Details

sample631.0ms

Algorithm

intervals

Results

241.0ms	55×	body	2560	valid
198.0ms	96×	body	1280	valid
60.0ms	56×	body	640	valid
18.0ms	22×	body	320	valid
8.0ms	15×	body	160	valid
3.0ms	12×	body	80	valid

simplify72.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize34.0ms

Local error

Found 3 expressions with local error:

1.4b	(- x (tan x))
1.2b	(- x (sin x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite59.0ms

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` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

Slowest

34.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series297.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

128.0ms	(- x (tan x))
102.0ms	(/ (- x (sin x)) (- x (tan x)))
67.0ms	(- x (sin x))

simplify544.0ms

Counts: 125 → 92

prune882.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

15.3b	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
0.1b	(* (* x x) 9/40)
0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) (* x x)) 27/2800)

rewrite220.0ms

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`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`insert-posit16`
3×	`associate-l` `*-commutative` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 126

Calls

4 calls:

Slowest

129.0ms	(* (* (* x x) (* x x)) 27/2800)
37.0ms	(* (* x x) (* x x))
32.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
17.0ms	(* (* x x) 9/40)

series290.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

159.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))
51.0ms	(* (* x x) 9/40)
43.0ms	(* (* (* x x) (* x x)) 27/2800)
37.0ms	(* (* x x) (* x x))

simplify454.0ms

Counts: 140 → 138

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.4b	(- x (tan x))
1.4b	(- x (tan x))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b	(/ (sin x) (- x (tan x)))

rewrite129.0ms

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` `insert-posit16`
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 → 98

Calls

4 calls:

Slowest

84.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
25.0ms	(/ (sin x) (- x (tan x)))
9.0ms	(- x (tan x))
8.0ms	(- x (tan x))

series535.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

250.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
105.0ms	(- x (tan x))
93.0ms	(- x (tan x))
87.0ms	(/ (sin x) (- x (tan x)))

simplify533.0ms

Counts: 139 → 110

prune943.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

1.4b	(- x (tan x))
1.4b	(- x (tan x))
1.4b	(- x (tan x))
1.2b	(- x (sin x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

Slowest

5.0ms	(- x (sin x))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series255.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

79.0ms	(- x (tan x))
63.0ms	(- x (tan x))
58.0ms	(- x (tan x))
56.0ms	(- x (sin x))

simplify410.0ms

Counts: 84 → 72

prune748.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes134.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch198.0ms

end0.0ms

sample16.1s

Algorithm

intervals

Results

7.2s	1619×	body	2560	valid
5.4s	2818×	body	1280	valid
2.4s	1814×	body	640	valid
732.0ms	912×	body	320	valid
220.0ms	498×	body	160	valid
79.0ms	339×	body	80	valid