Details

sample141.0ms

Algorithm

intervals

Results

69.0ms	48×	body	2560	valid
42.0ms	93×	body	1280	valid
15.0ms	64×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	16×	body	160	valid
0.0ms	6×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify82.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune144.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	44	14	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	14	59

Merged error: 0.3b

Counts

59 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(log (- 1.0 (cos x)))
0.2b	(exp (log (- 1.0 (cos x))))
1.2b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms	(log (- 1.0 (cos x)))
4.0ms	(exp (log (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series141.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
72.0ms	(log (- 1.0 (cos x)))
18.0ms	(exp (log (- 1.0 (cos x))))
17.0ms	(- 1.0 (cos x))

simplify84.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	289	829
1	791	761
2	2667	734
3	5001	708

prune226.0ms

Filtered

110 candidates to 67 candidates (60.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	107	17	124

Merged error: 0.2b

Counts

124 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.7b	(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
0.8b	(log (- (pow 1.0 3) (pow (cos x) 3)))
1.0b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
32×	`difference-of-squares`
28×	`log-prod`
26×	`*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod`
16×	`sqr-pow`
10×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt`
4×	`log-div` `add-cbrt-cube`
2×	`difference-cubes` `flip3--` `flip3-+` `rem-log-exp` `log-pow` `flip--` `flip-+`
1×	`+-commutative` `sub-neg` `sqr-cos` `associate-+l+` `distribute-rgt-out` `diff-log` `sum-log`

Counts

4 → 97

Calls

4 calls:

5.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
5.0ms	(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
12.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
12.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series334.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
137.0ms	(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
107.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
50.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	438	1083
1	1464	1003
2	5002	998

prune385.0ms

Filtered

109 candidates to 73 candidates (67.0%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	106	20	126

Merged error: 0.2b

Counts

126 → 20

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (cbrt (pow (log (- 1.0 (cos x))) 3)))
0.3b	(cbrt (pow (log (- 1.0 (cos x))) 3))
0.4b	(pow (log (- 1.0 (cos x))) 3)
1.2b	(- 1.0 (cos x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
17×	`exp-prod`
16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod`
11×	`pow1`
7×	`add-log-exp`
6×	`log-pow`
5×	`add-exp-log` `add-cbrt-cube`
3×	`cube-mult` `pow-unpow` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow1/3` `diff-log` `pow-exp` `flip--` `rem-cbrt-cube` `rem-exp-log` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

5.0ms	(exp (cbrt (pow (log (- 1.0 (cos x))) 3)))
2.0ms	(cbrt (pow (log (- 1.0 (cos x))) 3))
3.0ms	(pow (log (- 1.0 (cos x))) 3)
4.0ms	(- 1.0 (cos x))

series230.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(exp (cbrt (pow (log (- 1.0 (cos x))) 3)))
72.0ms	(cbrt (pow (log (- 1.0 (cos x))) 3))
118.0ms	(pow (log (- 1.0 (cos x))) 3)
21.0ms	(- 1.0 (cos x))

simplify44.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	345	614
1	1286	537
2	5002	522

prune173.0ms

Filtered

99 candidates to 51 candidates (51.5%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	98	21	119

Merged error: 0.2b

Counts

119 → 21

regimes217.0ms

Accuracy

98.2% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	41
1	49	41

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.2s	1600×	body	2560	valid
1.3s	2777×	body	1280	valid
456.0ms	1854×	body	640	valid
158.0ms	923×	body	320	valid
54.0ms	467×	body	160	valid
32.0ms	374×	body	80	valid
27.0ms	5×	body	5120	valid