Details

sample399.0ms

Algorithm

intervals

Results

36.0ms	61×	body	1280	valid
33.0ms	150×	body	80	valid
15.0ms	43×	body	640	valid
4.0ms	15×	body	320	valid
2.0ms	13×	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

0.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
8.0ms	(/ 1.0 (tan B))

series183.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
56.0ms	(/ 1.0 (tan B))

simplify58.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	246	416
1	694	382
2	2127	382
3	5002	377

prune240.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`fma-udef`

Counts

3 → 68

Calls

3 calls:

0.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
13.0ms	(/ (cos B) (sin B))

series147.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
21.0ms	(/ (cos B) (sin B))

simplify59.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	241	480
1	721	438
2	2196	438
3	5001	433

prune237.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x) (* 1.0 (* (cos B) (/ 1 (sin B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1 (sin B))
0.2b	(* (cos B) (/ 1 (sin B)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`associate-r` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l`
5×	`div-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-l` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 110

Calls

4 calls:

0.0ms	(fma (- x) (* 1.0 (* (cos B) (/ 1 (sin B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1 (sin B))
18.0ms	(* (cos B) (/ 1 (sin B)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(fma (- x) (* 1.0 (* (cos B) (/ 1 (sin B)))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
17.0ms	(/ 1 (sin B))
20.0ms	(* (cos B) (/ 1 (sin B)))

simplify88.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	359	693
1	1360	607
2	4481	577
3	5002	574

prune309.0ms

Pruning

10 alts after pruning (10 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	(/ 1 (sin B))
0.1b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite78.0ms

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:

38.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
6.0ms	(/ 1 (sin B))
8.0ms	(* x (cos B))
15.0ms	(/ (* x (cos B)) (sin B))

series249.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
14.0ms	(/ 1 (sin B))
37.0ms	(* x (cos B))
100.0ms	(/ (* x (cos B)) (sin B))

simplify77.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (52.0ms)

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

prune308.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	17
1	19	17

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1692×	body	1280	valid
498.0ms	1418×	body	640	valid
406.0ms	4969×	body	80	valid
162.0ms	690×	body	320	valid
62.0ms	369×	body	160	valid