Details

sample269.0ms

Algorithm

intervals

Results

146.0ms	113×	body	1280	valid
51.0ms	18×	body	2560	valid
40.0ms	60×	body	640	valid
10.0ms	23×	body	320	valid
4.0ms	32×	body	80	valid
3.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize18.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

35.0ms	(- (tan (+ x eps)) (tan x))
14.0ms	(tan (+ x eps))

series227.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(- (tan (+ x eps)) (tan x))
102.0ms	(tan (+ x eps))

simplify2.6s

Counts

31 → 31

Iterations

Useful iterations: 4 (375.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	278	341
3	528	337
4	1109	335
5	2471	335
done	5000	335

prune135.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.5b

localize22.0ms

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))
0.3b	(* (tan x) (tan eps))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite179.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

28.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
124.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

310.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
145.0ms	(+ (tan x) (tan eps))
103.0ms	(* (tan x) (tan eps))
536.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.7s

Counts

98 → 98

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	172	1724
1	397	1649
2	1095	1579
3	2939	1563
done	5000	1563

prune437.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b	(* (tan x) (tan eps))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
5.3b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
104×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
23×	`associate-/r*`
19×	`add-exp-log`
16×	`associate-/r/` `distribute-lft-out`
15×	`tan-quot`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1` `div-inv`
6×	`associate-/l*` `add-log-exp`
5×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `associate-/l/` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `pow-flip` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 178

Calls

4 calls:

32.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
16.0ms	(* (tan x) (tan eps))
36.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
167.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series1.4s

Counts

4 → 12

Calls

4 calls:

338.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
168.0ms	(* (tan x) (tan eps))
363.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
493.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify1.6s

Counts

190 → 190

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	298	4576
1	689	4210
2	1843	3880
done	5000	3829

prune520.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
8.2b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
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:

46.0ms	(* (+ (tan x) (tan eps)) (cos x))
17.0ms	(* (tan x) (tan eps))
30.0ms	(* (tan x) (tan eps))
39.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series844.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (+ (tan x) (tan eps)) (cos x))
148.0ms	(* (tan x) (tan eps))
151.0ms	(* (tan x) (tan eps))
345.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify1.4s

Counts

94 → 94

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	173	1626
1	515	1476
2	1917	1418
done	5001	1416

prune523.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes101.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	33
1	29	33
done	29	33

end0.0ms

sample7.5s

Algorithm

intervals

Results

3.5s	3329×	body	1280	valid
1.6s	673×	body	2560	valid
1.1s	1885×	body	640	valid
678.0ms	711×	body	320	valid
132.0ms	1071×	body	80	valid
86.0ms	331×	body	160	valid