Details

sample453.0ms

Algorithm

intervals

Results

243.0ms	106×	body	1280	valid
100.0ms	30×	body	2560	valid
60.0ms	49×	body	640	valid
22.0ms	26×	body	320	valid
8.0ms	34×	body	80	valid
6.0ms	11×	body	160	valid

simplify8.0ms

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: 39.4b

localize24.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
3.5b	(tan (+ x eps))

rewrite28.0ms

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:

19.0ms	(- (tan (+ x eps)) (tan x))
9.0ms	(tan (+ x eps))

series582.0ms

Counts

2 → 6

Calls

2 calls:

158.0ms	(- (tan (+ x eps)) (tan x))
423.0ms	(tan (+ x eps))

simplify1.3s

Counts

49 → 49

Iterations

Iter	Nodes
done	2002
4	2002
3	1357
2	454
1	205
0	96

prune221.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.1b

localize48.0ms

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))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite225.0ms

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:

49.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(+ (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
127.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
127.0ms	(+ (tan x) (tan eps))
137.0ms	(* (tan x) (tan eps))
576.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

185 → 185

Iterations

Iter	Nodes
done	2007
3	2007
2	1631
1	580
0	242

prune753.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (sin eps) (cos eps)))
0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin x) (cos x))
2.9b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

2645×	`times-frac`
1972×	`add-sqr-sqrt`
1957×	`*-un-lft-identity`
1400×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
185×	`div-inv`
84×	`fma-neg`
28×	`associate-/r/`
15×	`flip3--` `flip--`
13×	`add-cbrt-cube` `associate-r` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l`
2×	`quot-tan` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `frac-sub`

Counts

4 → 1298

Calls

4 calls:

29.0ms	(* (sin x) (/ (sin eps) (cos eps)))
16.0ms	(/ (sin x) (cos x))
16.0ms	(/ (sin x) (cos x))
212.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (sin x) (/ (sin eps) (cos eps)))
32.0ms	(/ (sin x) (cos x))
32.0ms	(/ (sin x) (cos x))
354.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify3.0s

Counts

1310 → 1310

Iterations

Iter	Nodes
done	2000
1	2000
0	1315

prune12.5s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(* (* (sin x) (sin eps)) (/ 1 (cos eps)))
0.2b	(* (sin x) (sin eps))
2.9b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (sin x) (sin eps)) (/ 1 (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

2635×	`times-frac`
1962×	`add-sqr-sqrt`
1950×	`*-un-lft-identity`
1393×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
184×	`div-inv`
84×	`fma-neg`
30×	`add-exp-log`
28×	`associate-/r/`
20×	`add-cbrt-cube`
16×	`associate-r`
15×	`flip3--` `flip--`
13×	`prod-exp`
11×	`pow1`
7×	`cbrt-unprod`
6×	`add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r` `sin-mult` `associate-/l`
2×	`rec-exp` `1-exp` `*-commutative`
1×	`frac-times` `quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-l/` `associate-r/` `un-div-inv` `frac-sub` `unswap-sqr`

Counts

4 → 1297

Calls

4 calls:

8.0ms	(/ (sin x) (cos x))
36.0ms	(* (* (sin x) (sin eps)) (/ 1 (cos eps)))
13.0ms	(* (sin x) (sin eps))
151.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (sin x) (sin eps)) (/ 1 (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (sin x) (cos x))
97.0ms	(* (* (sin x) (sin eps)) (/ 1 (cos eps)))
66.0ms	(* (sin x) (sin eps))
346.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (sin x) (sin eps)) (/ 1 (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify3.0s

Counts

1309 → 1309

Iterations

Iter	Nodes
done	2000
1	2000
0	1353

prune9.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.9b

regimes198.0ms

Accuracy

0% (0.4b remaining)

Error of 12.6b against oracle of 12.2b and baseline of 12.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample9.3s

Algorithm

intervals

Results

4.9s	3316×	body	1280	valid
1.7s	607×	body	2560	valid
1.6s	1855×	body	640	valid
729.0ms	769×	body	320	valid
166.0ms	1110×	body	80	valid
111.0ms	343×	body	160	valid