Details

sample800.0ms

Algorithm

intervals

Results

356.0ms	43×	body	2560	valid
192.0ms	98×	body	1280	valid
128.0ms	59×	body	640	valid
30.0ms	33×	body	320	valid
8.0ms	14×	body	160	valid
3.0ms	9×	body	80	valid

simplify28.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	19
3	19
2	17
1	13
0	6

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (sin x))
1.6b	(- x (tan x))

rewrite50.0ms

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` `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 → 110

Calls

3 calls:

17.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (sin x))
8.0ms	(- x (tan x))

series379.0ms

Counts

3 → 9

Calls

3 calls:

189.0ms	(/ (- x (sin x)) (- x (tan x)))
70.0ms	(- x (sin x))
120.0ms	(- x (tan x))

simplify2.1s

Counts

119 → 119

Iterations

Iter	Nodes
3	4522
2	1290
1	499
0	209

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.6b	(- x (tan x))
1.6b	(- x (tan x))

rewrite155.0ms

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` `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 → 588

Calls

4 calls:

23.0ms	(/ (sin x) (- x (tan x)))
86.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
8.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series535.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (sin x) (- x (tan x)))
295.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
78.0ms	(- x (tan x))
80.0ms	(- x (tan x))

simplify1.8s

Counts

600 → 600

Iterations

Iter	Nodes
2	3379
1	1398
0	617

prune7.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* (* x x) (* x x)) -27/2800)
0.1b	(* (* x x) (* x x))
18.9b	(fma 9/40 (* x x) (* (* (* x x) (* x x)) -27/2800))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

132×	`pow1`
36×	`pow-prod-down` `pow-prod-up`
33×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
21×	`prod-exp` `cbrt-unprod`
18×	`pow-plus`
13×	`pow2`
5×	`add-sqr-sqrt`
4×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`associate-l` `*-commutative` `unswap-sqr`
1×	`swap-sqr` `fma-udef`

Counts

3 → 105

Calls

3 calls:

90.0ms	(* (* (* x x) (* x x)) -27/2800)
28.0ms	(* (* x x) (* x x))
0.0ms	(fma 9/40 (* x x) (* (* (* x x) (* x x)) -27/2800))

series246.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* (* (* x x) (* x x)) -27/2800)
50.0ms	(* (* x x) (* x x))
144.0ms	(fma 9/40 (* x x) (* (* (* x x) (* x x)) -27/2800))

simplify4.6s

Counts

114 → 114

Iterations

Iter	Nodes
3	4985
2	940
1	256
0	95

prune928.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes94.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.4b

bsearch166.0ms

Steps

Iters	Range		Point
9	7.101228369635622e-07	0.9676876931049737	0.02756155658182702
10	-102.89153151738607	-2.897210331759478e-16	-0.02980072122437864

simplify7.0ms

Iterations

Iter	Nodes
2	24
1	24
0	23

end0.0ms

sample16.2s

Algorithm

intervals

Results

7.2s	1548×	body	2560	valid
5.1s	2772×	body	1280	valid
2.6s	1877×	body	640	valid
697.0ms	929×	body	320	valid
243.0ms	479×	body	160	valid
101.0ms	395×	body	80	valid