Details

sample397.0ms

Algorithm

intervals

Results

53.0ms	54×	body	1280	valid
14.0ms	41×	body	640	valid
14.0ms	172×	body	80	valid
4.0ms	18×	body	320	valid
4.0ms	12×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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:

22.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (tan B))
19.0ms	(* x (/ 1.0 (tan B)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
33.0ms	(/ 1.0 (tan B))
112.0ms	(* x (/ 1.0 (tan B)))

simplify51.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	438	696
1	1724	639
2	5002	635

prune339.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(* x (cos B))
0.1b	(/ 1 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
107×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
98×	`add-cube-cbrt`
91×	`prod-diff`
28×	`div-inv`
15×	`add-exp-log`
13×	`fma-neg` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 204

Calls

4 calls:

35.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
8.0ms	(* x (cos B))
8.0ms	(/ 1 (sin B))
12.0ms	(/ (* x (cos B)) (sin B))

series213.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
32.0ms	(* x (cos B))
14.0ms	(/ 1 (sin B))
85.0ms	(/ (* x (cos B)) (sin B))

simplify75.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	579	3808
1	2173	2513
2	5001	2510

prune321.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 115

Calls

4 calls:

5.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (sin B))
32.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
15.0ms	(* x (/ 1.0 (sin B)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1.0 (sin B))
17.0ms	(/ 1.0 (sin B))
94.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
52.0ms	(* x (/ 1.0 (sin B)))

simplify47.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	325	672
1	1587	587
2	5001	587

prune311.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (cos B))
0.1b	(/ 1 (sin B))
0.2b	(* (/ 1 (sin B)) (- 1 (* x (cos B))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
20×	`times-frac`
18×	`add-exp-log`
16×	`associate-l`
12×	`add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
4×	`div-exp` `unswap-sqr`
3×	`expm1-log1p-u` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `flip3--` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-*l/` `clear-num` `inv-pow`

Counts

3 → 104

Calls

3 calls:

8.0ms	(* x (cos B))
6.0ms	(/ 1 (sin B))
33.0ms	(* (/ 1 (sin B)) (- 1 (* x (cos B))))

series102.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(* x (cos B))
12.0ms	(/ 1 (sin B))
58.0ms	(* (/ 1 (sin B)) (- 1 (* x (cos B))))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	386	726
1	1853	594
2	5001	586

prune216.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	15	8

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	1806×	body	1280	valid
512.0ms	1442×	body	640	valid
392.0ms	4822×	body	80	valid
180.0ms	703×	body	320	valid
67.0ms	385×	body	160	valid