Details

sample51.0ms

Algorithm

intervals

Results

20.0ms	46×	body	2560	valid
8.0ms	39×	body	1280	valid
8.0ms	60×	body	640	valid
4.0ms	34×	body	320	valid
2.0ms	70×	body	80	valid
0.0ms	7×	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: 32.3b

localize11.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
13.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

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:

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

series62.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify75.0ms

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	5002	239

prune100.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/720 (pow x 4)) 1/2)
0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
13.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

4.0ms	(+ (* 1/720 (pow x 4)) 1/2)
6.0ms	(* 1/720 (pow x 4))
6.0ms	(* 1/24 (pow x 2))
25.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (* 1/720 (pow x 4)) 1/2)
37.0ms	(* 1/720 (pow x 4))
25.0ms	(* 1/24 (pow x 2))
49.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify50.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	312	411
1	1312	380
2	5001	373

prune183.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(/ (sqrt (- 1.0 (cos x))) x)
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
40×	`sqrt-prod`
38×	`add-cube-cbrt`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
4×	`pow1` `flip3--` `sqrt-div` `flip--` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 126

Calls

4 calls:

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

series232.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (sqrt (- 1.0 (cos x))) x)
95.0ms	(/ (sqrt (- 1.0 (cos x))) x)
23.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify100.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	242	1020
1	706	972
2	2968	960
3	5002	960

prune428.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (- 1.0 (cos x)) 3)
0.3b	(cbrt (pow (- 1.0 (cos x)) 3))
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`add-log-exp`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 84

Calls

4 calls:

5.0ms	(pow (- 1.0 (cos x)) 3)
5.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series106.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (- 1.0 (cos x)) 3)
18.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
18.0ms	(- 1.0 (cos x))
22.0ms	(- 1.0 (cos x))

simplify35.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	235	459
1	895	444
2	5001	438

prune202.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.7b

bsearch87.0ms

Steps

Iters	Range		Point
9	2.0114125408603258e-10	0.4954286465087044	0.028129396018266136
10	-1.7081313977704333	-1.7977825652338532e-10	-0.03302109030086143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	25
1	41	25

end0.0ms

sample1.6s

Algorithm

intervals

Results

748.0ms	1625×	body	2560	valid
302.0ms	1261×	body	1280	valid
207.0ms	1436×	body	640	valid
94.0ms	914×	body	320	valid
76.0ms	2294×	body	80	valid
35.0ms	470×	body	160	valid