Details

sample480.0ms

Algorithm

intervals

Results

244.0ms	94×	body	1280	valid
94.0ms	25×	body	2560	valid
91.0ms	66×	body	640	valid
22.0ms	25×	body	320	valid
10.0ms	37×	body	80	valid
6.0ms	9×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
2.0b	(tan (+ x eps))

rewrite49.0ms

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:

42.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series207.0ms

Counts

2 → 6

Calls

2 calls:

148.0ms	(- (tan (+ x eps)) (tan x))
58.0ms	(tan (+ x eps))

simplify1.7s

Counts

33 → 33

Iterations

Iter	Nodes
done	5001
4	1821
3	719
2	300
1	139
0	70

prune235.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.9b

localize45.0ms

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))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite188.0ms

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:

7.0ms	(+ (tan x) (tan eps))
43.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
28.0ms	(* (tan x) (tan eps))
107.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (tan x) (tan eps))
284.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
101.0ms	(* (tan x) (tan eps))
526.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	4143
2	1152
1	405
0	174

prune564.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

33.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
15.0ms	(/ (* (tan x) (sin eps)) (cos eps))
12.0ms	(* (tan x) (sin eps))
149.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

289.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
130.0ms	(/ (* (tan x) (sin eps)) (cos eps))
105.0ms	(* (tan x) (sin eps))
506.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify1.2s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1471
1	508
0	221

prune593.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin eps) (cos eps))
0.2b	(* (/ (sin eps) (cos eps)) (sin x))
0.2b	(* (/ (sin eps) (cos eps)) (sin x))
4.5b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos eps)) (sin x)) (cos x)))) (/ (sin x) (cos x)))

rewrite236.0ms

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:

10.0ms	(/ (sin eps) (cos eps))
32.0ms	(* (/ (sin eps) (cos eps)) (sin x))
33.0ms	(* (/ (sin eps) (cos eps)) (sin x))
159.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos eps)) (sin x)) (cos x)))) (/ (sin x) (cos x)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (sin eps) (cos eps))
83.0ms	(* (/ (sin eps) (cos eps)) (sin x))
88.0ms	(* (/ (sin eps) (cos eps)) (sin x))
310.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos eps)) (sin x)) (cos x)))) (/ (sin x) (cos x)))

simplify2.6s

Counts

130 → 130

Iterations

Iter	Nodes
done	5004
3	4288
2	1284
1	423
0	179

prune983.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.1b

regimes232.0ms

Accuracy

0% (0.4b remaining)

Error of 12.7b against oracle of 12.3b and baseline of 12.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample14.2s

Algorithm

intervals

Results

6.7s	3275×	body	1280	valid
3.7s	1814×	body	640	valid
2.3s	610×	body	2560	valid
742.0ms	764×	body	320	valid
326.0ms	1200×	body	80	valid
228.0ms	337×	body	160	valid