Details

sample472.0ms

Algorithm

intervals

Results

113.0ms	59×	body	2560	valid
71.0ms	92×	body	1280	valid
16.0ms	58×	body	640	valid
5.0ms	28×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	9×	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: 34.7b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.0b	(- x (tan x))
1.0b	(- x (sin x))

rewrite36.0ms

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:

22.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify150.0ms

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

prune178.0ms

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 3 expressions with local error:

0.2b	(* 9/40 (pow x 2))
0.5b	(* 27/2800 (pow x 4))
15.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite22.0ms

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:

8.0ms	(* 9/40 (pow x 2))
5.0ms	(* 27/2800 (pow x 4))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series107.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 9/40 (pow x 2))
39.0ms	(* 27/2800 (pow x 4))
44.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5002	315

prune124.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	75	3	78

Merged error: 0b

Counts

78 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.0b	(- x (tan x))
1.0b	(- x (tan x))

rewrite42.0ms

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)))
25.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series342.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (sin x) (- x (tan x)))
176.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
53.0ms	(- x (tan x))
52.0ms	(- x (tan x))

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

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

prune207.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0b

Counts

109 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- x (sin x)) 3)
1.0b	(- x (tan x))
1.0b	(- x (sin x))
19.2b	(cbrt (pow (- x (sin x)) 3))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`add-log-exp`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 84

Calls

4 calls:

5.0ms	(pow (- x (sin x)) 3)
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))
5.0ms	(cbrt (pow (- x (sin x)) 3))

series172.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (- x (sin x)) 3)
48.0ms	(- x (tan x))
35.0ms	(- x (sin x))
45.0ms	(cbrt (pow (- x (sin x)) 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	339	488
1	1169	466
2	5001	459

prune178.0ms

Filtered

96 candidates to 58 candidates (60.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	96	3	99

Merged error: 0b

Counts

99 → 3

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.1b

bsearch89.0ms

Steps

Iters	Range		Point
10	0.0002141056345597589	3206628.0142593775	0.029607457957696412
11	-4.816760182774211e+16	-0.0014803844373699059	-0.029680637313438188

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.7s	1570×	body	2560	valid
1.7s	2830×	body	1280	valid
484.0ms	1863×	body	640	valid
163.0ms	960×	body	320	valid
65.0ms	449×	body	160	valid
25.0ms	328×	body	80	valid