Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	51×	body	2560	valid
8.0ms	36×	body	1280	valid
7.0ms	49×	body	640	valid
3.0ms	35×	body	320	valid
2.0ms	68×	body	80	valid
1.0ms	17×	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: 31.0b

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
14.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite27.0ms

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:

6.0ms	(- 1.0 (cos x))
19.0ms	(/ (- 1.0 (cos x)) (* x x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 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

prune110.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

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)
2.0b	(- 1.0 (cos x))

rewrite67.0ms

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:

40.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
16.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series94.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
40.0ms	(/ (- 1.0 (cos x)) x)
16.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (51.0ms)

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

prune220.0ms

Pruning

8 alts after pruning (8 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))))
2.0b	(- 1.0 (cos x))

rewrite126.0ms

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:

69.0ms	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
11.0ms	(/ x (- 1.0 (cos x)))
22.0ms	(/ 1 (/ x (- 1.0 (cos x))))
6.0ms	(- 1.0 (cos x))

series143.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
40.0ms	(/ x (- 1.0 (cos x)))
43.0ms	(/ 1 (/ x (- 1.0 (cos x))))
17.0ms	(- 1.0 (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1106	2673
1	5001	2310

prune532.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (log (exp (- 1.0 (cos x)))) x)
0.1b	(exp (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))
2.1b	(log (exp (- 1.0 (cos x))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`exp-prod` `log-pow`
27×	`times-frac`
25×	`add-cube-cbrt`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log-prod`
4×	`exp-sum`
3×	`sub-neg` `exp-diff` `associate-/r*`
2×	`log-div` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 103

Calls

4 calls:

48.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
15.0ms	(exp (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))
18.0ms	(log (exp (- 1.0 (cos x))))

series111.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
40.0ms	(exp (- 1.0 (cos x)))
16.0ms	(- 1.0 (cos x))
17.0ms	(log (exp (- 1.0 (cos x))))

simplify121.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	304	679
1	935	604
2	3744	589
3	5001	587

prune214.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch69.0ms

Steps

Iters	Range		Point
10	8.950540206577903e-05	66689094922.78456	0.03257344431833417
10	-1500.694570789724	-6.177030851099824e-09	-0.03399406403260506

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	19
1	37	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

729.0ms	1597×	body	2560	valid
286.0ms	1307×	body	1280	valid
210.0ms	1444×	body	640	valid
91.0ms	915×	body	320	valid
76.0ms	2256×	body	80	valid
34.0ms	481×	body	160	valid