Details

sample543.0ms

Algorithm

intervals

Results

118.0ms	50×	body	2560	valid
83.0ms	85×	body	1280	valid
20.0ms	60×	body	640	valid
6.0ms	26×	body	320	valid
4.0ms	22×	body	160	valid
2.0ms	13×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5
done	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite43.0ms

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:

24.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series185.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- x (sin x)) (- x (tan x)))
55.0ms	(- x (tan x))
50.0ms	(- x (sin x))

simplify148.0ms

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685
done	5001	685

prune213.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
17.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite48.0ms

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:

12.0ms	(* 27/2800 (pow x 4))
12.0ms	(* 9/40 (pow x 2))
22.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series111.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 27/2800 (pow x 4))
28.0ms	(* 9/40 (pow x 2))
45.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify40.0ms

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315
done	5001	315

prune151.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin x) 3)
1.9b	(- (pow x 3) (pow (sin x) 3))
1.9b	(- x (tan x))
20.7b	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
49×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
16×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`frac-times`
3×	`difference-cubes` `pow-unpow` `flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 147

Calls

4 calls:

4.0ms	(pow (sin x) 3)
24.0ms	(- (pow x 3) (pow (sin x) 3))
6.0ms	(- x (tan x))
95.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sin x) 3)
102.0ms	(- (pow x 3) (pow (sin x) 3))
55.0ms	(- x (tan x))
250.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

simplify93.0ms

Counts

159 → 159

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	630	1900
1	3022	1778
2	5002	1734
done	5002	1734

prune410.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow x 3) (pow (sin x) 3))
1.9b	(- (* x x) (* (tan x) (tan x)))
16.0b	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
20.7b	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`difference-of-squares`
41×	`times-frac`
36×	`unpow-prod-down` `cube-prod`
29×	`associate-/l*`
24×	`sqr-pow`
16×	`add-cube-cbrt`
15×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
8×	`add-log-exp`
7×	`associate-/r/`
5×	`cbrt-undiv` `div-exp` `associate-/r*` `distribute-lft-out`
4×	`pow1` `flip3--` `flip--` `associate-/l/`
3×	`difference-cubes` `flip3-+` `flip-+`
2×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`
1×	`associate-*r/`

Counts

4 → 163

Calls

4 calls:

25.0ms	(- (pow x 3) (pow (sin x) 3))
8.0ms	(- (* x x) (* (tan x) (tan x)))
28.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
99.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))))

series648.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (pow x 3) (pow (sin x) 3))
86.0ms	(- (* x x) (* (tan x) (tan x)))
146.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
315.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))))

simplify111.0ms

Counts

175 → 175

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	824	2895
1	4183	2655
2	5003	2654
done	5003	2654

prune561.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch71.0ms

Steps

Iters	Range		Point
9	9.85435867085541e-08	110.15968793260775	0.02674499741262323
8	-0.1517943218839364	-1.6640733670284383e-05	-0.027801200389932522

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11
done	29	11

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.5s	1600×	body	2560	valid
1.9s	2816×	body	1280	valid
628.0ms	1873×	body	640	valid
194.0ms	892×	body	320	valid
72.0ms	465×	body	160	valid
32.0ms	354×	body	80	valid