Details

sample444.0ms

Algorithm

intervals

Results

128.0ms	64×	body	2560	valid
47.0ms	91×	body	1280	valid
12.0ms	50×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	10×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

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: 33.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- x (sin x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`flip3--` `flip--`
2×	`sub-neg` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `div-sub` `clear-num` `div-inv`

Counts

3 → 16

Calls

3 calls:

4.0ms	(/ (- x (sin x)) (- x (tan x)))
2.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series191.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
56.0ms	(- x (sin x))

simplify65.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	219	172
1	719	167
2	2394	167
3	5001	167

prune74.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Merged error: 0.1b

Counts

26 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
16.1b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`fma-udef`

Counts

2 → 2

Calls

2 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(fma 27/2800 (pow x 4) 1/2)
47.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify196.0ms

Algorithm

egg-herbie

Counts

8 → 8

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	25
1	87	25
2	245	25
3	799	25
4	4079	25
5	5001	25

prune11.0ms

Filtered

8 candidates to 2 candidates (25.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	8	0	8
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	8	4	12

Merged error: 0.1b

Counts

12 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.8b	(- (* x x) (* (tan x) (tan x)))
0.9b	(- x (sin x))
15.0b	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-commutative`
8×	`difference-of-squares`
4×	`tan-quot` `prod-diff` `associate-/l*`
3×	`flip3--` `flip--`
2×	`sub-neg` `fma-neg` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `associate-l/` `clear-num` `flip-+` `div-inv`

Counts

4 → 35

Calls

4 calls:

3.0ms	(* (tan x) (tan x))
5.0ms	(- (* x x) (* (tan x) (tan x)))
2.0ms	(- x (sin x))
7.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (tan x) (tan x))
86.0ms	(- (* x x) (* (tan x) (tan x)))
32.0ms	(- x (sin x))
148.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

simplify92.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	257	296
1	903	279
2	3204	269
3	5003	266

prune94.0ms

Filtered

47 candidates to 27 candidates (57.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	47	4	51

Merged error: 0.1b

Counts

51 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (/ (* x x) (+ x (tan x))) (/ (* (tan x) (tan x)) (+ x (tan x))))
0.9b	(- x (sin x))
16.6b	(/ (* (tan x) (tan x)) (+ x (tan x)))
31.4b	(/ (* x x) (+ x (tan x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

40×	`frac-sub`
30×	`associate-/l*`
24×	`tan-quot`
22×	`associate-/r/`
18×	`associate-/l/`
17×	`frac-2neg`
15×	`clear-num` `*-commutative`
11×	`flip3-+` `flip-+` `div-inv`
9×	`prod-diff`
6×	`frac-times` `associate-r/` `associate-l/`
3×	`distribute-rgt-out--` `fma-neg`
2×	`sub-neg` `flip3--` `flip--` `sub-div`

Counts

4 → 82

Calls

4 calls:

13.0ms	(- (/ (* x x) (+ x (tan x))) (/ (* (tan x) (tan x)) (+ x (tan x))))
2.0ms	(- x (sin x))
6.0ms	(/ (* (tan x) (tan x)) (+ x (tan x)))
4.0ms	(/ (* x x) (+ x (tan x)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(- (/ (* x x) (+ x (tan x))) (/ (* (tan x) (tan x)) (+ x (tan x))))
32.0ms	(- x (sin x))
61.0ms	(/ (* (tan x) (tan x)) (+ x (tan x)))
44.0ms	(/ (* x x) (+ x (tan x)))

simplify98.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	749	1639
1	3758	1499
2	5003	1479

prune247.0ms

Filtered

94 candidates to 67 candidates (71.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	93	5	98

Merged error: 0.0b

Counts

98 → 5

regimes41.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.2b

bsearch99.0ms

Steps

Iters	Range		Point
9	0.09117784756913819	2697524.489058797	2.373452251774501
10	-1421.6155834850151	-1.485944467815708e-07	-2.3608879863652965

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	26
1	39	26

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.9s	1643×	body	2560	valid
1.5s	2762×	body	1280	valid
439.0ms	1826×	body	640	valid
143.0ms	912×	body	320	valid
54.0ms	483×	body	160	valid
25.0ms	374×	body	80	valid