Details

sample357.0ms

Algorithm

intervals

Results

205.0ms	105×	body	1280	valid
52.0ms	59×	body	640	valid
50.0ms	17×	body	2560	valid
13.0ms	24×	body	320	valid
8.0ms	42×	body	80	valid
3.0ms	9×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize25.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite22.0ms

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))
8.0ms	(tan (+ x eps))

series222.0ms

Counts

2 → 6

Calls

2 calls:

131.0ms	(- (tan (+ x eps)) (tan x))
90.0ms	(tan (+ x eps))

simplify907.0ms

Counts

31 → 31

Iterations

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

prune217.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.2b

localize45.0ms

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))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite149.0ms

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:

31.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
13.0ms	(+ (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
80.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

338.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
177.0ms	(+ (tan x) (tan eps))
152.0ms	(* (tan x) (tan eps))
528.0ms	(- (/ (+ (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

prune747.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
7.0b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

24.0ms	(* (+ (tan x) (tan eps)) (cos x))
11.0ms	(* (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
51.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series827.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (+ (tan x) (tan eps)) (cos x))
144.0ms	(* (tan x) (tan eps))
150.0ms	(* (tan x) (tan eps))
355.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify2.3s

Counts

94 → 94

Iterations

Iter	Nodes
done	5004
2	3063
1	555
0	171

prune728.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(/ (* (sin x) (sin x)) (/ (cos x) (/ (sin eps) (cos eps))))
0.3b	(* (sin x) (sin x))
0.3b	(/ (cos x) (/ (sin eps) (cos eps)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

251×	`times-frac`
126×	`add-sqr-sqrt`
122×	`*-un-lft-identity` `add-cube-cbrt`
57×	`associate-/r*`
34×	`add-cbrt-cube` `add-exp-log`
15×	`cbrt-undiv` `div-exp`
14×	`div-inv`
13×	`pow1`
6×	`associate-r` `associate-l`
5×	`prod-exp` `cbrt-unprod`
4×	`tan-quot` `associate-/r/` `associate-/l*` `add-log-exp`
3×	`swap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative` `sqr-sin` `sin-mult` `unswap-sqr`
1×	`pow2` `frac-times` `pow-plus` `div-sub` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up` `associate-/l/`

Counts

4 → 232

Calls

4 calls:

12.0ms	(* (tan x) (tan eps))
39.0ms	(/ (* (sin x) (sin x)) (/ (cos x) (/ (sin eps) (cos eps))))
18.0ms	(* (sin x) (sin x))
17.0ms	(/ (cos x) (/ (sin eps) (cos eps)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (tan x) (tan eps))
152.0ms	(/ (* (sin x) (sin x)) (/ (cos x) (/ (sin eps) (cos eps))))
27.0ms	(* (sin x) (sin x))
115.0ms	(/ (cos x) (/ (sin eps) (cos eps)))

simplify1.4s

Counts

244 → 244

Iterations

Iter	Nodes
done	5000
1	1206
0	412

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes303.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample11.4s

Algorithm

intervals

Results

6.1s	3251×	body	1280	valid
1.9s	1865×	body	640	valid
1.8s	650×	body	2560	valid
627.0ms	1137×	body	80	valid
589.0ms	772×	body	320	valid
119.0ms	325×	body	160	valid