Details

sample425.0ms

Algorithm

intervals

Results

219.0ms	52×	body	2560	valid
96.0ms	91×	body	1280	valid
26.0ms	46×	body	640	valid
14.0ms	38×	body	320	valid
6.0ms	20×	body	160	valid
2.0ms	9×	body	80	valid

simplify27.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	6	9
1	18	9
2	19	9
done	19	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite98.0ms

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:

28.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
57.0ms	(- x (sin x))

series246.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(/ (- x (sin x)) (- x (tan x)))
68.0ms	(- x (tan x))
80.0ms	(- x (sin x))

simplify4.7s

Counts

89 → 89

Iterations

Useful iterations: done (4.7s)

Iter	Nodes	Cost
0	157	1237
1	828	1200
done	5001	1136

prune385.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
14.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite78.0ms

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:

15.0ms	(* 27/2800 (pow x 4))
32.0ms	(* 9/40 (pow x 2))
29.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series157.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* 27/2800 (pow x 4))
36.0ms	(* 9/40 (pow x 2))
56.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify2.0s

Counts

75 → 75

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	121	788
1	1328	689
done	5001	642

prune270.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
14.1b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite59.0ms

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`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

18.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
14.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series230.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* 27/2800 (pow x 4))
28.0ms	(* 9/40 (pow x 2))
145.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify2.8s

Counts

73 → 73

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	113	715
1	1286	614
done	5000	571

prune272.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

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))
1.8b	(- x (sin x))

rewrite130.0ms

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:

32.0ms	(/ (- x (tan x)) (- x (sin x)))
53.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
11.0ms	(- x (tan x))
14.0ms	(- x (sin x))

series423.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- x (tan x)) (- x (sin x)))
158.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
100.0ms	(- x (tan x))
49.0ms	(- x (sin x))

simplify5.0s

Counts

240 → 240

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	320	4580
1	2364	3983
done	5000	3851

prune599.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.3b

bsearch113.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.029468351736831863
8	-11.923248480236845	-0.0008047768791668974	-0.02915706671350092

simplify27.0ms

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	25	43
1	32	33
done	32	33

end0.0ms

sample13.5s

Algorithm

intervals

Results

5.9s	1596×	body	2560	valid
4.2s	2769×	body	1280	valid
2.4s	1873×	body	640	valid
400.0ms	958×	body	320	valid
138.0ms	470×	body	160	valid
110.0ms	334×	body	80	valid