Details

sample471.0ms

Algorithm

intervals

Results

148.0ms	61×	body	2560	valid
48.0ms	83×	body	1280	valid
18.0ms	66×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	12×	body	80	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 33.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- x (sin x))

rewrite37.0ms

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:

24.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify153.0ms

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

prune181.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 27/2800 (pow x 4)) 1/2)
0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
14.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

4.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
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))

series185.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
35.0ms	(* 27/2800 (pow x 4))
27.0ms	(* 9/40 (pow x 2))
43.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	316	413
1	1299	382
2	5002	377

prune152.0ms

Filtered

89 candidates to 56 candidates (62.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	89	5	94

Merged error: 0.0b

Counts

94 → 5

localize12.0ms

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))))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite43.0ms

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)))
27.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (sin x) (- x (tan x)))
173.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
48.0ms	(- x (tan x))
52.0ms	(- x (tan x))

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

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

prune210.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	106	5	111

Merged error: 0.0b

Counts

111 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x (tan x)))
0.1b	(* (- x (sin x)) (/ 1 (- x (tan x))))
1.3b	(- x (tan x))
1.3b	(- x (sin x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
32×	`times-frac`
24×	`add-cube-cbrt`
21×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3--` `flip--`
5×	`associate-l` `associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 119

Calls

4 calls:

5.0ms	(/ 1 (- x (tan x)))
13.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
6.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1 (- x (tan x)))
78.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
54.0ms	(- x (tan x))
30.0ms	(- x (sin x))

simplify62.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	462	906
1	2072	813
2	5002	771

prune199.0ms

Filtered

131 candidates to 82 candidates (62.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	131	5	136

Merged error: 0.0b

Counts

136 → 5

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.5b

bsearch74.0ms

Steps

Iters	Range		Point
8	6.042829624826513e-05	0.09081442282169057	0.027426138134751147
8	-6.238959787773506	-0.00010711273713490883	-0.02830752052435383

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	46
1	39	46

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.9s	1558×	body	2560	valid
1.6s	2785×	body	1280	valid
489.0ms	1878×	body	640	valid
164.0ms	939×	body	320	valid
58.0ms	477×	body	160	valid
27.0ms	363×	body	80	valid

Details

sample471.0ms

simplify14.0ms

prune4.0ms

localize12.0ms

rewrite37.0ms

series175.0ms

simplify153.0ms

prune181.0ms

localize13.0ms

rewrite24.0ms

series185.0ms

simplify47.0ms

prune152.0ms

localize12.0ms

rewrite43.0ms

series329.0ms

simplify40.0ms

prune210.0ms

localize9.0ms

rewrite33.0ms

series210.0ms

simplify62.0ms

prune199.0ms

regimes37.0ms

bsearch74.0ms

simplify2.0ms

end0.0ms

sample6.5s

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