Details

sample308.0ms

Algorithm

intervals

Results

152.0ms	101×	body	1280	valid
73.0ms	29×	body	2560	valid
44.0ms	61×	body	640	valid
12.0ms	24×	body	320	valid
5.0ms	33×	body	80	valid
3.0ms	8×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize78.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (tan (+ eps x)) (tan x))
2.3b	(tan (+ eps x))

rewrite37.0ms

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:

26.0ms	(- (tan (+ eps x)) (tan x))
10.0ms	(tan (+ eps x))

series284.0ms

Counts

2 → 6

Calls

2 calls:

180.0ms	(- (tan (+ eps x)) (tan x))
104.0ms	(tan (+ eps x))

simplify4.7s

Counts

31 → 31

Iterations

Iter	Nodes
done	5001
4	4214
3	960
2	312
1	129
0	68

prune173.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan eps) (tan x))
0.2b	(* (tan x) (tan eps))
2.2b	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite141.0ms

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:

29.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
12.0ms	(+ (tan eps) (tan x))
13.0ms	(* (tan x) (tan eps))
84.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
125.0ms	(+ (tan eps) (tan x))
119.0ms	(* (tan x) (tan eps))
597.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify838.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1612
1	407
0	169

prune588.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.6b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
3.5b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
64×	`times-frac`
46×	`*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`add-cbrt-cube` `add-exp-log`
26×	`associate-r` `associate-l`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp` `difference-of-squares`
5×	`div-inv`
3×	`associate-/r` `associate-/l`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `distribute-lft-out--`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 149

Calls

4 calls:

7.0ms	(/ (sin x) (cos x))
39.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
39.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
111.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin x) (cos x))
181.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
137.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
788.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

simplify1.4s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	2599
1	547
0	206

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
3.6b	(- (sin x) (* (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (sin x)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
66×	`times-frac`
47×	`*-un-lft-identity`
46×	`add-cube-cbrt`
40×	`add-cbrt-cube` `add-exp-log`
39×	`associate-r` `associate-l`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
10×	`pow1`
6×	`div-inv` `add-log-exp`
3×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `flip--`

Counts

4 → 163

Calls

4 calls:

46.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
30.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
36.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
7.0ms	(- (sin x) (* (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (sin x)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
122.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
113.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
168.0ms	(- (sin x) (* (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (sin x)))

simplify1.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	2579
1	477
0	164

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes252.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	34
1	34
0	24

end0.0ms

sample10.8s

Algorithm

intervals

Results

5.0s	3232×	body	1280	valid
2.1s	633×	body	2560	valid
2.0s	1874×	body	640	valid
843.0ms	759×	body	320	valid
353.0ms	1135×	body	80	valid
148.0ms	367×	body	160	valid