Details

sample326.0ms

Algorithm

intervals

Results

31.0ms	61×	body	1280	valid
17.0ms	54×	body	640	valid
13.0ms	146×	body	80	valid
5.0ms	23×	body	320	valid
2.0ms	12×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune9.0ms

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

rewrite53.0ms

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:

26.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
13.0ms	(* x (/ 1.0 (tan B)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
35.0ms	(/ 1.0 (tan B))
120.0ms	(* x (/ 1.0 (tan B)))

simplify52.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (43.0ms)

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

prune310.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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

rewrite35.0ms

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:

27.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series240.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
107.0ms	(/ (* x 1.0) (tan B))

simplify39.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (33.0ms)

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

prune191.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))
0.2b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

9.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
3.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))

series252.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
35.0ms	(* x (cos B))
93.0ms	(/ (* x (cos B)) (sin B))

simplify45.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	359	603
1	1463	536
2	5002	530

prune232.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
6.0ms	(* (cbrt x) (cbrt x))

series711.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt x)
174.0ms	(cbrt x)
173.0ms	(cbrt x)
193.0ms	(* (cbrt x) (cbrt x))

simplify93.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	115	288
1	479	261
2	2963	238
3	5002	235

prune241.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

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

sample2.2s

Algorithm

intervals

Results

826.0ms	1690×	body	1280	valid
470.0ms	1401×	body	640	valid
448.0ms	4956×	body	80	valid
184.0ms	742×	body	320	valid
63.0ms	366×	body	160	valid