Details

sample316.0ms

Algorithm

intervals

Results

170.0ms	110×	body	1280	valid
64.0ms	22×	body	2560	valid
38.0ms	50×	body	640	valid
17.0ms	30×	body	320	valid
6.0ms	16×	body	160	valid
4.0ms	28×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize25.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite20.0ms

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`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

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

series232.0ms

Counts

2 → 6

Calls

2 calls:

114.0ms	(- (tan (+ x eps)) (tan x))
117.0ms	(tan (+ x eps))

simplify909.0ms

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
3	1176
2	355
1	137
0	68

prune189.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.6b

localize37.0ms

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))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite128.0ms

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×	`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 → 86

Calls

4 calls:

30.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
6.0ms	(+ (tan x) (tan eps))
12.0ms	(* (tan x) (tan eps))
77.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

344.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
138.0ms	(+ (tan x) (tan eps))
147.0ms	(* (tan x) (tan eps))
524.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1663
1	411
0	170

prune688.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.3b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite155.0ms

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`
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 → 110

Calls

4 calls:

14.0ms	(* (tan x) (tan eps))
13.0ms	(* (tan x) (tan eps))
88.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
34.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.8s

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (tan x) (tan eps))
152.0ms	(* (tan x) (tan eps))
148.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.4s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify3.3s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	4708
1	658
0	201

prune647.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.5b

localize117.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.3b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (cbrt (* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
13.9b	(cbrt (* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))

rewrite3.7s

Algorithm

rewrite-expression-head

Rules

24645×	`tan-quot`
20517×	`frac-times`
9686×	`associate-*l/`
8151×	`associate-*r/`
4095×	`cbrt-div`
82×	`pow1`
35×	`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`
2×	`pow2` `flip3-+` `swap-sqr` `associate-r` `associate-l` `pow3` `associate--l+` `*-commutative` `flip-+`
1×	`cbrt-prod` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `pow1/3` `diff-log` `rem-cbrt-cube` `flip--`

Counts

4 → 4222

Calls

4 calls:

85.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
80.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
22.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (cbrt (* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.7s	(cbrt (* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
202.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.4s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (cbrt (* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
184.0ms	(cbrt (* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))

simplify9.2s

Counts

4234 → 4234

Iterations

Iter	Nodes
done	10881
0	10881

prune36.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.5b

regimes180.0ms

Accuracy

87.1% (1.0b remaining)

Error of 15.5b against oracle of 14.6b and baseline of 22.0b

bsearch166.0ms

Steps

Iters	Range		Point
6	3.588278197868876e-48	3.5838321097583617e-47	1.0662756818064793e-47
10	-1212215.9807367995	-5.980124527132304e-10	-6.095793693328762e-10

simplify8.0ms

Iterations

Iter	Nodes
done	51
1	51
0	35

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.3s	3309×	body	1280	valid
1.5s	1843×	body	640	valid
1.5s	655×	body	2560	valid
329.0ms	775×	body	320	valid
135.0ms	1098×	body	80	valid
65.0ms	320×	body	160	valid