Details

sample45.0ms

Algorithm

intervals

Results

18.0ms	40×	body	2560	valid
9.0ms	40×	body	1280	valid
6.0ms	40×	body	640	valid
3.0ms	30×	body	320	valid
3.0ms	89×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize6.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1.0 (cos x))
12.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite14.0ms

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))

series65.0ms

Counts

2 → 6

Calls

2 calls:

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

prune126.0ms

Filtered

64 candidates to 43 candidates (67.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.6b	(- 1.0 (cos x))
2.6b	(- 1.0 (cos x))

rewrite71.0ms

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)
39.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
5.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series172.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (sqrt (- 1.0 (cos x))) x)
46.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
17.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify99.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 2 (78.0ms)

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

prune437.0ms

Filtered

250 candidates to 141 candidates (56.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
2.6b	(- 1.0 (cos x))
2.6b	(- 1.0 (cos x))
2.8b	(log (exp (- 1.0 (cos x))))

rewrite86.0ms

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-r`
28×	`associate-l`
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:

62.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
9.0ms	(log (exp (- 1.0 (cos x))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
18.0ms	(- 1.0 (cos x))
23.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify74.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	688	2088
1	2841	1468
2	5001	1375

prune442.0ms

Filtered

198 candidates to 121 candidates (61.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ 1.0 (cos x))
2.6b	(- 1.0 (cos x))
2.6b	(- (* 1.0 1.0) (* (cos x) (cos x)))
2.8b	(log (exp (- 1.0 (cos x))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
19×	`prod-diff`
14×	`log-prod`
11×	`exp-sum`
10×	`add-log-exp`
6×	`log-pow`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `fma-def` `difference-of-squares`
2×	`flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`+-commutative` `log-div` `sqr-cos` `flip3-+` `exp-diff` `rem-log-exp` `sum-log` `flip-+` `distribute-lft-out` `associate--r+`

Counts

4 → 94

Calls

4 calls:

6.0ms	(+ 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))
9.0ms	(log (exp (- 1.0 (cos x))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ 1.0 (cos x))
17.0ms	(- 1.0 (cos x))
32.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))
18.0ms	(log (exp (- 1.0 (cos x))))

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	344	708
1	1202	491
2	5002	403

prune298.0ms

Filtered

106 candidates to 73 candidates (68.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch74.0ms

Steps

Iters	Range		Point
10	9.558161037350472e-13	0.8818080259852756	0.034074837610598666
5	-0.041603525395973645	-0.015510049556855336	-0.03305941206486147

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	44
1	50	44

end0.0ms

sample1.5s

Algorithm

intervals

Results

723.0ms	1582×	body	2560	valid
273.0ms	1255×	body	1280	valid
210.0ms	1427×	body	640	valid
92.0ms	942×	body	320	valid
67.0ms	2280×	body	80	valid
36.0ms	514×	body	160	valid