Details

sample407.0ms

Algorithm

intervals

Results

160.0ms	48×	body	2560	valid
146.0ms	97×	body	1280	valid
29.0ms	49×	body	640	valid
12.0ms	32×	body	320	valid
4.0ms	17×	body	160	valid
2.0ms	13×	body	80	valid

simplify61.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize71.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.8b	(- x (tan x))
1.8b	(- x (sin x))

rewrite426.0ms

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:

21.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
393.0ms	(- x (sin x))

series219.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(/ (- x (sin x)) (- x (tan x)))
62.0ms	(- x (tan x))
54.0ms	(- x (sin x))

simplify1.9s

Counts

89 → 89

Iterations

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

prune419.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* x 9/40)
0.2b	(* x (* x 9/40))
15.1b	(- (* x (* x 9/40)) (* 27/2800 (* (* x x) (* x x))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

25.0ms	(* (* x x) (* x x))
9.0ms	(* x 9/40)
13.0ms	(* x (* x 9/40))
15.0ms	(- (* x (* x 9/40)) (* 27/2800 (* (* x x) (* x x))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* x x) (* x x))
19.0ms	(* x 9/40)
37.0ms	(* x (* x 9/40))
173.0ms	(- (* x (* x 9/40)) (* 27/2800 (* (* x x) (* x x))))

simplify3.8s

Counts

123 → 123

Iterations

Iter	Nodes
done	5002
3	4417
2	1284
1	340
0	110

prune305.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.6b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.8b	(- x (tan x))
1.8b	(- x (tan x))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`flip3--` `add-cbrt-cube` `add-exp-log` `associate-/r/` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/ (sin x) (- x (tan x)))
90.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series451.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (sin x) (- x (tan x)))
245.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
66.0ms	(- x (tan x))
57.0ms	(- x (tan x))

simplify2.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
3	4025
2	1132
1	389
0	177

prune476.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin x))
1.8b	(- (* (* x x) x) (* (* (sin x) (sin x)) (sin x)))
1.8b	(- x (tan x))
33.3b	(/ (- (* (* x x) x) (* (* (sin x) (sin x)) (sin x))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1`
10×	`pow3`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`difference-cubes`
4×	`associate-/l*`
3×	`associate-/r` `flip3--` `swap-sqr` `associate-r` `associate-l*` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `sqr-sin` `div-inv` `sin-mult` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

18.0ms	(* (sin x) (sin x))
37.0ms	(- (* (* x x) x) (* (* (sin x) (sin x)) (sin x)))
4.0ms	(- x (tan x))
114.0ms	(/ (- (* (* x x) x) (* (* (sin x) (sin x)) (sin x))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (sin x) (sin x))
138.0ms	(- (* (* x x) x) (* (* (sin x) (sin x)) (sin x)))
76.0ms	(- x (tan x))
322.0ms	(/ (- (* (* x x) x) (* (* (sin x) (sin x)) (sin x))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))

simplify2.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	2221
1	529
0	197

prune551.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes104.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.2b

bsearch123.0ms

Steps

Iters	Range		Point
6	0.0022991053059264813	0.02586244036059231	0.02458873884700214
10	-733100.9210806559	-4.034181863829644e-08	-0.026370186168873697

simplify9.0ms

Iterations

Iter	Nodes
done	28
1	28
0	25

end0.0ms

sample12.8s

Algorithm

intervals

Results

6.3s	1598×	body	2560	valid
3.9s	2738×	body	1280	valid
1.6s	1859×	body	640	valid
520.0ms	948×	body	320	valid
173.0ms	490×	body	160	valid
59.0ms	367×	body	80	valid