Details

sample62.0ms

Algorithm

intervals

Results

24.0ms	45×	body	2560	valid
11.0ms	37×	body	1280	valid
10.0ms	51×	body	640	valid
5.0ms	37×	body	320	valid
4.0ms	71×	body	80	valid
2.0ms	15×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize6.0ms

Local error

Found 2 expressions with local error:

1.4b	(- 1.0 (cos x))
13.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

2.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
48.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune147.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.4b	(- 1.0 (cos x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

24.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
7.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series107.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
42.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5001	690

prune223.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
0.1b	(/ x (- 1.0 (cos x)))
0.1b	(/ 1 (/ x (- 1.0 (cos x))))
1.4b	(- 1.0 (cos x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

283×	`times-frac`
227×	`add-sqr-sqrt`
191×	`*-un-lft-identity`
128×	`add-cube-cbrt`
100×	`add-exp-log`
68×	`associate-r`
50×	`div-exp`
32×	`add-cbrt-cube`
28×	`prod-exp`
26×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
18×	`associate-/r/`
17×	`rec-exp` `1-exp`
15×	`unswap-sqr`
13×	`cbrt-undiv` `associate-l`
11×	`div-inv`
9×	`pow1` `flip3--` `flip--`
6×	`cbrt-unprod` `associate-/l*` `add-log-exp`
3×	`pow-flip` `pow-prod-down` `inv-pow`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sub-neg` `diff-log` `associate-r/` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 304

Calls

4 calls:

49.0ms	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
5.0ms	(/ x (- 1.0 (cos x)))
10.0ms	(/ 1 (/ x (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

series152.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
45.0ms	(/ x (- 1.0 (cos x)))
42.0ms	(/ 1 (/ x (- 1.0 (cos x))))
23.0ms	(- 1.0 (cos x))

simplify53.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1106	2673
1	5001	2310

prune518.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 x) (/ (/ 1 x) (/ 1 (- 1.0 (cos x)))))
0.1b	(/ 1 (- 1.0 (cos x)))
0.2b	(/ (/ 1 x) (/ 1 (- 1.0 (cos x))))
1.4b	(- 1.0 (cos x))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

1445×	`times-frac`
853×	`add-sqr-sqrt`
766×	`*-un-lft-identity`
566×	`add-cube-cbrt`
297×	`add-exp-log`
278×	`associate-r`
196×	`div-exp`
86×	`distribute-lft-out--` `difference-of-squares`
74×	`div-inv`
68×	`prod-exp`
59×	`add-cbrt-cube`
58×	`rec-exp` `1-exp` `associate-/r/`
30×	`cbrt-undiv` `unswap-sqr`
29×	`flip3--` `flip--`
26×	`associate-/r*`
16×	`associate-/l*`
13×	`associate-l`
10×	`cbrt-unprod`
7×	`pow1`
6×	`add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sub-neg` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 805

Calls

4 calls:

127.0ms	(* (/ 1 x) (/ (/ 1 x) (/ 1 (- 1.0 (cos x)))))
5.0ms	(/ 1 (- 1.0 (cos x)))
17.0ms	(/ (/ 1 x) (/ 1 (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

series135.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ 1 x) (/ (/ 1 x) (/ 1 (- 1.0 (cos x)))))
32.0ms	(/ 1 (- 1.0 (cos x)))
42.0ms	(/ (/ 1 x) (/ 1 (- 1.0 (cos x))))
19.0ms	(- 1.0 (cos x))

simplify133.0ms

Algorithm

egg-herbie

Counts

817 → 817

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	3197	9054
1	5001	7894

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.0b

bsearch61.0ms

Steps

Iters	Range		Point
8	0.003211336228265424	0.8894813891870064	0.03412323894191713
8	-1.3862719480695398	-4.2961337728369966e-05	-0.03592633558566007

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	19
1	36	19

end0.0ms

sample2.0s

Algorithm

intervals

Results

892.0ms	1653×	body	2560	valid
371.0ms	1236×	body	1280	valid
309.0ms	1491×	body	640	valid
131.0ms	877×	body	320	valid
113.0ms	2278×	body	80	valid
47.0ms	465×	body	160	valid