Details

sample47.0ms

Algorithm

intervals

Results

20.0ms	47×	body	2560	valid
8.0ms	61×	body	640	valid
6.0ms	28×	body	1280	valid
3.0ms	86×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	13×	body	160	valid

simplify8.0ms

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: 28.7b

localize7.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
14.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

8.0ms	(- 1.0 (cos x))
26.0ms	(/ (- 1.0 (cos x)) (* x x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317

prune138.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
156×	`times-frac`
104×	`sqrt-prod`
103×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `prod-diff` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
6×	`fma-neg`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 238

Calls

4 calls:

19.0ms	(/ (sqrt (- 1.0 (cos x))) x)
68.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
8.0ms	(- 1.0 (cos x))
8.0ms	(- 1.0 (cos x))

series173.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (sqrt (- 1.0 (cos x))) x)
48.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify97.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	729	2762
1	3588	2273
2	5002	2108

prune449.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
0.1b	(/ (- 1.0 (cos x)) x)
1.8b	(- 1.0 (cos x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
46×	`times-frac`
36×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-l`
17×	`add-cbrt-cube`
13×	`associate-r`
9×	`div-exp` `prod-diff`
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×	`expm1-log1p-u` `fma-neg` `associate-/r*` `log1p-expm1-u` `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` `un-div-inv` `*-commutative`

Counts

3 → 133

Calls

3 calls:

41.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
19.0ms	(/ (- 1.0 (cos x)) x)
8.0ms	(- 1.0 (cos x))

series108.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
41.0ms	(/ (- 1.0 (cos x)) x)
20.0ms	(- 1.0 (cos x))

simplify68.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	598	1004
1	2536	831
2	5001	809

prune259.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (- 1.0 (cos x)))
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))
2.0b	(log (exp (- 1.0 (cos x))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
33×	`add-cube-cbrt`
22×	`exp-sum`
14×	`log-prod`
11×	`add-log-exp`
10×	`exp-prod`
6×	`fma-neg` `log-pow`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`flip3--` `exp-diff` `flip--` `rem-exp-log`
1×	`log-div` `rem-log-exp`

Counts

4 → 115

Calls

4 calls:

17.0ms	(exp (- 1.0 (cos x)))
8.0ms	(- 1.0 (cos x))
8.0ms	(- 1.0 (cos x))
17.0ms	(log (exp (- 1.0 (cos x))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(exp (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify99.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	228	986
1	622	631
2	2632	451
3	5001	406

prune258.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch50.0ms

Steps

Iters	Range		Point
8	0.002806896206153352	41.96612619086958	0.02935328501821784
7	-0.5149414008252181	-0.002950799818357885	-0.020329540819315716

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	10
1	31	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

742.0ms	1644×	body	2560	valid
289.0ms	1276×	body	1280	valid
196.0ms	1428×	body	640	valid
89.0ms	916×	body	320	valid
66.0ms	2254×	body	80	valid
33.0ms	482×	body	160	valid