Details

sample56.0ms

Algorithm

intervals

Results

26.0ms	59×	body	2560	valid
7.0ms	50×	body	640	valid
6.0ms	26×	body	1280	valid
5.0ms	42×	body	320	valid
4.0ms	17×	body	160	valid
2.0ms	62×	body	80	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: 32.4b

localize6.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1.0 (cos x))
17.1b	(/ (- 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:

19.0ms	(- 1.0 (cos x))
49.0ms	(/ (- 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

prune131.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1/2 (* 1/24 (pow x 2)))
0.2b	(* 1/24 (pow x 2))
11.6b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
8×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-neg` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef`

Counts

3 → 59

Calls

3 calls:

3.0ms	(- 1/2 (* 1/24 (pow x 2)))
6.0ms	(* 1/24 (pow x 2))
0.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series132.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(- 1/2 (* 1/24 (pow x 2)))
25.0ms	(* 1/24 (pow x 2))
47.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify184.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (179.0ms)

Iter	Nodes	Cost
0	209	318
1	817	281
2	4271	278
3	5001	273

prune167.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (pow x 2) 1/576 1/48) (pow x 2) 1/4)
0.1b	(fma (pow x 2) 1/576 1/48)
11.6b	(fma (pow x 4) 1/720 (/ (fma (- (pow x 6)) 1/13824 1/8) (fma (fma (pow x 2) 1/576 1/48) (pow x 2) 1/4)))
27.0b	(/ (fma (- (pow x 6)) 1/13824 1/8) (fma (fma (pow x 2) 1/576 1/48) (pow x 2) 1/4))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (fma (pow x 2) 1/576 1/48) (pow x 2) 1/4)
0.0ms	(fma (pow x 2) 1/576 1/48)
0.0ms	(fma (pow x 4) 1/720 (/ (fma (- (pow x 6)) 1/13824 1/8) (fma (fma (pow x 2) 1/576 1/48) (pow x 2) 1/4)))
2.0ms	(/ (fma (- (pow x 6)) 1/13824 1/8) (fma (fma (pow x 2) 1/576 1/48) (pow x 2) 1/4))

series421.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma (fma (pow x 2) 1/576 1/48) (pow x 2) 1/4)
55.0ms	(fma (pow x 2) 1/576 1/48)
91.0ms	(fma (pow x 4) 1/720 (/ (fma (- (pow x 6)) 1/13824 1/8) (fma (fma (pow x 2) 1/576 1/48) (pow x 2) 1/4)))
230.0ms	(/ (fma (- (pow x 6)) 1/13824 1/8) (fma (fma (pow x 2) 1/576 1/48) (pow x 2) 1/4))

simplify73.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	171	676
1	522	604
2	2330	603
3	5001	603

prune292.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.6b	(- 1.0 (cos x))

rewrite42.0ms

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:

25.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
9.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series113.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
44.0ms	(/ (- 1.0 (cos x)) x)
19.0ms	(- 1.0 (cos x))

simplify71.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (61.0ms)

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

prune240.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes43.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.7b

bsearch77.0ms

Steps

Iters	Range		Point
7	0.003064448021395057	0.16998237910242062	0.028183382960144138
10	-4.508778152722845	-1.8057709034692785e-13	-0.030137210439935006

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	27
1	46	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

730.0ms	1603×	body	2560	valid
278.0ms	1238×	body	1280	valid
208.0ms	1466×	body	640	valid
100.0ms	938×	body	320	valid
76.0ms	2310×	body	80	valid
31.0ms	445×	body	160	valid