Details

sample294.0ms

Algorithm

intervals

Results

131.0ms	98×	body	1280	valid
66.0ms	24×	body	2560	valid
57.0ms	56×	body	640	valid
13.0ms	22×	body	320	valid
8.0ms	44×	body	80	valid
4.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune47.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize17.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.9b	(tan (+ x eps))

rewrite28.0ms

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:

21.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series240.0ms

Counts

2 → 6

Calls

2 calls:

145.0ms	(- (tan (+ x eps)) (tan x))
95.0ms	(tan (+ x eps))

simplify1.5s

Counts

33 → 33

Iterations

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

prune205.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.6b

localize26.0ms

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))
2.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite153.0ms

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:

29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(+ (tan x) (tan eps))
27.0ms	(* (tan x) (tan eps))
81.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

284.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
145.0ms	(+ (tan x) (tan eps))
122.0ms	(* (tan x) (tan eps))
468.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.7s

Counts

102 → 102

Iterations

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

prune565.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.9b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

30.0ms	(* (tan x) (tan eps))
26.0ms	(* (tan x) (tan eps))
87.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
66.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.7s

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (tan x) (tan eps))
117.0ms	(* (tan x) (tan eps))
151.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.3s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify2.0s

Counts

126 → 126

Iterations

Iter	Nodes
done	5005
2	2572
1	655
0	204

prune677.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.9b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))
30.4b	(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

rewrite501.0ms

Algorithm

rewrite-expression-head

Rules

261×	`tan-quot`
165×	`frac-times`
98×	`associate-*l/`
87×	`associate-*r/`
82×	`pow1`
63×	`cbrt-div`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-log-exp`
5×	`frac-sub`
4×	`add-sqr-sqrt` `*-un-lft-identity` `pow-plus` `add-cube-cbrt` `insert-posit16`
2×	`pow2` `flip3-+` `swap-sqr` `associate-r` `associate-l` `associate--l+` `*-commutative` `flip-+`
1×	`cbrt-prod` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `pow1/3` `diff-log` `pow3` `rem-cbrt-cube` `flip--`

Counts

4 → 194

Calls

4 calls:

113.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
110.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
43.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))
224.0ms	(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

series1.7s

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
185.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.3s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))
142.0ms	(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

simplify2.6s

Counts

206 → 206

Iterations

Iter	Nodes
done	5000
2	3459
1	958
0	384

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.4b

regimes361.0ms

Accuracy

87.7% (0.9b remaining)

Error of 15.5b against oracle of 14.6b and baseline of 21.8b

bsearch371.0ms

Steps

Iters	Range		Point
10	3.302217848673879e-63	5.871316347800174e-52	5.810306508670788e-52
9	-5.469986621237647e-61	-8.278077243234882e-66	-2.1089423986131282e-63

simplify17.0ms

Iterations

Iter	Nodes
done	49
1	49
0	35

end0.0ms

sample10.8s

Algorithm

intervals

Results

5.7s	3269×	body	1280	valid
2.3s	1897×	body	640	valid
1.7s	649×	body	2560	valid
459.0ms	761×	body	320	valid
241.0ms	1083×	body	80	valid
169.0ms	341×	body	160	valid