Details

sample59.0ms

Algorithm

intervals

Results

27.0ms	52×	body	2560	valid
9.0ms	37×	body	1280	valid
8.0ms	48×	body	640	valid
3.0ms	25×	body	320	valid
3.0ms	78×	body	80	valid
2.0ms	16×	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: 30.1b

localize11.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite30.0ms

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:

7.0ms	(- 1.0 (cos x))
21.0ms	(/ (- 1.0 (cos x)) (* x x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- 1.0 (cos x))
45.0ms	(/ (- 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

prune135.0ms

Pruning

11 alts after pruning (11 fresh and 0 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))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))

rewrite110.0ms

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:

15.0ms	(/ (sqrt (- 1.0 (cos x))) x)
64.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
10.0ms	(- 1.0 (cos x))
8.0ms	(- 1.0 (cos x))

series163.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (sqrt (- 1.0 (cos x))) x)
39.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
21.0ms	(- 1.0 (cos x))
17.0ms	(- 1.0 (cos x))

simplify99.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 2 (77.0ms)

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

prune467.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.1b	(- 1.0 (cos x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 165

Calls

3 calls:

23.0ms	(/ (/ (- 1.0 (cos x)) x) x)
18.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series102.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (/ (- 1.0 (cos x)) x) x)
38.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify62.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	592	1453
1	2212	1292
2	5001	1283

prune347.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.2b	(log (exp (- 1.0 (cos x))))

rewrite142.0ms

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:

102.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
7.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))
17.0ms	(log (exp (- 1.0 (cos x))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
17.0ms	(- 1.0 (cos x))
22.0ms	(- 1.0 (cos x))
18.0ms	(log (exp (- 1.0 (cos x))))

simplify76.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (55.0ms)

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

prune437.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes62.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.1b

bsearch69.0ms

Steps

Iters	Range		Point
8	0.00015704816827310668	9.114942375872904	0.03119086400759214
9	-0.2945747773639613	-3.489101517161873e-08	-0.034379388822557394

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	28
1	45	28
2	45	28

end0.0ms

sample1.7s

Algorithm

intervals

Results

785.0ms	1577×	body	2560	valid
318.0ms	1259×	body	1280	valid
230.0ms	1462×	body	640	valid
103.0ms	908×	body	320	valid
83.0ms	2355×	body	80	valid
35.0ms	439×	body	160	valid