Details

sample277.0ms

Algorithm

intervals

Results

12.0ms	42×	body	1280	valid
7.0ms	44×	body	640	valid
5.0ms	142×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	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: 0.4b

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))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

8×	`tan-quot`
2×	`pow2` `frac-times` `flip3--` `associate-r/` `associate-l/` `associate-/r/` `*-commutative` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+` `div-inv`

Counts

4 → 22

Calls

4 calls:

4.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
3.0ms	(* (tan x) (tan x))
6.0ms	(* (tan x) (tan x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(- 1.0 (* (tan x) (tan x)))
48.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	159	224
1	448	215
2	1307	213
3	5002	199

prune94.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	25	9	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	9	35

Merged error: 0.1b

Counts

35 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`tan-quot` `frac-times`
5×	`flip3--` `associate-*r/` `flip--`
4×	`associate-*l/` `clear-num`
3×	`frac-2neg` `associate-r` `*-commutative`
2×	`pow2` `associate-/r/` `un-div-inv`
1×	`sub-neg` `flip3-+` `flip-+` `div-inv`

Counts

4 → 31

Calls

4 calls:

2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
4.0ms	(* (tan x) (tan x))
4.0ms	(* (tan x) (tan x))

series195.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
94.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
36.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify149.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	188	326
1	771	300
2	4197	271
3	5001	264

prune100.0ms

Filtered

43 candidates to 23 candidates (53.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	39	4	43
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	42	10	52

Merged error: 0.1b

Counts

52 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow-to-exp` `unpow2` `sqr-pow`

Counts

4 → 12

Calls

4 calls:

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)
22.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)

simplify122.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	62	60
1	209	56
2	639	56
3	3044	56
4	5001	56

prune73.0ms

Filtered

24 candidates to 12 candidates (50.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	24	10	34

Merged error: 0.1b

Counts

34 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (- (pow (tan x) 3)) (tan x) (* 1.0 1.0))
0.2b	(/ (fma (- (pow (tan x) 3)) (tan x) (* 1.0 1.0)) (fma (tan x) (tan x) 1.0))
0.3b	(* (tan x) (tan x))
0.4b	(pow (tan x) 3)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot`
1×	`pow2` `frac-times` `pow-to-exp` `frac-2neg` `unpow3` `associate-r/` `associate-l/` `clear-num` `*-commutative` `fma-udef` `div-inv` `sqr-pow`

Counts

4 → 12

Calls

4 calls:

1.0ms	(fma (- (pow (tan x) 3)) (tan x) (* 1.0 1.0))
2.0ms	(/ (fma (- (pow (tan x) 3)) (tan x) (* 1.0 1.0)) (fma (tan x) (tan x) 1.0))
3.0ms	(* (tan x) (tan x))
2.0ms	(pow (tan x) 3)

series311.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma (- (pow (tan x) 3)) (tan x) (* 1.0 1.0))
148.0ms	(/ (fma (- (pow (tan x) 3)) (tan x) (* 1.0 1.0)) (fma (tan x) (tan x) 1.0))
31.0ms	(* (tan x) (tan x))
49.0ms	(pow (tan x) 3)

simplify50.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	148	130
1	454	129
2	1533	126
3	5001	123

prune68.0ms

Filtered

24 candidates to 17 candidates (70.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	22	12	34

Merged error: 0.1b

Counts

34 → 12

regimes183.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms

sample924.0ms

Algorithm

intervals

Results

379.0ms	1538×	body	1280	valid
196.0ms	1266×	body	640	valid
150.0ms	4303×	body	80	valid
65.0ms	595×	body	320	valid
23.0ms	298×	body	160	valid