Details

sample444.0ms

Algorithm

intervals

Results

183.0ms	94×	body	1280	valid
90.0ms	25×	body	2560	valid
81.0ms	66×	body	640	valid
64.0ms	25×	body	320	valid
10.0ms	37×	body	80	valid
5.0ms	9×	body	160	valid

simplify4.0ms

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

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

45.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series212.0ms

Counts

2 → 6

Calls

2 calls:

134.0ms	(- (tan (+ x eps)) (tan x))
78.0ms	(tan (+ x eps))

simplify3.2s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	4082
3	1357
2	454
1	205
0	96

prune288.0ms

Pruning

10 alts after pruning (10 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))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

15.0ms	(+ (tan x) (tan eps))
52.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(* (tan x) (tan eps))
114.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (tan x) (tan eps))
310.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
164.0ms	(* (tan x) (tan eps))
520.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.2s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
2	1636
1	580
0	242

prune735.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (* (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))) (cos eps)))
0.3b	(* (/ (sin eps) (cos x)) (sin x))
0.3b	(* (/ (sin eps) (cos x)) (sin x))
4.5b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

2640×	`times-frac`
1971×	`add-sqr-sqrt`
1951×	`*-un-lft-identity`
1394×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
185×	`div-inv`
84×	`fma-neg`
30×	`associate-/r/`
26×	`associate-l`
19×	`add-cbrt-cube` `add-exp-log`
16×	`flip3--` `flip--`
8×	`pow1`
6×	`associate-r` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-*l/` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`associate-/l*`
2×	`pow-prod-down` `*-commutative`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `frac-sub`

Counts

4 → 1297

Calls

4 calls:

20.0ms	(/ (sin eps) (* (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))) (cos eps)))
26.0ms	(* (/ (sin eps) (cos x)) (sin x))
29.0ms	(* (/ (sin eps) (cos x)) (sin x))
134.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (sin eps) (* (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))) (cos eps)))
127.0ms	(* (/ (sin eps) (cos x)) (sin x))
141.0ms	(* (/ (sin eps) (cos x)) (sin x))
334.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

simplify3.1s

Counts

1309 → 1309

Iterations

Iter	Nodes
done	5001
1	2968
0	1337

prune10.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))) (cos eps)) (sin eps)))
0.3b	(* (/ (sin eps) (cos x)) (sin x))
0.3b	(* (/ (sin eps) (cos x)) (sin x))
4.5b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

2670×	`times-frac`
1985×	`add-sqr-sqrt`
1965×	`*-un-lft-identity`
1408×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
189×	`div-inv`
186×	`distribute-lft-out--`
84×	`fma-neg`
35×	`add-exp-log`
29×	`associate-/r/`
26×	`associate-l`
23×	`add-cbrt-cube`
15×	`flip3--` `flip--`
14×	`div-exp`
9×	`pow1`
7×	`cbrt-undiv` `associate-/r*` `prod-exp`
6×	`associate-r` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`rec-exp` `1-exp` `associate-/l*`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub` `pow-flip` `inv-pow`

Counts

4 → 1330

Calls

4 calls:

25.0ms	(/ 1 (/ (* (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))) (cos eps)) (sin eps)))
16.0ms	(* (/ (sin eps) (cos x)) (sin x))
17.0ms	(* (/ (sin eps) (cos x)) (sin x))
119.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ 1 (/ (* (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))) (cos eps)) (sin eps)))
88.0ms	(* (/ (sin eps) (cos x)) (sin x))
84.0ms	(* (/ (sin eps) (cos x)) (sin x))
261.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

simplify2.6s

Counts

1342 → 1342

Iterations

Iter	Nodes
done	5001
1	3152
0	1395

prune10.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.0b

regimes247.0ms

Accuracy

0% (0.4b remaining)

Error of 12.8b against oracle of 12.3b and baseline of 12.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample9.3s

Algorithm

intervals

Results

4.7s	3275×	body	1280	valid
1.7s	1814×	body	640	valid
1.7s	610×	body	2560	valid
504.0ms	1200×	body	80	valid
442.0ms	764×	body	320	valid
159.0ms	337×	body	160	valid