Details

sample450.0ms

Algorithm

intervals

Results

101.0ms	41×	body	2560	valid
60.0ms	90×	body	1280	valid
14.0ms	53×	body	640	valid
5.0ms	31×	body	320	valid
3.0ms	24×	body	160	valid
1.0ms	17×	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: 27.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.4b	(- x (tan x))
2.5b	(- x (sin x))

rewrite39.0ms

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 (tan x))
6.0ms	(- x (sin x))

series179.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify154.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune200.0ms

Filtered

89 candidates to 63 candidates (70.8%)

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
2.1b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.4b	(- x (tan x))
2.4b	(- x (tan x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

6.0ms	(/ (sin x) (- x (tan x)))
28.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series344.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (sin x) (- x (tan x)))
182.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
51.0ms	(- x (tan x))
54.0ms	(- x (tan x))

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872

prune231.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Merged error: 0b

Counts

109 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
16.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite24.0ms

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:

6.0ms	(* 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))

series113.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
46.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify43.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315

prune137.0ms

Filtered

75 candidates to 46 candidates (61.3%)

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

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (tan x) 3)
2.4b	(- (pow x 3) (pow (tan x) 3))
2.5b	(- x (sin x))
33.7b	(/ (- (pow x 3) (pow (tan x) 3)) (+ (* (tan x) (+ (tan x) x)) (pow x 2)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

159×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
81×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
26×	`distribute-lft-out--`
25×	`associate-/l*`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`tan-quot` `cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 192

Calls

4 calls:

3.0ms	(pow (tan x) 3)
12.0ms	(- (pow x 3) (pow (tan x) 3))
4.0ms	(- x (sin x))
25.0ms	(/ (- (pow x 3) (pow (tan x) 3)) (+ (* (tan x) (+ (tan x) x)) (pow x 2)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (tan x) 3)
127.0ms	(- (pow x 3) (pow (tan x) 3))
32.0ms	(- x (sin x))
260.0ms	(/ (- (pow x 3) (pow (tan x) 3)) (+ (* (tan x) (+ (tan x) x)) (pow x 2)))

simplify99.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	625	2980
1	2604	2912
2	5002	2833

prune466.0ms

Filtered

204 candidates to 106 candidates (52.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	204	3	207

Merged error: 0b

Counts

207 → 3

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch84.0ms

Steps

Iters	Range		Point
10	0.00022027325057658872	62623256.830634765	0.027715773861404648
9	-17.831791951177678	-3.7534567552478157e-06	-0.027340075628349603

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.9s	1626×	body	2560	valid
1.6s	2738×	body	1280	valid
503.0ms	1868×	body	640	valid
179.0ms	980×	body	320	valid
58.0ms	471×	body	160	valid
29.0ms	317×	body	80	valid

Details

sample450.0ms

simplify12.0ms

prune4.0ms

localize11.0ms

rewrite39.0ms

series179.0ms

simplify154.0ms

prune200.0ms

localize10.0ms

rewrite47.0ms

series344.0ms

simplify41.0ms

prune231.0ms

localize11.0ms

rewrite24.0ms

series113.0ms

simplify43.0ms

prune137.0ms

localize19.0ms

rewrite58.0ms

series471.0ms

simplify99.0ms

prune466.0ms

regimes31.0ms

bsearch84.0ms

simplify2.0ms

end0.0ms

sample6.5s

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