Details

sample52.0ms

Algorithm

intervals

Results

23.0ms	50×	body	2560	valid
10.0ms	48×	body	1280	valid
6.0ms	42×	body	640	valid
4.0ms	38×	body	320	valid
2.0ms	59×	body	80	valid
1.0ms	19×	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: 34.1b

localize6.0ms

Local error

Found 2 expressions with local error:

2.5b	(- 1.0 (cos x))
14.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite15.0ms

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:

3.0ms	(- 1.0 (cos x))
10.0ms	(/ (- 1.0 (cos x)) (* x x))

series68.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
50.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (26.0ms)

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

prune124.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 1/24 (pow x 2))
9.6b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 39

Calls

2 calls:

9.0ms	(* 1/24 (pow x 2))
0.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series68.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(* 1/24 (pow x 2))
43.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify105.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	139	194
1	532	171
2	2601	171
3	5001	170

prune107.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

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))
2.5b	(- 1.0 (cos x))
2.5b	(- 1.0 (cos x))

rewrite73.0ms

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:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
46.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series180.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (sqrt (- 1.0 (cos x))) x)
42.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
18.0ms	(- 1.0 (cos x))
22.0ms	(- 1.0 (cos x))

simplify101.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 2 (77.0ms)

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

prune431.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (log (exp (- 1.0 (cos x))))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.5b	(- 1.0 (cos x))
2.5b	(- 1.0 (cos x))
2.6b	(log (exp (- 1.0 (cos x))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
72×	`times-frac`
63×	`add-cube-cbrt`
48×	`sqrt-prod`
40×	`associate-l`
28×	`associate-r`
27×	`prod-diff`
24×	`log-pow`
20×	`exp-prod`
16×	`add-exp-log` `add-cbrt-cube`
14×	`log-prod`
11×	`exp-sum`
10×	`pow1`
9×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
8×	`add-log-exp`
6×	`fma-neg`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3--` `diff-log` `flip--` `div-inv`
1×	`frac-times` `log-div` `exp-diff` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 186

Calls

4 calls:

67.0ms	(* (/ (sqrt (log (exp (- 1.0 (cos x))))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))
9.0ms	(log (exp (- 1.0 (cos x))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify71.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	695	2142
1	2776	1482
2	5001	1385

prune416.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 32.4b

bsearch67.0ms

Steps

Iters	Range		Point
10	7.712829756242493e-08	8770343.893451896	0.023960596481684263
9	-1827977.1926269082	-0.00043085380315138777	-0.030927381235145903

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	12
1	32	12

end0.0ms

sample1.5s

Algorithm

intervals

Results

734.0ms	1615×	body	2560	valid
266.0ms	1171×	body	1280	valid
219.0ms	1519×	body	640	valid
94.0ms	943×	body	320	valid
72.0ms	2276×	body	80	valid
33.0ms	476×	body	160	valid