Details

sample442.0ms

Algorithm

intervals

Results

224.0ms	106×	body	1280	valid
114.0ms	34×	body	2560	valid
55.0ms	47×	body	640	valid
26.0ms	32×	body	320	valid
6.0ms	25×	body	80	valid
6.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize53.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
3.5b	(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` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 27

Calls

2 calls:

27.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series622.0ms

Counts

2 → 6

Calls

2 calls:

135.0ms	(- (tan (+ x eps)) (tan x))
487.0ms	(tan (+ x eps))

simplify3.7s

Counts

33 → 33

Iterations

Iter	Nodes
5	3750
4	1478
3	672
2	285
1	137
0	70

prune347.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.4b

localize47.0ms

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

rewrite116.0ms

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×	`insert-posit16` `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 → 90

Calls

4 calls:

24.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(+ (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
58.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

293.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
105.0ms	(+ (tan x) (tan eps))
115.0ms	(* (tan x) (tan eps))
517.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
3	3734
2	1101
1	402
0	174

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (/ (sin eps) (cos x)) (sin x))
0.2b	(* (/ (sin eps) (cos x)) (sin x))
3.4b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (- (/ (sin x) (cos x)) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))))))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
47×	`add-sqr-sqrt`
44×	`times-frac`
28×	`add-cube-cbrt`
26×	`associate-l`
16×	`add-cbrt-cube` `add-exp-log`
15×	`distribute-lft-out--`
9×	`add-log-exp`
8×	`pow1`
6×	`associate-r`
4×	`prod-exp` `frac-sub` `cbrt-unprod` `insert-posit16` `unswap-sqr`
3×	`cbrt-undiv` `associate-/r` `diff-log` `div-exp` `div-inv` `associate-/l` `difference-of-squares`
2×	`sub-neg` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--` `associate--r+`
1×	`quot-tan` `clear-num` `frac-2neg` `associate--r-`

Counts

4 → 124

Calls

4 calls:

8.0ms	(/ (sin eps) (cos eps))
27.0ms	(* (/ (sin eps) (cos x)) (sin x))
28.0ms	(* (/ (sin eps) (cos x)) (sin x))
260.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (- (/ (sin x) (cos x)) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))))))

series823.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (sin eps) (cos eps))
117.0ms	(* (/ (sin eps) (cos x)) (sin x))
118.0ms	(* (/ (sin eps) (cos x)) (sin x))
550.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (- (/ (sin x) (cos x)) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))))))

simplify956.0ms

Counts

136 → 136

Iterations

Iter	Nodes
2	2007
1	554
0	222

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (/ (sin eps) (cos x)) (sin x))
0.2b	(* (/ (sin eps) (cos x)) (sin x))
2.0b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
42×	`times-frac`
39×	`*-un-lft-identity`
28×	`add-cube-cbrt`
26×	`associate-l`
16×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `add-log-exp` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out--` `unswap-sqr`
3×	`cbrt-undiv` `associate-/r` `div-exp` `div-inv` `associate-/l`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 118

Calls

4 calls:

8.0ms	(/ (sin eps) (cos eps))
17.0ms	(* (/ (sin eps) (cos x)) (sin x))
25.0ms	(* (/ (sin eps) (cos x)) (sin x))
138.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (sin eps) (cos eps))
102.0ms	(* (/ (sin eps) (cos x)) (sin x))
128.0ms	(* (/ (sin eps) (cos x)) (sin x))
360.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

simplify5.8s

Counts

130 → 130

Iterations

Iter	Nodes
3	4824
2	1460
1	458
0	200

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.2b

regimes299.0ms

Accuracy

0% (0.4b remaining)

Error of 12.9b against oracle of 12.5b and baseline of 12.9b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample14.3s

Algorithm

intervals

Results

7.5s	3382×	body	1280	valid
2.9s	1731×	body	640	valid
2.5s	645×	body	2560	valid
668.0ms	795×	body	320	valid
279.0ms	1072×	body	80	valid
211.0ms	375×	body	160	valid