Details

sample55.0ms

Algorithm

intervals

Results

25.0ms	59×	body	2560	valid
7.0ms	50×	body	640	valid
6.0ms	26×	body	1280	valid
5.0ms	62×	body	80	valid
4.0ms	42×	body	320	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

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))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

2.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
41.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify59.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5001	239

prune102.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
11.6b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 1/720 (pow x 4))
5.0ms	(* 1/24 (pow x 2))
23.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series103.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 1/720 (pow x 4))
23.0ms	(* 1/24 (pow x 2))
43.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify38.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	268	347
1	1132	316
2	5001	310

prune143.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))))
0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
11.6b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`log-prod` `associate-l` `prod-exp`
5×	`pow1`
4×	`log-pow` `sqr-pow`
3×	`exp-prod` `exp-sum`
2×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unpow2`
1×	`log-div` `flip3--` `exp-diff` `rem-log-exp` `sum-log` `flip--`

Counts

4 → 85

Calls

4 calls:

46.0ms	(log (exp (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))))
5.0ms	(* 1/720 (pow x 4))
5.0ms	(* 1/24 (pow x 2))
23.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series141.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(log (exp (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))))
36.0ms	(* 1/720 (pow x 4))
23.0ms	(* 1/24 (pow x 2))
41.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	303	537
1	1254	484
2	5002	478

prune210.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

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))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
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×	`associate-/r*` `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 → 114

Calls

3 calls:

21.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
7.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series102.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
44.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify61.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5001	690

prune191.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes38.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 32.0b

bsearch64.0ms

Steps

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

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	25
1	44	25

end0.0ms

sample1.5s

Algorithm

intervals

Results

721.0ms	1603×	body	2560	valid
284.0ms	1238×	body	1280	valid
205.0ms	1466×	body	640	valid
98.0ms	938×	body	320	valid
73.0ms	2310×	body	80	valid
30.0ms	445×	body	160	valid