Details

sample315.0ms

Algorithm

intervals

Results

178.0ms	104×	body	1280	valid
54.0ms	19×	body	2560	valid
42.0ms	54×	body	640	valid
14.0ms	26×	body	320	valid
8.0ms	44×	body	80	valid
3.0ms	9×	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: 34.7b

localize12.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (tan (+ x eps)) (tan x))
3.4b	(tan (+ x eps))

rewrite28.0ms

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:

17.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series259.0ms

Counts

2 → 6

Calls

2 calls:

136.0ms	(- (tan (+ x eps)) (tan x))
122.0ms	(tan (+ x eps))

simplify2.7s

Counts

31 → 31

Iterations

Useful iterations: 4 (486.0ms)

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

prune123.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite206.0ms

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:

18.0ms	(+ (tan x) (tan eps))
47.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
16.0ms	(* (tan x) (tan eps))
120.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

136.0ms	(+ (tan x) (tan eps))
313.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
142.0ms	(* (tan x) (tan eps))
576.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.5s

Counts

98 → 98

Iterations

Useful iterations: 3 (993.0ms)

Iter	Nodes	Cost
0	172	1724
1	397	1649
2	1091	1579
3	2924	1563
done	5001	1563

prune419.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

localize36.0ms

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))
7.1b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite212.0ms

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:

63.0ms	(* (+ (tan x) (tan eps)) (cos x))
30.0ms	(* (tan x) (tan eps))
31.0ms	(* (tan x) (tan eps))
82.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series831.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (+ (tan x) (tan eps)) (cos x))
142.0ms	(* (tan x) (tan eps))
150.0ms	(* (tan x) (tan eps))
348.0ms	(- (* (+ (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

prune641.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

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:

41.0ms	(* (pow (sin x) 2) (sin eps))
7.0ms	(pow (sin x) 2)
33.0ms	(* (tan x) (tan eps))
41.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (pow (sin x) 2) (sin eps))
28.0ms	(pow (sin x) 2)
169.0ms	(* (tan x) (tan eps))
123.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))

simplify1.2s

Counts

104 → 104

Iterations

Useful iterations: 2 (335.0ms)

Iter	Nodes	Cost
0	175	1232
1	427	1143
2	1632	961
done	5002	961

prune497.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes228.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	33
1	28	33
done	28	33

end0.0ms

sample10.0s

Algorithm

intervals

Results

4.7s	3378×	body	1280	valid
1.9s	1844×	body	640	valid
1.7s	611×	body	2560	valid
1.1s	713×	body	320	valid
147.0ms	1105×	body	80	valid
103.0ms	349×	body	160	valid