Details

sample301.0ms

Algorithm

intervals

Results

136.0ms	59×	body	1280	valid
35.0ms	43×	body	640	valid
29.0ms	146×	body	80	valid
12.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid

simplify67.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	60	11
6	62	11
done	62	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (tan B))
0.1b	(/ 1.0 (sin B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

47.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (tan B))
12.0ms	(/ 1.0 (sin B))
40.0ms	(* x (/ 1.0 (tan B)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
69.0ms	(/ 1.0 (tan B))
27.0ms	(/ 1.0 (sin B))
180.0ms	(* x (/ 1.0 (tan B)))

simplify1.2s

Counts

129 → 129

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	188	1244
1	462	1184
2	1711	1083
done	5000	1074

prune612.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (* x 1.0) (tan B))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`fma-def`
18×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-neg-in`
8×	`distribute-lft-neg-in`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`div-inv` `associate-/l*`
3×	`tan-quot` `pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 91

Calls

3 calls:

93.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (sin B))
13.0ms	(/ (* x 1.0) (tan B))

series416.0ms

Counts

3 → 9

Calls

3 calls:

207.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
31.0ms	(/ 1.0 (sin B))
178.0ms	(/ (* x 1.0) (tan B))

simplify1.1s

Counts

100 → 100

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	150	887
1	369	843
2	1548	761
done	5000	752

prune527.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`distribute-rgt-neg-in` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

27.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
11.0ms	(/ 1.0 (sin B))
10.0ms	(* x (cos B))
14.0ms	(/ (* x (cos B)) (sin B))

series393.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
23.0ms	(/ 1.0 (sin B))
54.0ms	(* x (cos B))
152.0ms	(/ (* x (cos B)) (sin B))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	162	1113
1	394	1066
2	1606	956
done	5001	943

prune508.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.6b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

6.0ms	(cbrt (/ 1.0 (sin B)))
6.0ms	(cbrt (/ 1.0 (sin B)))
6.0ms	(cbrt (/ 1.0 (sin B)))
67.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series922.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(cbrt (/ 1.0 (sin B)))
193.0ms	(cbrt (/ 1.0 (sin B)))
189.0ms	(cbrt (/ 1.0 (sin B)))
295.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify1.5s

Counts

164 → 164

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	174	2305
1	344	2134
2	1561	2047
done	5000	1990

prune774.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes149.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	22	15
3	28	15
done	28	15

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.2s	1742×	body	1280	valid
1.7s	1462×	body	640	valid
1.6s	4957×	body	80	valid
376.0ms	647×	body	320	valid
122.0ms	365×	body	160	valid