Details

sample452.0ms

Algorithm

intervals

Results

92.0ms	41×	body	2560	valid
68.0ms	98×	body	1280	valid
19.0ms	59×	body	640	valid
6.0ms	28×	body	320	valid
3.0ms	21×	body	160	valid
1.0ms	9×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite24.0ms

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×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

11.0ms	(/ (- x (sin x)) (- x (tan x)))
2.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
40.0ms	(- x (sin x))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	952	1147
3	2624	1147
done	5001	1145

prune209.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
200×	`add-sqr-sqrt` `*-un-lft-identity`
92×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 228

Calls

4 calls:

11.0ms	(/ (- x (tan x)) (- x (sin x)))
15.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
2.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- x (tan x)) (- x (sin x)))
78.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
49.0ms	(- x (tan x))
36.0ms	(- x (sin x))

simplify1.2s

Counts

240 → 240

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	320	4580
1	749	4150
2	2098	3747
done	5000	3735

prune375.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
16.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

9.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
8.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series110.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* 27/2800 (pow x 4))
24.0ms	(* 9/40 (pow x 2))
45.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify1.7s

Counts

75 → 75

Iterations

Useful iterations: 3 (518.0ms)

Iter	Nodes	Cost
0	121	788
1	279	703
2	721	643
3	2833	637
done	5001	637

prune148.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.9b

bsearch81.0ms

Steps

Iters	Range		Point
9	0.00016167321766412214	1766.3470775505596	0.028078975194333212
10	-3752817.331716861	-5.670122129476186e-07	-0.02894118494710049

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	43
1	33	33
done	33	33

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1564×	body	2560	valid
1.9s	2744×	body	1280	valid
661.0ms	1876×	body	640	valid
209.0ms	925×	body	320	valid
86.0ms	494×	body	160	valid
37.0ms	397×	body	80	valid