Details

sample218.0ms

Algorithm

intervals

Results

113.0ms	41×	body	2560	valid
65.0ms	91×	body	1280	valid
15.0ms	55×	body	640	valid
7.0ms	37×	body	320	valid
3.0ms	22×	body	160	valid
1.0ms	10×	body	80	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

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: 30.5b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite22.0ms

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:

9.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series44.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(- x (tan x))
15.0ms	(- x (sin x))

simplify720.0ms

Counts

89 → 89

Iterations

Useful iterations: done (717.0ms)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	1051	1149
3	2912	1147
done	5000	1145

prune116.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

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: 0.1b

Counts

90 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (- x (sin x)) (- x (tan x))))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt` `*-un-lft-identity`
62×	`exp-prod`
50×	`times-frac`
32×	`log-pow`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
9×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
3×	`log-prod`
2×	`sub-neg` `exp-diff` `diff-log` `div-sub` `div-inv`
1×	`log-div` `rem-log-exp` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

10.0ms	(exp (/ (- x (sin x)) (- x (tan x))))
12.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
4.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series55.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(exp (/ (- x (sin x)) (- x (tan x))))
19.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
11.0ms	(- x (tan x))
5.0ms	(- x (sin x))

simplify973.0ms

Counts

124 → 124

Iterations

Useful iterations: 3 (335.0ms)

Iter	Nodes	Cost
0	217	1621
1	416	1473
2	1177	1408
3	3949	1383
done	5000	1383

prune154.0ms

Filtered

88 candidates to 124 candidates (-40.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	123	6	129

Merged error: 0.0b

Counts

129 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp -1/2) (+ (+ (* 9/40 (pow x 2)) 1) (* 351/22400 (pow x 4))))
0.1b	(* 351/22400 (pow x 4))
0.1b	(* 9/40 (pow x 2))
22.6b	(log (* (exp -1/2) (+ (+ (* 9/40 (pow x 2)) 1) (* 351/22400 (pow x 4)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
18×	`associate-r`
17×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-cbrt-cube`
9×	`pow1` `associate-l`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
4×	`associate-*r/` `add-log-exp` `sqr-pow`
3×	`*-commutative` `cbrt-unprod`
2×	`pow-to-exp` `log-div` `flip3-+` `rem-log-exp` `pow-prod-down` `pow-exp` `log-pow` `flip-+` `unpow2`
1×	`distribute-rgt-in` `log-prod` `distribute-lft-in`

Counts

4 → 88

Calls

4 calls:

12.0ms	(* (exp -1/2) (+ (+ (* 9/40 (pow x 2)) 1) (* 351/22400 (pow x 4))))
6.0ms	(* 351/22400 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
11.0ms	(log (* (exp -1/2) (+ (+ (* 9/40 (pow x 2)) 1) (* 351/22400 (pow x 4)))))

series32.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (exp -1/2) (+ (+ (* 9/40 (pow x 2)) 1) (* 351/22400 (pow x 4))))
4.0ms	(* 351/22400 (pow x 4))
3.0ms	(* 9/40 (pow x 2))
15.0ms	(log (* (exp -1/2) (+ (+ (* 9/40 (pow x 2)) 1) (* 351/22400 (pow x 4)))))

simplify492.0ms

Counts

100 → 100

Iterations

Useful iterations: done (490.0ms)

Iter	Nodes	Cost
0	183	1398
1	450	1307
2	1486	1150
done	5000	1149

prune224.0ms

Filtered

68 candidates to 100 candidates (-47.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	100	6	106

Merged error: 0.0b

Counts

106 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x 4)
0.1b	(* 9/40 (pow x 2))
0.1b	(* 27/2800 (pow x 4))
15.8b	(- (* 9/40 (pow x 2)) (+ 1/2 (* 27/2800 (pow x 4))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

2.0ms	(pow x 4)
6.0ms	(* 9/40 (pow x 2))
6.0ms	(* 27/2800 (pow x 4))
7.0ms	(- (* 9/40 (pow x 2)) (+ 1/2 (* 27/2800 (pow x 4))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.1s

Counts

95 → 95

Iterations

Useful iterations: 3 (306.0ms)

Iter	Nodes	Cost
0	132	893
1	314	804
2	844	730
3	3381	718
done	5000	718

prune142.0ms

Filtered

61 candidates to 95 candidates (-55.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	95	6	101

Merged error: 0.0b

Counts

101 → 6

regimes107.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch36.0ms

Steps

Iters	Range		Point
9	0.009971872296741319	901.3230478674768	0.028213698630483845
7	-0.0552767792151412	-0.0004813576712207844	-0.026253755058246165

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	43
1	30	33
done	30	33

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.9s	1644×	body	2560	valid
1.8s	2772×	body	1280	valid
500.0ms	1835×	body	640	valid
169.0ms	919×	body	320	valid
60.0ms	460×	body	160	valid
29.0ms	370×	body	80	valid

Details

sample218.0ms

simplify25.0ms

prune4.0ms

localize10.0ms

rewrite22.0ms

series44.0ms

simplify720.0ms

prune116.0ms

localize11.0ms

rewrite36.0ms

series55.0ms

simplify973.0ms

prune154.0ms

localize15.0ms

rewrite37.0ms

series32.0ms

simplify492.0ms

prune224.0ms

localize9.0ms

rewrite26.0ms

series17.0ms

simplify1.1s

prune142.0ms

regimes107.0ms

bsearch36.0ms

simplify3.0ms

end0.0ms

sample6.7s

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