Details

sample698.0ms

Algorithm

intervals

Results

229.0ms	55×	body	2560	valid
107.0ms	86×	body	1280	valid
44.0ms	57×	body	640	valid
19.0ms	36×	body	320	valid
6.0ms	14×	body	160	valid
2.0ms	8×	body	80	valid

simplify61.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (tan x))
1.1b	(- 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×	`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:

21.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series209.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(/ (- x (sin x)) (- x (tan x)))
65.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify573.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	2010
2	964
1	375
0	160

prune411.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) 9/40)
0.3b	(* (* (* x x) (* x x)) 27/2800)
16.1b	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

138×	`pow1`
39×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
36×	`pow-prod-up`
24×	`prod-exp` `cbrt-unprod`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
9×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16`
3×	`diff-log` `associate-l` `*-commutative` `unswap-sqr`
2×	`sub-neg` `associate--l+`
1×	`associate--l-` `flip3--` `swap-sqr` `flip--`

Counts

4 → 130

Calls

4 calls:

46.0ms	(* (* x x) (* x x))
32.0ms	(* (* x x) 9/40)
140.0ms	(* (* (* x x) (* x x)) 27/2800)
214.0ms	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

series184.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* x x) (* x x))
29.0ms	(* (* x x) 9/40)
49.0ms	(* (* (* x x) (* x x)) 27/2800)
69.0ms	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

simplify856.0ms

Counts

142 → 142

Iterations

Iter	Nodes
done	2005
2	1196
1	405
0	135

prune262.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(- x (tan x))
1.1b	(- x (sin x))
1.1b	(- x (sin x))
1.1b	(- x (sin x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

5.0ms	(- x (tan x))
6.0ms	(- x (sin x))
6.0ms	(- x (sin x))
6.0ms	(- x (sin x))

series230.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- x (tan x))
61.0ms	(- x (sin x))
38.0ms	(- x (sin x))
48.0ms	(- x (sin x))

simplify958.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	2000
4	1619
3	720
2	357
1	155
0	78

prune356.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x (tan x)))
0.1b	(* (- x (sin x)) (/ 1 (- x (tan x))))
1.1b	(- x (tan x))
1.1b	(- x (sin x))

rewrite62.0ms

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-/r` `associate-l*`
4×	`div-exp` `prod-exp` `associate-/r/` `insert-posit16`
3×	`associate-/l*` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `diff-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 123

Calls

4 calls:

10.0ms	(/ 1 (- x (tan x)))
39.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
5.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1 (- x (tan x)))
112.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
75.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify912.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	2004
2	1415
1	487
0	209

prune541.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.5b

bsearch209.0ms

Steps

Iters	Range		Point
11	0.0038666078177206752	9.350013159855062e+31	2.412135160853593
10	-121993772661.31783	-0.0015977726548224043	-4.773716110019835

simplify20.0ms

Iterations

Iter	Nodes
done	41
1	41
0	30

end0.0ms

sample16.2s

Algorithm

intervals

Results

7.0s	1651×	body	2560	valid
5.9s	2716×	body	1280	valid
2.0s	1864×	body	640	valid
819.0ms	986×	body	320	valid
253.0ms	442×	body	160	valid
105.0ms	341×	body	80	valid