Details

sample138.0ms

Algorithm

intervals

Results

65.0ms	47×	body	2560	valid
45.0ms	98×	body	1280	valid
13.0ms	56×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	13×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 1.0 (cos x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

10.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune179.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms	(- 1.0 (cos x))

series137.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
42.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
39.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify41.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	1009
1	1099	873
2	5002	871

prune346.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.1b	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`exp-prod`
31×	`log-pow`
30×	`add-cube-cbrt`
28×	`log-prod`
24×	`times-frac`
20×	`exp-sum`
9×	`prod-diff`
7×	`pow1`
6×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`exp-diff` `rem-log-exp`
1×	`sub-neg` `diff-log` `div-inv` `rem-exp-log`

Counts

4 → 109

Calls

4 calls:

3.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
21.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
3.0ms	(- 1.0 (cos x))

series153.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(exp (log (- 1.0 (cos x))))
75.0ms	(log (- 1.0 (cos x)))
35.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify130.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	367	813
1	961	664
2	3989	643
3	5001	640

prune342.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
1.7b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
222×	`add-sqr-sqrt`
218×	`*-un-lft-identity`
210×	`add-cube-cbrt`
169×	`prod-diff`
31×	`div-inv`
13×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

3 → 265

Calls

3 calls:

6.0ms	(/ 1.0 (sin x))
3.0ms	(/ (cos x) (sin x))
25.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series123.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ 1.0 (sin x))
19.0ms	(/ (cos x) (sin x))
85.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	810	7180
1	2234	5060
2	5001	4434

prune337.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

regimes172.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 30.4b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	26
1	34	26

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.1s	1593×	body	2560	valid
1.4s	2747×	body	1280	valid
469.0ms	1853×	body	640	valid
161.0ms	952×	body	320	valid
58.0ms	477×	body	160	valid
36.0ms	375×	body	80	valid
13.0ms	3×	body	5120	valid