Details

sample593.0ms

Algorithm

intervals

Results

215.0ms	47×	body	2560	valid
137.0ms	90×	body	1280	valid
90.0ms	56×	body	640	valid
19.0ms	33×	body	320	valid
7.0ms	18×	body	160	valid
3.0ms	12×	body	80	valid

simplify16.0ms

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: 30.5b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.3b	(- x (sin x))

rewrite102.0ms

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:

68.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
17.0ms	(- x (sin x))

series206.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (- x (sin x)) (- x (tan x)))
64.0ms	(- x (tan x))
47.0ms	(- x (sin x))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5017
3	3306
2	964
1	375
0	160

prune307.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.2b	(- x (tan x))
1.2b	(- x (tan x))

rewrite116.0ms

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:

15.0ms	(/ (sin x) (- x (tan x)))
87.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series505.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (sin x) (- x (tan x)))
290.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
58.0ms	(- x (tan x))
69.0ms	(- x (tan x))

simplify2.6s

Counts

110 → 110

Iterations

Iter	Nodes
done	5183
3	4000
2	1111
1	392
0	180

prune459.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.2b	(- x (tan x))
1.2b	(- x (tan x))

rewrite132.0ms

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:

16.0ms	(/ (sin x) (- x (tan x)))
100.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
7.0ms	(- x (tan x))
7.0ms	(- x (tan x))

series544.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (sin x) (- x (tan x)))
273.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
73.0ms	(- x (tan x))
81.0ms	(- x (tan x))

simplify2.4s

Counts

110 → 110

Iterations

Iter	Nodes
done	5183
3	4000
2	1111
1	392
0	180

prune577.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x 9/40) x)
0.1b	(* x 9/40)
0.2b	(* 27/2800 (* x x))
15.3b	(- (* (* x 9/40) x) (+ 1/2 (* (* 27/2800 (* x x)) (* x x))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16`
3×	`*-commutative`
2×	`diff-log` `unswap-sqr`
1×	`sum-log` `sub-neg` `flip3--` `flip--` `associate--r+`

Counts

4 → 73

Calls

4 calls:

18.0ms	(* (* x 9/40) x)
10.0ms	(* x 9/40)
27.0ms	(* 27/2800 (* x x))
39.0ms	(- (* (* x 9/40) x) (+ 1/2 (* (* 27/2800 (* x x)) (* x x))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* x 9/40) x)
28.0ms	(* x 9/40)
57.0ms	(* 27/2800 (* x x))
74.0ms	(- (* (* x 9/40) x) (+ 1/2 (* (* 27/2800 (* x x)) (* x x))))

simplify1.6s

Counts

85 → 85

Iterations

Iter	Nodes
done	5002
2	1306
1	331
0	116

prune296.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes56.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch137.0ms

Steps

Iters	Range		Point
9	1.7877411926250683e-07	0.113095154289168	0.032993602201721775
7	-1.1375194732999505	-0.018988436667384805	-0.030916815840808982

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample14.5s

Algorithm

intervals

Results

7.3s	1631×	body	2560	valid
3.9s	2720×	body	1280	valid
1.7s	1836×	body	640	valid
1.1s	953×	body	320	valid
176.0ms	515×	body	160	valid
111.0ms	345×	body	80	valid