Details

sample417.0ms

Algorithm

intervals

Results

240.0ms	88×	body	1280	valid
138.0ms	51×	body	2560	valid
14.0ms	52×	body	640	valid
8.0ms	43×	body	320	valid
2.0ms	9×	body	80	valid
2.0ms	13×	body	160	valid

simplify11.0ms

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

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: 31.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (sin x))
1.6b	(- x (tan x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
7.0ms	(- x (tan x))

series37.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))
20.0ms	(- x (tan x))

simplify153.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	684
2	4781	684
3	5001	684

prune87.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Merged error: 0b

Counts

90 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
1.6b	(- x (sin x))
1.6b	(- x (tan x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 188

Calls

4 calls:

15.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
12.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
3.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series47.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
13.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
5.0ms	(- x (sin x))
10.0ms	(- x (tan x))

simplify84.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	736	2195
1	3051	2082
2	5002	2068

prune130.0ms

Filtered

87 candidates to 200 candidates (-129.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	200	3	203

Merged error: 0b

Counts

203 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
15.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series11.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* 27/2800 (pow x 4))
3.0ms	(* 9/40 (pow x 2))
5.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify40.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	316
2	5001	313

prune99.0ms

Filtered

46 candidates to 75 candidates (-63.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	75	3	78

Merged error: 0b

Counts

78 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ (pow (- x (sin x)) 3) (pow (- x (tan x)) 3)))
1.6b	(- x (sin x))
1.6b	(- x (tan x))
19.9b	(/ (pow (- x (sin x)) 3) (pow (- x (tan x)) 3))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

512×	`times-frac`
471×	`add-sqr-sqrt` `*-un-lft-identity`
330×	`unpow-prod-down` `cube-prod`
262×	`cbrt-prod`
203×	`add-cube-cbrt`
134×	`distribute-lft-out--` `difference-of-squares`
66×	`cube-mult` `unpow3` `sqr-pow`
16×	`add-exp-log` `associate-/r` `associate-/l`
9×	`div-exp`
8×	`add-log-exp`
6×	`cube-div` `pow-to-exp` `pow-exp` `add-cbrt-cube`
5×	`flip3--` `flip--`
4×	`pow1` `associate-/r/`
2×	`sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `cbrt-div` `frac-2neg` `pow1/3` `clear-num`

Counts

4 → 611

Calls

4 calls:

25.0ms	(cbrt (/ (pow (- x (sin x)) 3) (pow (- x (tan x)) 3)))
3.0ms	(- x (sin x))
3.0ms	(- x (tan x))
17.0ms	(/ (pow (- x (sin x)) 3) (pow (- x (tan x)) 3))

series46.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cbrt (/ (pow (- x (sin x)) 3) (pow (- x (tan x)) 3)))
5.0ms	(- x (sin x))
10.0ms	(- x (tan x))
18.0ms	(/ (pow (- x (sin x)) 3) (pow (- x (tan x)) 3))

simplify186.0ms

Algorithm

egg-herbie

Counts

623 → 623

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	907	8729
1	4449	8558
2	5001	8531

prune325.0ms

Filtered

170 candidates to 623 candidates (-266.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	623	0	623
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	623	3	626

Merged error: 0b

Counts

626 → 3

regimes74.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch40.0ms

Steps

Iters	Range		Point
8	2.4879688186424768e-05	0.3609580473631881	0.031796315249784685
10	-522.1368722912733	-5.949899967025005e-16	-0.025835475030384893

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	13
1	32	13

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.0s	1609×	body	2560	valid
1.6s	2726×	body	1280	valid
494.0ms	1921×	body	640	valid
162.0ms	926×	body	320	valid
52.0ms	440×	body	160	valid
27.0ms	378×	body	80	valid

Details

sample417.0ms

simplify11.0ms

prune4.0ms

localize11.0ms

rewrite21.0ms

series37.0ms

simplify153.0ms

prune87.0ms

localize11.0ms

rewrite43.0ms

series47.0ms

simplify84.0ms

prune130.0ms

localize10.0ms

rewrite18.0ms

series11.0ms

simplify40.0ms

prune99.0ms

localize13.0ms

rewrite92.0ms

series46.0ms

simplify186.0ms

prune325.0ms

regimes74.0ms

bsearch40.0ms

simplify2.0ms

end0.0ms

sample6.5s

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