Details

sample500.0ms

Algorithm

intervals

Results

202.0ms	51×	body	2560	valid
157.0ms	87×	body	1280	valid
39.0ms	52×	body	640	valid
20.0ms	36×	body	320	valid
6.0ms	16×	body	160	valid
2.0ms	14×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize60.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (tan x))
1.1b	(- x (sin x))

rewrite37.0ms

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:

19.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series250.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (- x (sin x)) (- x (tan x)))
82.0ms	(- x (tan x))
81.0ms	(- x (sin x))

simplify2.0s

Counts

89 → 89

Iterations

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

prune467.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin x) (cos x))
1.4b	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
14.9b	(/ (sin x) (* x x))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`times-frac`
28×	`*-un-lft-identity`
22×	`add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
7×	`associate-/r*`
6×	`add-log-exp` `difference-of-squares`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`clear-num` `frac-2neg` `div-inv`
2×	`quot-tan` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `flip--`

Counts

4 → 98

Calls

4 calls:

7.0ms	(/ (sin x) (cos x))
7.0ms	(/ (sin x) (cos x))
102.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
18.0ms	(/ (sin x) (* x x))

series213.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (sin x) (cos x))
32.0ms	(/ (sin x) (cos x))
119.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
42.0ms	(/ (sin x) (* x x))

simplify1.4s

Counts

110 → 110

Iterations

Iter	Nodes
done	5003
2	1162
1	359
0	162

prune794.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize135.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
1.4b	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
5.1b	(log (exp (- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))))
14.9b	(/ (sin x) (* x x))

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
34×	`times-frac`
28×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`log-pow` `difference-of-squares`
11×	`exp-prod` `add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r*` `distribute-lft-out--`
3×	`cbrt-undiv` `div-exp`
2×	`clear-num` `sub-neg` `frac-2neg` `exp-sum` `div-inv`
1×	`log-div` `quot-tan` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `prod-exp` `frac-sub` `cbrt-unprod` `flip--`

Counts

4 → 96

Calls

4 calls:

11.0ms	(/ (sin x) (cos x))
74.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
269.0ms	(log (exp (- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))))
18.0ms	(/ (sin x) (* x x))

series352.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (sin x) (cos x))
129.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
148.0ms	(log (exp (- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))))
47.0ms	(/ (sin x) (* x x))

simplify1.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	1338
1	433
0	201

prune743.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (* (* x x) (* x x)))
0.1b	(* x (* x 9/40))
0.2b	(* x 9/40)
16.3b	(- (* x (* x 9/40)) (* 27/2800 (* (* x x) (* x x))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`associate-l`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-r`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 76

Calls

4 calls:

106.0ms	(* 27/2800 (* (* x x) (* x x)))
24.0ms	(* x (* x 9/40))
8.0ms	(* x 9/40)
23.0ms	(- (* x (* x 9/40)) (* 27/2800 (* (* x x) (* x x))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* 27/2800 (* (* x x) (* x x)))
27.0ms	(* x (* x 9/40))
15.0ms	(* x 9/40)
187.0ms	(- (* x (* x 9/40)) (* 27/2800 (* (* x x) (* x x))))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
done	5005
2	1427
1	347
0	115

prune273.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch142.0ms

Steps

Iters	Range		Point
7	0.778402845272117	28.34319947931986	4.73799013283022
8	-2980.3304644899954	-0.1501579911863904	-2.4760687007512083

simplify13.0ms

Iterations

Iter	Nodes
done	44
1	44
0	33

end0.0ms

sample12.9s

Algorithm

intervals

Results

6.5s	1561×	body	2560	valid
3.7s	2812×	body	1280	valid
1.8s	1804×	body	640	valid
483.0ms	952×	body	320	valid
141.0ms	500×	body	160	valid
60.0ms	371×	body	80	valid