Details

sample646.0ms

Algorithm

intervals

Results

165.0ms	47×	body	640	valid
148.0ms	41×	body	1280	valid
137.0ms	175×	body	80	valid
28.0ms	22×	body	320	valid
14.0ms	41×	body	80	nan
7.0ms	9×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5020
7	4228
6	1403
5	705
4	360
3	169
2	91
1	46
0	20

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
1.3b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
17.1b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`add-exp-log`
19×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`times-frac`
7×	`unpow-prod-down` `associate-l`
6×	`associate-/r*` `prod-exp`
5×	`pow1` `div-exp`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `div-inv`
1×	`pow-pow` `tan-quot` `associate-/r/` `*-commutative`

Counts

4 → 97

Calls

4 calls:

10.0ms	(/ x (tan B))
140.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
65.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
40.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series622.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ x (tan B))
129.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
210.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
126.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.6s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	1400
1	458
0	199

prune769.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
1.3b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
17.1b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
18×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
13×	`*-un-lft-identity` `add-cube-cbrt`
7×	`unpow-prod-down` `associate-l` `prod-exp`
6×	`associate-/r*` `times-frac` `div-exp`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `pow-exp` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`
1×	`pow-pow` `*-commutative`

Counts

4 → 90

Calls

4 calls:

23.0ms	(/ (* x (cos B)) (sin B))
83.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
36.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
44.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series633.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (* x (cos B)) (sin B))
101.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
253.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
124.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5005
2	1563
1	469
0	185

prune684.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)))
1.3b	(/ (* (* (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))) F) (sin B))
17.6b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
17.6b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-exp-log`
42×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `add-cube-cbrt`
28×	`prod-exp`
26×	`pow-unpow`
24×	`unpow-prod-down`
21×	`times-frac`
15×	`add-cbrt-cube`
14×	`pow-to-exp` `pow-exp`
12×	`sqr-pow`
11×	`div-exp`
9×	`unswap-sqr`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow1`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `div-inv`
2×	`pow-pow`
1×	`pow2` `clear-num` `frac-2neg` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `associate-/l`

Counts

4 → 141

Calls

4 calls:

155.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)))
216.0ms	(/ (* (* (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))) F) (sin B))
37.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
35.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

series511.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)))
220.0ms	(/ (* (* (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))) F) (sin B))
116.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
107.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

simplify2.3s

Counts

153 → 153

Iterations

Iter	Nodes
done	5000
2	1941
1	600
0	215

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
1.3b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
17.1b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`add-exp-log`
20×	`associate-l`
19×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube`
13×	`times-frac`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-r`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-/r*` `pow-exp` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `associate-/l`

Counts

4 → 101

Calls

4 calls:

28.0ms	(* (/ x (sin B)) (cos B))
83.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
53.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
38.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series476.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (/ x (sin B)) (cos B))
102.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
180.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
94.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.7s

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
2	1603
1	510
0	206

prune690.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes422.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.7b

bsearch699.0ms

Steps

Iters	Range		Point
9	7.143616659564812e-05	13.66253041814236	13.525519432605135
10	-1987689.5348206805	-4.652517827429915e-11	-13373.23580706387

simplify32.0ms

Iterations

Iter	Nodes
done	35
1	35
0	30

end0.0ms

sample13.7s

Algorithm

intervals

Results

5.4s	1570×	body	1280	valid
2.6s	1366×	body	640	valid
2.2s	4857×	body	80	valid
1.6s	730×	body	320	valid
1.2s	1684×	body	80	nan
359.0ms	348×	body	160	valid