Details

sample637.0ms

Algorithm

intervals

Results

237.0ms	63×	body	2560	valid
226.0ms	91×	body	1280	valid
46.0ms	54×	body	640	valid
10.0ms	18×	body	320	valid
7.0ms	15×	body	160	valid
3.0ms	15×	body	80	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize375.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.4b	(- x (sin x))
0.4b	(- x (tan x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 113

Calls

3 calls:

18.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (sin x))
7.0ms	(- x (tan x))

series286.0ms

Counts

3 → 9

Calls

3 calls:

150.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
99.0ms	(- x (tan x))

simplify3.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
3	4949
2	1283
1	504
0	212

prune403.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* x x) 9/40 -1/2)
0.1b	(* 27/2800 (* (* x x) (* x x)))
0.1b	(* (* x x) (* x x))
15.3b	(- (fma (* x x) 9/40 -1/2) (* 27/2800 (* (* x x) (* x x))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

133×	`pow1`
36×	`pow-prod-down` `pow-prod-up`
34×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
21×	`prod-exp` `cbrt-unprod`
18×	`pow-plus`
13×	`pow2`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`associate-r` `*-commutative` `fma-udef` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `swap-sqr` `associate--l+` `flip--`

Counts

4 → 130

Calls

4 calls:

0.0ms	(fma (* x x) 9/40 -1/2)
93.0ms	(* 27/2800 (* (* x x) (* x x)))
33.0ms	(* (* x x) (* x x))
7.0ms	(- (fma (* x x) 9/40 -1/2) (* 27/2800 (* (* x x) (* x x))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(fma (* x x) 9/40 -1/2)
49.0ms	(* 27/2800 (* (* x x) (* x x)))
42.0ms	(* (* x x) (* x x))
62.0ms	(- (fma (* x x) 9/40 -1/2) (* 27/2800 (* (* x x) (* x x))))

simplify1.2s

Counts

142 → 142

Iterations

Iter	Nodes
done	5003
2	1097
1	337
0	128

prune322.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.4b	(- x (tan x))
0.4b	(- x (tan x))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 592

Calls

4 calls:

14.0ms	(/ (sin x) (- x (tan x)))
70.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series520.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (sin x) (- x (tan x)))
282.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
75.0ms	(- x (tan x))
93.0ms	(- x (tan x))

simplify2.4s

Counts

604 → 604

Iterations

Iter	Nodes
done	5000
2	3356
1	1405
0	620

prune2.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.4b	(- x (tan x))
0.4b	(- x (tan x))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 592

Calls

4 calls:

13.0ms	(/ (sin x) (- x (tan x)))
64.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
9.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series583.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (sin x) (- x (tan x)))
283.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
89.0ms	(- x (tan x))
102.0ms	(- x (tan x))

simplify2.4s

Counts

604 → 604

Iterations

Iter	Nodes
done	5000
2	3356
1	1405
0	620

prune3.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes104.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch192.0ms

Steps

Iters	Range		Point
11	4.21785760657603e-35	57.56933376468871	0.02825639784178301
9	-34.11472770615283	-3.67231414207575e-08	-0.027836888459983777

simplify8.0ms

Iterations

Iter	Nodes
done	26
1	26
0	25

end0.0ms

sample12.6s

Algorithm

intervals

Results

6.1s	1588×	body	2560	valid
4.3s	2730×	body	1280	valid
1.3s	1915×	body	640	valid
456.0ms	911×	body	320	valid
159.0ms	379×	body	80	valid
133.0ms	477×	body	160	valid