Details

sample213.0ms

Algorithm

intervals

Results

109.0ms	106×	body	1280	valid
45.0ms	21×	body	2560	valid
32.0ms	56×	body	640	valid
8.0ms	21×	body	320	valid
4.0ms	37×	body	80	valid
4.0ms	15×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize54.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (tan (+ x eps)) (tan x))
2.5b	(tan (+ x eps))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

13.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series179.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(- (tan (+ x eps)) (tan x))
62.0ms	(tan (+ x eps))

simplify1.8s

Counts

33 → 33

Iterations

Iter	Nodes
done	5001
4	1821
3	719
2	300
1	139
0	70

prune177.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`insert-posit16` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `flip3--` `frac-add` `associate-/r/` `flip-+` `flip--` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

39.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(+ (tan x) (tan eps))
27.0ms	(* (tan x) (tan eps))
83.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

293.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
134.0ms	(+ (tan x) (tan eps))
140.0ms	(* (tan x) (tan eps))
527.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5008
3	4112
2	1148
1	405
0	174

prune615.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.5b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan eps) (tan x))
0.3b	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.0b	(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

84×	`pow1`
73×	`tan-quot`
37×	`frac-times`
35×	`pow-prod-down`
30×	`add-cbrt-cube` `add-exp-log`
25×	`associate-*r/`
24×	`associate-*l/`
17×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `pow-sqr` `pow-prod-up`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`associate-r` `associate-l` `frac-sub`
4×	`pow-plus` `insert-posit16`
3×	`*-commutative`
2×	`pow2` `flip3-+` `swap-sqr` `associate--l+` `flip-+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

14.0ms	(* (tan eps) (tan x))
65.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
114.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
97.0ms	(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series2.4s

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (tan eps) (tan x))
156.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
127.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.0s	(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify2.4s

Counts

154 → 154

Iterations

Iter	Nodes
done	5009
2	3794
1	889
0	273

prune838.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.3b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan eps) (tan x))
0.2b	(* (tan x) (* (tan eps) (tan x)))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.0b	(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (* (tan x) (* (tan eps) (tan x)))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

53×	`tan-quot`
50×	`pow1`
25×	`frac-times`
23×	`add-cbrt-cube` `add-exp-log`
21×	`pow-prod-down`
19×	`associate-*r/`
16×	`associate-*l/`
12×	`prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-r` `frac-sub`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `swap-sqr` `flip--` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

15.0ms	(* (tan eps) (tan x))
52.0ms	(* (tan x) (* (tan eps) (tan x)))
87.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
79.0ms	(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (* (tan x) (* (tan eps) (tan x)))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series2.1s

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (tan eps) (tan x))
110.0ms	(* (tan x) (* (tan eps) (tan x)))
111.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.7s	(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (* (tan x) (* (tan eps) (tan x)))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify2.6s

Counts

130 → 130

Iterations

Iter	Nodes
done	5013
2	3726
1	858
0	269

prune699.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.3b

regimes385.0ms

Accuracy

93.8% (0.5b remaining)

Error of 13.8b against oracle of 13.2b and baseline of 21.8b

bsearch276.0ms

Steps

Iters	Range		Point
8	6.608106750126326e-54	3.070722928872959e-51	2.106612565673929e-51
9	-1.9094137902975774e-15	-1.0692349298420692e-20	-5.135442363002646e-18

simplify23.0ms

Iterations

Iter	Nodes
done	55
1	55
0	38

end0.0ms

sample8.8s

Algorithm

intervals

Results

4.5s	3287×	body	1280	valid
2.0s	1828×	body	640	valid
1.4s	629×	body	2560	valid
331.0ms	758×	body	320	valid
246.0ms	1138×	body	80	valid
96.0ms	360×	body	160	valid