Details

sample135.0ms

Algorithm

intervals

Results

60.0ms	46×	body	2560	valid
42.0ms	94×	body	1280	valid
17.0ms	66×	body	640	valid
6.0ms	33×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	9×	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: 31.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
26.0ms	(- 1.0 (cos x))

simplify81.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune170.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.8b	(- 1.0 (cos x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `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 → 112

Calls

4 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
13.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series141.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
47.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
23.0ms	(- 1.0 (cos x))

simplify89.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune335.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) (sin x)))
0.2b	(/ (sqrt (- 1.0 (cos x))) (sin x))
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
52×	`times-frac`
45×	`sqrt-prod`
38×	`add-cube-cbrt`
28×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-l` `associate-/l*` `add-log-exp`
6×	`pow1` `sqrt-div` `unswap-sqr`
5×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `sub-neg` `diff-log` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 137

Calls

4 calls:

35.0ms	(* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) (sin x)))
9.0ms	(/ (sqrt (- 1.0 (cos x))) (sin x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series176.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) (sin x)))
97.0ms	(/ (sqrt (- 1.0 (cos x))) (sin x))
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify55.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	428	1395
1	1749	1249
2	5002	1199

prune368.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(cbrt (pow (/ (- 1.0 (cos x)) (sin x)) 3))
0.4b	(pow (/ (- 1.0 (cos x)) (sin x)) 3)
1.8b	(- 1.0 (cos x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt` `*-un-lft-identity`
75×	`times-frac`
52×	`add-cube-cbrt`
44×	`cbrt-prod`
38×	`unpow-prod-down` `cube-prod`
17×	`distribute-lft-out--` `difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv` `associate-/l*`
3×	`pow-unpow` `associate-/r*`
2×	`cbrt-undiv` `cube-div` `cube-mult` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `clear-num` `rem-cbrt-cube`

Counts

4 → 164

Calls

4 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
9.0ms	(cbrt (pow (/ (- 1.0 (cos x)) (sin x)) 3))
12.0ms	(pow (/ (- 1.0 (cos x)) (sin x)) 3)
3.0ms	(- 1.0 (cos x))

series161.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
35.0ms	(cbrt (pow (/ (- 1.0 (cos x)) (sin x)) 3))
68.0ms	(pow (/ (- 1.0 (cos x)) (sin x)) 3)
18.0ms	(- 1.0 (cos x))

simplify64.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	531	1514
1	2278	1419
2	5002	1401

prune298.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes145.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.3b

bsearch98.0ms

Steps

Iters	Range		Point
9	2.0114125408603258e-10	0.4954286465087044	0.02145283746761365
10	-1.7081313977704333	-1.7977825652338532e-10	-0.019990581307716814

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	15
1	36	15

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.2s	1621×	body	2560	valid
1.3s	2805×	body	1280	valid
483.0ms	1822×	body	640	valid
376.0ms	909×	body	320	valid
61.0ms	469×	body	160	valid
35.0ms	370×	body	80	valid
18.0ms	4×	body	5120	valid