Details

sample306.0ms

Algorithm

intervals

Results

22.0ms	53×	body	1280	valid
12.0ms	49×	body	640	valid
9.0ms	149×	body	80	valid
6.0ms	26×	body	320	valid
2.0ms	13×	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

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

99×	`frac-sub`
96×	`add-sqr-sqrt`
90×	`associate-*r/`
84×	`*-un-lft-identity`
79×	`associate-/l*`
70×	`add-cube-cbrt`
69×	`associate-/r*`
33×	`times-frac` `clear-num`
23×	`frac-2neg`
20×	`un-div-inv`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp` `difference-of-squares` `unswap-sqr`
4×	`associate-l`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`tan-quot` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 217

Calls

4 calls:

45.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
4.0ms	(/ 1.0 (tan B))
4.0ms	(/ 1.0 (sin B))
11.0ms	(* x (/ 1.0 (tan B)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
34.0ms	(/ 1.0 (tan B))
22.0ms	(/ 1.0 (sin B))
124.0ms	(* x (/ 1.0 (tan B)))

simplify53.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1166	2295
1	5001	2214

prune488.0ms

Filtered

229 candidates to 146 candidates (63.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	221	8	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	8	230

Merged error: 0.0b

Counts

230 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

323×	`add-sqr-sqrt`
289×	`associate-/l*`
288×	`frac-sub`
280×	`*-un-lft-identity`
262×	`add-cube-cbrt`
214×	`times-frac`
200×	`associate-r`
199×	`associate-/r*`
149×	`distribute-rgt-neg-in`
147×	`distribute-lft-neg-in`
62×	`associate-l`
49×	`neg-mul-1`
43×	`frac-2neg` `clear-num`
22×	`unswap-sqr`
20×	`*-commutative`
10×	`add-exp-log` `add-cbrt-cube`
6×	`difference-of-squares`
5×	`distribute-lft-out--` `add-log-exp`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`div-inv`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `distribute-frac-neg` `prod-exp` `associate-/r/` `distribute-rgt-neg-out` `flip--` `cbrt-unprod` `distribute-neg-frac`

Counts

3 → 573

Calls

3 calls:

146.0ms	(- (/ 1.0 (sin B)) (/ (* x (- 1.0)) (- (tan B))))
15.0ms	(/ (* x (- 1.0)) (- (tan B)))
4.0ms	(/ 1.0 (sin B))

series252.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(- (/ 1.0 (sin B)) (/ (* x (- 1.0)) (- (tan B))))
109.0ms	(/ (* x (- 1.0)) (- (tan B)))
19.0ms	(/ 1.0 (sin B))

simplify136.0ms

Algorithm

egg-herbie

Counts

582 → 582

Iterations

Useful iterations: 1 (66.0ms)

Iter	Nodes	Cost
0	3614	8670
1	5002	8621

prune1.4s

Filtered

582 candidates to 403 candidates (69.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	576	6	582
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	582	8	590

Merged error: 0.0b

Counts

590 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin B))
0.7b	(cbrt (sin B))
0.7b	(cbrt (sin B))
2.6b	(/ (- (* (/ 1.0 (* (cbrt (sin B)) (cbrt (sin B)))) (tan B)) (* (cbrt (sin B)) (/ (* x (- 1.0)) (- 1)))) (* (tan B) (cbrt (sin B))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

10233×	`add-sqr-sqrt`
3679×	`unswap-sqr`
3163×	`times-frac`
2744×	`cbrt-prod`
2576×	`associate-/r*`
2347×	`associate-/l/`
2345×	`frac-sub`
2179×	`associate-*r/`
1870×	`*-un-lft-identity`
1701×	`associate-/l*`
1600×	`add-cube-cbrt` `associate-r`
1309×	`difference-of-squares`
1191×	`tan-quot`
1156×	`associate-*l/`
1155×	`frac-times`
1011×	`associate-l`
658×	`swap-sqr`
402×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
341×	`*-commutative`
205×	`clear-num`
201×	`un-div-inv`
138×	`frac-2neg`
134×	`neg-mul-1`
68×	`distribute-lft-out--`
11×	`add-cbrt-cube`
9×	`add-exp-log`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `pow1/3`
2×	`div-exp` `cbrt-unprod`
1×	`flip3--` `div-sub` `prod-exp` `associate-/r/` `flip--` `div-inv`

Counts

4 → 3841

Calls

4 calls:

2.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))
1.2s	(/ (- (* (/ 1.0 (* (cbrt (sin B)) (cbrt (sin B)))) (tan B)) (* (cbrt (sin B)) (/ (* x (- 1.0)) (- 1)))) (* (tan B) (cbrt (sin B))))

series664.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (sin B))
95.0ms	(cbrt (sin B))
95.0ms	(cbrt (sin B))
380.0ms	(/ (- (* (/ 1.0 (* (cbrt (sin B)) (cbrt (sin B)))) (tan B)) (* (cbrt (sin B)) (/ (* x (- 1.0)) (- 1)))) (* (tan B) (cbrt (sin B))))

simplify732.0ms

Algorithm

egg-herbie

Counts

3853 → 3853

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5001	103925

prune12.5s

Filtered

3853 candidates to 2506 candidates (65.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	3852	1	3853
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	3853	8	3861

Merged error: 0b

Counts

3861 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin B))
0.7b	(cbrt (sin B))
0.7b	(cbrt (sin B))
2.2b	(/ (* (cbrt (- (* (/ 1.0 (* (cbrt (sin B)) (cbrt (sin B)))) (tan B)) (* (cbrt (sin B)) (/ (* x (- 1.0)) (- 1))))) (cbrt (- (* (/ 1.0 (* (cbrt (sin B)) (cbrt (sin B)))) (tan B)) (* (cbrt (sin B)) (/ (* x (- 1.0)) (- 1)))))) (* (tan B) (* (cbrt (cbrt (sin B))) (cbrt (cbrt (sin B))))))

rewrite9.7m

Algorithm

rewrite-expression-head

Calls

4 calls:

2.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))
36.0ms	(cbrt (sin B))
9.5m	(/ (* (cbrt (- (* (/ 1.0 (* (cbrt (sin B)) (cbrt (sin B)))) (tan B)) (* (cbrt (sin B)) (/ (* x (- 1.0)) (- 1))))) (cbrt (- (* (/ 1.0 (* (cbrt (sin B)) (cbrt (sin B)))) (tan B)) (* (cbrt (sin B)) (/ (* x (- 1.0)) (- 1)))))) (* (tan B) (* (cbrt (cbrt (sin B))) (cbrt (cbrt (sin B))))))