Details

sample300.0ms

Algorithm

intervals

Results

138.0ms	106×	body	1280	valid
76.0ms	58×	body	640	valid
43.0ms	16×	body	2560	valid
14.0ms	25×	body	320	valid
6.0ms	36×	body	80	valid
5.0ms	15×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize19.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite85.0ms

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:

71.0ms	(- (tan (+ x eps)) (tan x))
13.0ms	(tan (+ x eps))

series214.0ms

Counts

2 → 6

Calls

2 calls:

155.0ms	(- (tan (+ x eps)) (tan x))
58.0ms	(tan (+ x eps))

simplify2.3s

Counts

31 → 31

Iterations

Useful iterations: 4 (410.0ms)

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

prune138.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.2b

localize25.0ms

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))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite167.0ms

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:

30.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
11.0ms	(+ (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
104.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

376.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
136.0ms	(+ (tan x) (tan eps))
122.0ms	(* (tan x) (tan eps))
448.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.3s

Counts

98 → 98

Iterations

Useful iterations: 3 (935.0ms)

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

prune430.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.1b

localize22.0ms

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))
8.8b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite110.0ms

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:

33.0ms	(* (+ (tan x) (tan eps)) (cos x))
16.0ms	(* (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
41.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (+ (tan x) (tan eps)) (cos x))
146.0ms	(* (tan x) (tan eps))
125.0ms	(* (tan x) (tan eps))
283.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify1.3s

Counts

94 → 94

Iterations

Useful iterations: done (1.3s)

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

prune637.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
0.2b	(* (tan x) (tan eps))
0.2b	(* (pow (sin x) 2) (sin eps))
0.3b	(pow (sin x) 2)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`prod-exp`
11×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`div-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-r` `cbrt-unprod`
5×	`unswap-sqr`
4×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp` `add-log-exp`
3×	`pow-unpow` `unpow2` `sqr-pow`
2×	`*-commutative`
1×	`frac-times` `pow-pow` `frac-2neg` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `div-inv` `associate-/l`

Counts

4 → 92

Calls

4 calls:

40.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
16.0ms	(* (tan x) (tan eps))
24.0ms	(* (pow (sin x) 2) (sin eps))
8.0ms	(pow (sin x) 2)

series493.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
182.0ms	(* (tan x) (tan eps))
97.0ms	(* (pow (sin x) 2) (sin eps))
37.0ms	(pow (sin x) 2)

simplify1.8s

Counts

104 → 104

Iterations

Useful iterations: 2 (443.0ms)

Iter	Nodes	Cost
0	175	1232
1	427	1143
2	1638	961
done	5000	961

prune580.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes229.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: done (6.0ms)

Iter	Nodes	Cost
0	23	38
1	32	36
done	32	34

end0.0ms

sample10.6s

Algorithm

intervals

Results

5.7s	3225×	body	1280	valid
2.1s	633×	body	2560	valid
1.7s	1918×	body	640	valid
378.0ms	737×	body	320	valid
226.0ms	1136×	body	80	valid
110.0ms	351×	body	160	valid