Details

sample312.0ms

Algorithm

intervals

Results

13.0ms	44×	body	1280	valid
6.0ms	36×	body	640	valid
6.0ms	143×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	14×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

prune3.0ms

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: 0.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

28.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series204.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
37.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824

prune228.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 0.0b

Counts

118 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `difference-of-squares`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 165

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series189.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- 1.0 (* (tan x) (tan x)))
91.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify74.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	545	2148
1	2567	1966
2	5001	1864

prune225.0ms

Filtered

177 candidates to 88 candidates (49.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	177	12	189

Merged error: 0.0b

Counts

189 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `distribute-rgt-out--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
14.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
151.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify39.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	266	869
1	914	800
2	5002	784

prune187.0ms

Filtered

118 candidates to 69 candidates (58.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	118	12	130

Merged error: 0.0b

Counts

130 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

2.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)
2.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)

series74.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (sin x) 2)
18.0ms	(pow (sin x) 2)
16.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)

simplify63.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1588	240
3	5001	236

prune157.0ms

Filtered

84 candidates to 48 candidates (57.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	83	13	96

Merged error: 0b

Counts

96 → 13

regimes182.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	9	14

end0.0ms

sample963.0ms

Algorithm

intervals

Results

377.0ms	1501×	body	1280	valid
207.0ms	1240×	body	640	valid
164.0ms	4305×	body	80	valid
75.0ms	646×	body	320	valid
25.0ms	308×	body	160	valid

Details

sample312.0ms

simplify14.0ms

prune3.0ms

localize10.0ms

rewrite47.0ms

series204.0ms

simplify43.0ms

prune228.0ms

localize9.0ms

rewrite29.0ms

series189.0ms

simplify74.0ms

prune225.0ms

localize9.0ms

rewrite32.0ms

series248.0ms

simplify39.0ms

prune187.0ms

localize13.0ms

rewrite12.0ms

series74.0ms

simplify63.0ms

prune157.0ms

regimes182.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample963.0ms

Profiling