Details

sample212.0ms

Algorithm

intervals

Results

113.0ms	41×	body	2560	valid
61.0ms	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

simplify14.0ms

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

prune11.0ms

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

series42.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(- x (tan x))
14.0ms	(- x (sin x))

simplify892.0ms

Counts

89 → 89

Iterations

Useful iterations: done (889.0ms)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	1029	1147
3	2663	1147
done	5000	1145

prune118.0ms

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))

rewrite38.0ms

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:

11.0ms	(exp (/ (- x (sin x)) (- x (tan x))))
11.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
4.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series51.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (/ (- x (sin x)) (- x (tan x))))
15.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
11.0ms	(- x (tan x))
5.0ms	(- x (sin x))

simplify882.0ms

Counts

124 → 124

Iterations

Useful iterations: 3 (326.0ms)

Iter	Nodes	Cost
0	217	1621
1	416	1473
2	1152	1408
3	3534	1383
done	5001	1383

prune146.0ms

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

rewrite40.0ms

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

series33.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (exp -1/2) (+ (* 351/22400 (pow x 4)) (+ (* 9/40 (pow x 2)) 1)))
4.0ms	(* 351/22400 (pow x 4))
3.0ms	(* 9/40 (pow x 2))
16.0ms	(log (* (exp -1/2) (+ (* 351/22400 (pow x 4)) (+ (* 9/40 (pow x 2)) 1))))

simplify517.0ms

Counts

100 → 100

Iterations

Useful iterations: done (514.0ms)

Iter	Nodes	Cost
0	183	1398
1	456	1265
2	1583	1139
done	5000	1138

prune216.0ms

Filtered

65 candidates to 100 candidates (-53.8%)

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

localize12.0ms

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))))

rewrite22.0ms

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))
6.0ms	(- (* 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))))

simplify764.0ms

Counts

95 → 95

Iterations

Useful iterations: 3 (244.0ms)

Iter	Nodes	Cost
0	132	893
1	314	791
2	852	724
3	2764	714
done	5000	714

prune134.0ms

Filtered

58 candidates to 95 candidates (-63.8%)

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

regimes105.0ms

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

sample6.4s

Algorithm

intervals

Results

3.9s	1644×	body	2560	valid
1.5s	2772×	body	1280	valid
490.0ms	1835×	body	640	valid
171.0ms	919×	body	320	valid
64.0ms	460×	body	160	valid
28.0ms	370×	body	80	valid

Details

sample212.0ms

simplify14.0ms

prune11.0ms

localize10.0ms

rewrite22.0ms

series42.0ms

simplify892.0ms

prune118.0ms

localize11.0ms

rewrite38.0ms

series51.0ms

simplify882.0ms

prune146.0ms

localize15.0ms

rewrite40.0ms

series33.0ms

simplify517.0ms

prune216.0ms

localize12.0ms

rewrite22.0ms

series17.0ms

simplify764.0ms

prune134.0ms

regimes105.0ms

bsearch36.0ms

simplify3.0ms

end0.0ms

sample6.4s

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