Details

sample724.0ms

Algorithm

intervals

Results

300.0ms	54×	body	2560	valid
198.0ms	82×	body	1280	valid
75.0ms	67×	body	640	valid
24.0ms	29×	body	320	valid
7.0ms	13×	body	160	valid
3.0ms	11×	body	80	valid

simplify38.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	19
3	19
2	17
1	13
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite74.0ms

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×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

35.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
12.0ms	(- x (sin x))

series265.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(/ (- x (sin x)) (- x (tan x)))
96.0ms	(- x (tan x))
65.0ms	(- x (sin x))

simplify1.3s

Counts

92 → 92

Iterations

Iter	Nodes
3	3119
2	973
1	373
0	160

prune321.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (tan x))

rewrite91.0ms

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×	`flip3--` `add-cbrt-cube` `add-exp-log` `associate-/r/` `flip--`
5×	`associate-/r*`
4×	`pow1` `insert-posit16`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 98

Calls

4 calls:

13.0ms	(/ (sin x) (- x (tan x)))
66.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series489.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (sin x) (- x (tan x)))
232.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
95.0ms	(- x (tan x))
84.0ms	(- x (tan x))

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
3	3355
2	1115
1	390
0	180

prune472.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* x x) (- 9/40 (* 27/2800 (* x x)))) -1/2)
0.0b	(- 9/40 (* 27/2800 (* x x)))
0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.4b	(* 27/2800 (* x x))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-r` `associate-l` `insert-posit16`
2×	`flip3--` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `diff-log` `flip-+`

Counts

4 → 75

Calls

4 calls:

17.0ms	(+ (* (* x x) (- 9/40 (* 27/2800 (* x x)))) -1/2)
5.0ms	(- 9/40 (* 27/2800 (* x x)))
29.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
22.0ms	(* 27/2800 (* x x))

series325.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* (* x x) (- 9/40 (* 27/2800 (* x x)))) -1/2)
75.0ms	(- 9/40 (* 27/2800 (* x x)))
147.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
43.0ms	(* 27/2800 (* x x))

simplify1.9s

Counts

87 → 87

Iterations

Iter	Nodes
3	3589
2	1074
1	349
0	115

prune268.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

1.9b	(- x (tan x))
19.1b	(/ (- (* (pow x 7) 1/5040) (- (* 1/120 (pow x 5)) (* x (* 1/6 (* x x))))) (- x (tan x)))
20.8b	(- (* 1/120 (pow x 5)) (* x (* 1/6 (* x x))))
24.7b	(- (* (pow x 7) 1/5040) (- (* 1/120 (pow x 5)) (* x (* 1/6 (* x x)))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
14×	`add-cube-cbrt`
13×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
4×	`pow1` `sub-neg` `insert-posit16`
3×	`associate-/l*`
2×	`associate-/r/` `associate--r+` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv` `associate--r-`

Counts

4 → 86

Calls

4 calls:

9.0ms	(- x (tan x))
72.0ms	(/ (- (* (pow x 7) 1/5040) (- (* 1/120 (pow x 5)) (* x (* 1/6 (* x x))))) (- x (tan x)))
22.0ms	(- (* 1/120 (pow x 5)) (* x (* 1/6 (* x x))))
27.0ms	(- (* (pow x 7) 1/5040) (- (* 1/120 (pow x 5)) (* x (* 1/6 (* x x)))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- x (tan x))
142.0ms	(/ (- (* (pow x 7) 1/5040) (- (* 1/120 (pow x 5)) (* x (* 1/6 (* x x))))) (- x (tan x)))
219.0ms	(- (* 1/120 (pow x 5)) (* x (* 1/6 (* x x))))
146.0ms	(- (* (pow x 7) 1/5040) (- (* 1/120 (pow x 5)) (* x (* 1/6 (* x x)))))

simplify3.7s

Counts

98 → 98

Iterations

Iter	Nodes
3	7795
2	1640
1	472
0	180

prune527.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.8b

bsearch238.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	0.03210649578243009
9	-0.030639508246526274	-1.9696345359431407e-07	-0.025621427997812182

simplify9.0ms

Iterations

Iter	Nodes
2	27
1	27
0	21

end0.0ms

sample16.7s

Algorithm

intervals

Results

7.2s	1537×	body	2560	valid
5.8s	2771×	body	1280	valid
2.4s	1907×	body	640	valid
795.0ms	955×	body	320	valid
210.0ms	447×	body	160	valid
138.0ms	383×	body	80	valid