Details

sample384.0ms

Algorithm

intervals

Results

213.0ms	102×	body	1280	valid
60.0ms	19×	body	2560	valid
57.0ms	51×	body	640	valid
23.0ms	27×	body	320	valid
12.0ms	48×	body	80	valid
4.0ms	9×	body	160	valid

simplify42.0ms

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: 34.1b

localize28.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
2.9b	(tan (+ x eps))

rewrite29.0ms

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:

19.0ms	(- (tan (+ x eps)) (tan x))
9.0ms	(tan (+ x eps))

series199.0ms

Counts

2 → 6

Calls

2 calls:

131.0ms	(- (tan (+ x eps)) (tan x))
69.0ms	(tan (+ x eps))

simplify1.3s

Counts

33 → 33

Iterations

Iter	Nodes
done	2017
5	2017
4	1821
3	719
2	300
1	139
0	70

prune221.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.6b

localize43.0ms

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))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite171.0ms

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:

49.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
99.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

295.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
128.0ms	(+ (tan x) (tan eps))
124.0ms	(* (tan x) (tan eps))
506.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
3	2000
2	1148
1	405
0	174

prune562.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.5b

localize40.0ms

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)))
2.4b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite169.0ms

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:

27.0ms	(* (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
95.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
17.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.7s

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (tan x) (tan eps))
143.0ms	(* (tan x) (tan eps))
169.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.2s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	2006
2	2006
1	664
0	205

prune768.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.5b

localize80.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
27.5b	(cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))
27.5b	(cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))
27.5b	(cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

101×	`tan-quot`
53×	`frac-times`
45×	`cbrt-div`
35×	`associate-*r/`
34×	`associate-*l/`
6×	`add-log-exp`
5×	`frac-sub`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`cbrt-prod` `pow1/3`
2×	`flip3-+` `associate--l+` `flip-+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--`

Counts

4 → 95

Calls

4 calls:

33.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
83.0ms	(cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))
78.0ms	(cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))
50.0ms	(cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))

series1.9s

Counts

4 → 12

Calls

4 calls:

1.2s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
236.0ms	(cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))
248.0ms	(cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))
245.0ms	(cbrt (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
done	2001
2	2001
1	523
0	190

prune814.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.5b

regimes277.0ms

Accuracy

90.3% (0.7b remaining)

Error of 15.5b against oracle of 14.8b and baseline of 22.3b

bsearch335.0ms

Steps

Iters	Range		Point
10	1.2035886760163307e-31	1.514112904485791e-15	6.057698547984444e-19
9	-6.13921394360303e-24	-4.043160302816128e-29	-1.3912258087269967e-24

simplify24.0ms

Iterations

Iter	Nodes
done	53
1	53
0	39

end0.0ms

sample13.3s

Algorithm

intervals

Results

7.0s	3297×	body	1280	valid
2.8s	641×	body	2560	valid
2.2s	1868×	body	640	valid
551.0ms	744×	body	320	valid
289.0ms	1111×	body	80	valid
176.0ms	339×	body	160	valid