Details

sample795.0ms

Algorithm

intervals

Results

304.0ms	45×	body	640	valid
167.0ms	54×	body	1280	valid
120.0ms	148×	body	80	valid
28.0ms	18×	body	320	valid
24.0ms	42×	body	80	nan
13.0ms	10×	body	160	valid

simplify8.0s

Counts

1 → 1

Iterations

Iter	Nodes
7	8510
6	1843
5	606
4	239
3	124
2	80
1	46
0	20

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
0.7b	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
19.1b	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-exp-log`
19×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`times-frac`
9×	`unpow-prod-down`
8×	`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` `distribute-lft-out`
1×	`pow-pow` `tan-quot` `associate-/r/` `*-commutative`

Counts

4 → 99

Calls

4 calls:

5.0ms	(/ x (tan B))
114.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
50.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
32.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

series810.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ x (tan B))
124.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
263.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
257.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

simplify2.0s

Counts

111 → 111

Iterations

Iter	Nodes
3	4660
2	1225
1	453
0	213

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
0.5b	(/ 1 (/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)))
0.6b	(/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F))
19.1b	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
26×	`div-exp`
20×	`add-cbrt-cube`
15×	`prod-exp`
9×	`unpow-prod-down`
8×	`associate-/r` `associate-l*`
7×	`cbrt-undiv`
6×	`pow-to-exp` `pow1` `pow-exp` `div-inv` `associate-/l*`
5×	`rec-exp` `1-exp`
4×	`insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-r` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `distribute-lft-out`
1×	`pow-pow` `associate-/r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 133

Calls

4 calls:

95.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
63.0ms	(/ 1 (/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)))
29.0ms	(/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F))
43.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

series730.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
154.0ms	(/ 1 (/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)))
163.0ms	(/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F))
314.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

simplify4.6s

Counts

145 → 145

Iterations

Iter	Nodes
3	7560
2	1780
1	607
0	255

prune1.9s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.2b	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
0.7b	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
19.1b	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`add-exp-log`
23×	`*-un-lft-identity`
21×	`associate-l`
19×	`add-cube-cbrt`
16×	`add-cbrt-cube`
13×	`times-frac`
9×	`unpow-prod-down`
8×	`prod-exp`
7×	`pow1`
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` `distribute-lft-out`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `associate-/l`

Counts

4 → 103

Calls

4 calls:

28.0ms	(* (/ x (sin B)) (cos B))
92.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
28.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
18.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

series756.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (/ x (sin B)) (cos B))
140.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
199.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
265.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

simplify2.2s

Counts

115 → 115

Iterations

Iter	Nodes
3	5717
2	1536
1	512
0	220

prune1.8s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 10.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (* (* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))) F) (sin B))
0.7b	(* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)))
19.7b	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))
19.7b	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))

rewrite613.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-exp-log`
48×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
34×	`unpow-prod-down`
30×	`add-cube-cbrt`
28×	`prod-exp`
26×	`pow-unpow`
21×	`times-frac`
15×	`add-cbrt-cube`
14×	`pow-to-exp` `pow-exp`
12×	`sqr-pow`
11×	`div-exp`
10×	`swap-sqr`
9×	`unswap-sqr`
8×	`associate-r` `associate-l` `distribute-lft-out`
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 → 148

Calls

4 calls:

281.0ms	(/ (* (* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))) F) (sin B))
253.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)))
40.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))
37.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))

series930.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (* (* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))) F) (sin B))
88.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)))
289.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))
335.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))

simplify5.4s

Counts

160 → 160

Iterations

Iter	Nodes
3	8611
2	1904
1	599
0	222

prune2.4s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.0b

regimes477.0ms

Accuracy

0% (0.6b remaining)

Error of 10.4b against oracle of 9.7b and baseline of 10.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	22
1	22
0	17

end0.0ms

sample13.4s

Algorithm

intervals

Results

5.1s	1696×	body	1280	valid
3.5s	1406×	body	640	valid
2.1s	4738×	body	80	valid
1.1s	1698×	body	80	nan
1000.0ms	721×	body	320	valid
266.0ms	331×	body	160	valid