Details

sample237.0ms

Algorithm

intervals

Results

109.0ms	90×	body	1280	valid
53.0ms	23×	body	2560	valid
33.0ms	52×	body	640	valid
17.0ms	42×	body	320	valid
5.0ms	16×	body	160	valid
5.0ms	33×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune57.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize32.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite38.0ms

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 (+ x eps)) (tan x))
11.0ms	(tan (+ x eps))

series221.0ms

Counts

2 → 6

Calls

2 calls:

116.0ms	(- (tan (+ x eps)) (tan x))
105.0ms	(tan (+ x eps))

simplify1.6s

Counts

31 → 31

Iterations

Iter	Nodes
done	5001
4	1748
3	709
2	298
1	137
0	68

prune189.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.9b

localize35.0ms

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))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite156.0ms

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:

46.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
12.0ms	(+ (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
71.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

351.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
138.0ms	(+ (tan x) (tan eps))
124.0ms	(* (tan x) (tan eps))
524.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.8s

Counts

98 → 98

Iterations

Iter	Nodes
done	5045
3	4214
2	1148
1	401
0	170

prune537.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.8b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.3b	(* (sin x) (/ (sin eps) (cos eps)))
0.3b	(* (sin x) (/ (sin eps) (cos eps)))
2.1b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
42×	`times-frac`
39×	`*-un-lft-identity`
28×	`add-cube-cbrt`
26×	`associate-r`
16×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-l` `add-log-exp` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
3×	`cbrt-undiv` `associate-/r` `div-exp` `div-inv` `associate-/l`
2×	`pow-prod-down` `associate-r/` `-commutative`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 114

Calls

4 calls:

12.0ms	(/ (sin eps) (cos eps))
29.0ms	(* (sin x) (/ (sin eps) (cos eps)))
17.0ms	(* (sin x) (/ (sin eps) (cos eps)))
221.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (sin eps) (cos eps))
107.0ms	(* (sin x) (/ (sin eps) (cos eps)))
102.0ms	(* (sin x) (/ (sin eps) (cos eps)))
347.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify2.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
3	4717
2	1352
1	419
0	174

prune936.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.8b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(/ (sin eps) (cos eps))
0.3b	(* (sin x) (/ (sin eps) (cos eps)))
2.1b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (/ (* (sin x) (sin eps)) (cos eps)) (cos x)))) (/ (sin x) (cos x)))

rewrite463.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
41×	`times-frac`
39×	`*-un-lft-identity`
28×	`add-cube-cbrt`
13×	`add-cbrt-cube` `associate-r` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp` `difference-of-squares`
4×	`distribute-lft-out--`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`quot-tan` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `frac-sub` `flip--`

Counts

4 → 110

Calls

4 calls:

9.0ms	(/ (sin eps) (cos eps))
7.0ms	(/ (sin eps) (cos eps))
21.0ms	(* (sin x) (/ (sin eps) (cos eps)))
420.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (/ (* (sin x) (sin eps)) (cos eps)) (cos x)))) (/ (sin x) (cos x)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin eps) (cos eps))
35.0ms	(/ (sin eps) (cos eps))
108.0ms	(* (sin x) (/ (sin eps) (cos eps)))
356.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (/ (* (sin x) (sin eps)) (cos eps)) (cos x)))) (/ (sin x) (cos x)))

simplify3.0s

Counts

122 → 122

Iterations

Iter	Nodes
done	5002
3	4664
2	1413
1	418
0	174

prune932.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.8b

regimes635.0ms

Accuracy

0% (0.2b remaining)

Error of 12.7b against oracle of 12.5b and baseline of 12.7b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample10.5s

Algorithm

intervals

Results

5.5s	3293×	body	1280	valid
2.1s	1807×	body	640	valid
1.7s	645×	body	2560	valid
542.0ms	816×	body	320	valid
188.0ms	341×	body	160	valid
155.0ms	1098×	body	80	valid