001	14
done	5001	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
7.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite270.0ms

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×	`expm1-log1p-u` `pow-neg` `cbrt-unprod` `log1p-expm1-u` `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 → 162

Calls

4 calls:

6.0ms	(/ F (sin B))
18.0ms	(* x (/ 1.0 (tan B)))
178.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
61.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ F (sin B))
116.0ms	(* x (/ 1.0 (tan B)))
296.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
161.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify87.0ms

Counts

174 → 174

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	780	1466
1	3262	1352
2	5001	1349
done	5001	1349

prune701.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.2b	(* (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))))
17.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `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 → 116

Calls

4 calls:

19.0ms	(* x (/ 1.0 (tan B)))
165.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
51.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
52.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series837.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* x (/ 1.0 (tan B)))
263.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
316.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
143.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify79.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	671	1143
1	2919	1016
2	5001	1009
done	5001	1009

prune492.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(* (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))))
17.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite277.0ms

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` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `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 → 105

Calls

4 calls:

11.0ms	(/ (* x 1.0) (tan B))
164.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
49.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
50.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series818.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (* x 1.0) (tan B))
256.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
307.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
136.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify64.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	625	1088
1	2653	961
2	5001	954
done	5001	954

prune453.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.4b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
17.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
73×	`times-frac`
59×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
30×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`pow1` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`associate-l` `prod-exp` `unswap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `associate-/r*`
2×	`neg-sub0` `pow-neg` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/` `pow-sub`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `clear-num` `associate-/r/`

Counts

4 → 182

Calls

4 calls:

18.0ms	(* x (/ 1.0 (tan B)))
165.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
128.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
54.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series952.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* x (/ 1.0 (tan B)))
364.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
326.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify99.0ms

Counts

194 → 194

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	868	2139
1	3804	2002
2	5001	1988
done	5001	1988

prune732.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.3b

bsearch280.0ms

Steps

Iters	Range		Point
8	51.26549425761527	36428.8834987219	23947.606194417258
9	-2.6502145472017594e+23	-2.313726191220495e+16	-1.354270687656808e+18

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	43
1	72	43
2	77	43
3	77	43
done	77	43

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1746×	body	1280	valid
878.0ms	1383×	body	640	valid
654.0ms	4697×	body	80	valid
286.0ms	660×	body	320	valid
171.0ms	1675×	body	80	nan
113.0ms	352×	body	160	valid