Details

sample485.0ms

Algorithm

intervals

Results

170.0ms	86×	body	1280	valid
156.0ms	42×	body	2560	valid
42.0ms	68×	body	640	valid
14.0ms	33×	body	320	valid
5.0ms	18×	body	160	valid
1.0ms	9×	body	80	valid

simplify14.0ms

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: 29.2b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (tan x))
0.8b	(- x (sin x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 80

Calls

3 calls:

40.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
13.0ms	(- x (sin x))

series288.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(/ (- x (sin x)) (- x (tan x)))
91.0ms	(- x (tan x))
45.0ms	(- x (sin x))

simplify1.7s

Counts

89 → 89

Iterations

Iter	Nodes
done	5006
3	3260
2	952
1	372
0	157

prune393.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(* (/ (sin x) (* x x)) (/ (sin x) (cos x)))
1.4b	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
12.4b	(/ (sin x) (* x x))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
88×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
57×	`add-cube-cbrt`
35×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
13×	`associate-r`
12×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
8×	`div-inv`
7×	`associate-l`
6×	`pow1` `add-log-exp` `difference-of-squares`
4×	`associate-/r*` `unswap-sqr`
2×	`clear-num` `frac-2neg` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 160

Calls

4 calls:

12.0ms	(/ (/ (sin x) x) (cos x))
45.0ms	(* (/ (sin x) (* x x)) (/ (sin x) (cos x)))
105.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
9.0ms	(/ (sin x) (* x x))

series336.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (/ (sin x) x) (cos x))
78.0ms	(* (/ (sin x) (* x x)) (/ (sin x) (cos x)))
131.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
44.0ms	(/ (sin x) (* x x))

simplify1.9s

Counts

172 → 172

Iterations

Iter	Nodes
done	5006
2	2925
1	818
0	308

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x 9/40))
0.2b	(* (* x x) (* x x))
0.3b	(* 27/2800 (* (* x x) (* x x)))
16.3b	(- (* x (* x 9/40)) (* 27/2800 (* (* x x) (* x x))))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

138×	`pow1`
39×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
36×	`pow-prod-up`
24×	`prod-exp` `cbrt-unprod`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
7×	`add-sqr-sqrt` `associate-l`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`associate-r` `*-commutative`
2×	`unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 121

Calls

4 calls:

24.0ms	(* x (* x 9/40))
47.0ms	(* (* x x) (* x x))
99.0ms	(* 27/2800 (* (* x x) (* x x)))
14.0ms	(- (* x (* x 9/40)) (* 27/2800 (* (* x x) (* x x))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* x (* x 9/40))
59.0ms	(* (* x x) (* x x))
56.0ms	(* 27/2800 (* (* x x) (* x x)))
182.0ms	(- (* x (* x 9/40)) (* 27/2800 (* (* x x) (* x x))))

simplify1.7s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	1199
1	341
0	120

prune322.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.9b

bsearch244.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	2.424314253224005
10	-17239113253358.373	-4.96108325192681e-05	-2.41224692961804

simplify13.0ms

Iterations

Iter	Nodes
done	42
1	42
0	31

end0.0ms

sample14.2s

Algorithm

intervals

Results

6.3s	1666×	body	2560	valid
4.6s	2699×	body	1280	valid
1.8s	1879×	body	640	valid
768.0ms	474×	body	160	valid
467.0ms	944×	body	320	valid
66.0ms	338×	body	80	valid