Details

sample253.0ms

Algorithm

intervals

Results

140.0ms	109×	body	1280	valid
44.0ms	63×	body	640	valid
35.0ms	14×	body	2560	valid
11.0ms	23×	body	320	valid
5.0ms	37×	body	80	valid
3.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune68.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize22.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ eps x)) (tan x))
3.1b	(tan (+ eps x))

rewrite29.0ms

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:

19.0ms	(- (tan (+ eps x)) (tan x))
10.0ms	(tan (+ eps x))

series614.0ms

Counts

2 → 6

Calls

2 calls:

166.0ms	(- (tan (+ eps x)) (tan x))
449.0ms	(tan (+ eps x))

simplify5.0s

Counts

31 → 31

Iterations

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

prune205.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.2b

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))
4.1b	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite133.0ms

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:

23.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan eps) (tan x))
15.0ms	(* (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:

357.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
127.0ms	(+ (tan eps) (tan x))
142.0ms	(* (tan x) (tan eps))
523.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify986.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1612
1	407
0	169

prune617.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
4.5b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

rewrite213.0ms

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:

13.0ms	(/ (sin eps) (cos eps))
30.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
29.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
131.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

series641.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (sin eps) (cos eps))
137.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
157.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
312.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

simplify1.7s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	2975
1	570
0	209

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
0.3b	(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
0.3b	(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
4.4b	(- (/ (sin x) 1) (* (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))) (sin x)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
66×	`times-frac`
46×	`*-un-lft-identity` `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`
5×	`associate-*l/`
3×	`frac-times` `pow-prod-down` `associate-r/` `-commutative`
2×	`flip3--` `frac-sub` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 164

Calls

4 calls:

41.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
22.0ms	(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
23.0ms	(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
46.0ms	(- (/ (sin x) 1) (* (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))) (sin x)))

series584.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
124.0ms	(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
145.0ms	(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
175.0ms	(- (/ (sin x) 1) (* (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))) (sin x)))

simplify494.0ms

Counts

176 → 176

Iterations

Iter	Nodes
done	5000
1	868
0	262

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes203.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample11.7s

Algorithm

intervals

Results

6.0s	3268×	body	1280	valid
2.2s	1860×	body	640	valid
2.0s	652×	body	2560	valid
558.0ms	765×	body	320	valid
224.0ms	1081×	body	80	valid
181.0ms	374×	body	160	valid