Details

sample111.0ms

Algorithm

intervals

Results

47.0ms	57×	body	1280	valid
23.0ms	38×	body	640	valid
19.0ms	167×	body	80	valid
7.0ms	19×	body	320	valid
3.0ms	11×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

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))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
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` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

8.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
33.0ms	(/ 1.0 (tan B))
114.0ms	(* x (/ 1.0 (tan B)))

simplify46.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	419	664
1	1645	609
2	5001	604

prune301.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

26.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
6.0ms	(/ (* x 1.0) (tan B))

series238.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
104.0ms	(/ (* x 1.0) (tan B))

simplify38.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	336	465
1	1303	419
2	5001	414

prune196.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-log-exp`
7×	`associate-l`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/l*`
3×	`associate-r` `div-inv`
2×	`frac-2neg` `associate-*l/` `clear-num` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

9.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
3.0ms	(/ (* x 1.0) (sin B))
11.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series273.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
55.0ms	(/ (* x 1.0) (sin B))
98.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify57.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	422	714
1	1971	620
2	5001	614

prune261.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

110×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
17×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`tan-quot` `cbrt-div` `associate-/r/` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `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 → 150

Calls

4 calls:

24.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
2.0ms	(cbrt (/ 1.0 (tan B)))
2.0ms	(cbrt (/ 1.0 (tan B)))
2.0ms	(cbrt (/ 1.0 (tan B)))

series698.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
164.0ms	(cbrt (/ 1.0 (tan B)))
154.0ms	(cbrt (/ 1.0 (tan B)))
165.0ms	(cbrt (/ 1.0 (tan B)))

simplify50.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	320	1480
1	1165	1424
2	5001	1354

prune548.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	9
1	22	9
2	28	9
3	28	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1717×	body	1280	valid
532.0ms	1472×	body	640	valid
400.0ms	4894×	body	80	valid
174.0ms	681×	body	320	valid
70.0ms	376×	body	160	valid