Details

sample52.0ms

Algorithm

intervals

Results

22.0ms	51×	body	2560	valid
8.0ms	36×	body	1280	valid
7.0ms	49×	body	640	valid
4.0ms	35×	body	320	valid
2.0ms	68×	body	80	valid
1.0ms	17×	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: 31.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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:

11.0ms	(- 1.0 (cos x))
21.0ms	(/ (- 1.0 (cos x)) (* x x))

series55.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- 1.0 (cos x))
39.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify31.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (26.0ms)

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

prune130.0ms

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))

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-r`
17×	`add-cbrt-cube`
13×	`associate-l`
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` `*-commutative`

Counts

3 → 132

Calls

3 calls:

40.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
18.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series93.0ms

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))

simplify69.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	582	999
1	2640	823
2	5001	787

prune243.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

283×	`times-frac`
234×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
135×	`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--` `prod-diff` `flip--`
6×	`cbrt-unprod` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-flip` `fma-neg` `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 → 324

Calls

4 calls:

72.0ms	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
11.0ms	(/ x (- 1.0 (cos x)))
18.0ms	(/ 1 (/ x (- 1.0 (cos x))))
7.0ms	(- 1.0 (cos x))

series133.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
42.0ms	(/ x (- 1.0 (cos x)))
37.0ms	(/ 1 (/ x (- 1.0 (cos x))))
16.0ms	(- 1.0 (cos x))

simplify57.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1170	2869
1	5001	2418

prune564.0ms

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))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
30×	`exp-prod` `log-pow`
27×	`times-frac` `prod-diff`
22×	`exp-sum`
14×	`log-prod`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `exp-diff` `fma-neg` `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 → 141

Calls

4 calls:

53.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
17.0ms	(exp (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))
20.0ms	(log (exp (- 1.0 (cos x))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
39.0ms	(exp (- 1.0 (cos x)))
16.0ms	(- 1.0 (cos x))
16.0ms	(log (exp (- 1.0 (cos x))))

simplify42.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	393	1192
1	1234	873
2	5001	725

prune271.0ms

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	34	18
1	34	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

727.0ms	1597×	body	2560	valid
300.0ms	1307×	body	1280	valid
201.0ms	1444×	body	640	valid
104.0ms	915×	body	320	valid
76.0ms	2256×	body	80	valid
34.0ms	481×	body	160	valid