Details

sample459.0ms

Algorithm

intervals

Results

262.0ms	104×	body	1280	valid
76.0ms	21×	body	2560	valid
61.0ms	52×	body	640	valid
27.0ms	28×	body	320	valid
10.0ms	35×	body	80	valid
10.0ms	16×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize26.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
3.9b	(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))

series245.0ms

Counts

2 → 6

Calls

2 calls:

144.0ms	(- (tan (+ x eps)) (tan x))
101.0ms	(tan (+ x eps))

simplify841.0ms

Counts

33 → 33

Iterations

Iter	Nodes
done	5000
3	1179
2	357
1	139
0	70

prune178.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`insert-posit16`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`frac-times` `+-commutative` `sum-log` `flip3-+` `times-frac` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

5.0ms	(- 1 (* (tan x) (tan eps)))
7.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
72.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series851.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- 1 (* (tan x) (tan eps)))
134.0ms	(+ (tan x) (tan eps))
122.0ms	(* (tan x) (tan eps))
450.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify925.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	1611
1	371
0	149

prune515.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (sin x) (sin eps))
0.2b	(* (sin x) (sin eps))
3.1b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (/ (* (sin x) (sin eps)) (cos eps)) (cos x)))) (/ (sin x) (cos x)))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

9.0ms	(/ (sin eps) (cos eps))
12.0ms	(* (sin x) (sin eps))
11.0ms	(* (sin x) (sin eps))
227.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (/ (* (sin x) (sin eps)) (cos eps)) (cos x)))) (/ (sin x) (cos x)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (sin eps) (cos eps))
72.0ms	(* (sin x) (sin eps))
61.0ms	(* (sin x) (sin eps))
309.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (/ (* (sin x) (sin eps)) (cos eps)) (cos x)))) (/ (sin x) (cos x)))

simplify1.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1453
1	356
0	162

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (sin x) (sin eps))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
3.1b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

8.0ms	(/ (sin eps) (cos eps))
19.0ms	(* (sin x) (sin eps))
36.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
64.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (sin eps) (cos eps))
56.0ms	(* (sin x) (sin eps))
153.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
390.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

simplify2.4s

Counts

134 → 134

Iterations

Iter	Nodes
done	5002
2	3857
1	623
0	229

prune966.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.1b

regimes282.0ms

Accuracy

0% (0.4b remaining)

Error of 12.5b against oracle of 12.1b and baseline of 12.5b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample13.3s

Algorithm

intervals

Results

6.9s	3245×	body	1280	valid
2.4s	1924×	body	640	valid
2.0s	617×	body	2560	valid
1.0s	760×	body	320	valid
599.0ms	1085×	body	80	valid
205.0ms	369×	body	160	valid