Details

sample274.0ms

Algorithm

intervals

Results

123.0ms	51×	body	2560	valid
100.0ms	87×	body	1280	valid
23.0ms	52×	body	640	valid
11.0ms	36×	body	320	valid
3.0ms	15×	body	160	valid
2.0ms	15×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize19.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

14.0ms	(/ (- 1.0 (cos x)) (sin x))
9.0ms	(- 1.0 (cos x))

series108.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(/ (- 1.0 (cos x)) (sin x))
27.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	1941
2	596
1	240
0	106

prune313.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.3b	(* (cos x) (cos x))
0.6b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.2b	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
3×	`sqr-cos`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`difference-cubes` `+-commutative` `associate-+l+` `sum-log` `sub-neg` `flip3-+` `distribute-rgt-out` `flip3--` `diff-log` `cube-unmult` `pow3` `flip-+` `flip--`

Counts

4 → 80

Calls

4 calls:

14.0ms	(* (cos x) (cos x))
13.0ms	(* (cos x) (cos x))
10.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
23.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (cos x) (cos x))
26.0ms	(* (cos x) (cos x))
65.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
68.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

simplify2.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
3	4007
2	1234
1	336
0	115

prune523.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.4b	(+ 1/2 (* 1/2 (cos (* 2 x))))
0.6b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.2b	(- (* 1.0 (* 1.0 1.0)) (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (cos x)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt` `add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`+-commutative` `sqr-cos` `sum-log` `flip3-+` `flip-+`
1×	`pow2` `associate-+l+` `sub-neg` `pow-plus` `distribute-rgt-out` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

15.0ms	(* (cos x) (cos x))
18.0ms	(+ 1/2 (* 1/2 (cos (* 2 x))))
20.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
19.0ms	(- (* 1.0 (* 1.0 1.0)) (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (cos x)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (cos x) (cos x))
48.0ms	(+ 1/2 (* 1/2 (cos (* 2 x))))
63.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
145.0ms	(- (* 1.0 (* 1.0 1.0)) (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (cos x)))

simplify1.7s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
2	1526
1	408
0	140

prune576.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize135.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.6b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.2b	(- (* 1.0 (* 1.0 1.0)) (* (/ (+ (* (* (cos (+ x x)) (* (cos (+ x x)) (cos (+ x x)))) 1/8) 1/8) (+ 1/4 (* 1/4 (- (* (cos (+ x x)) (cos (+ x x))) (cos (+ x x)))))) (cos x)))
1.4b	(- (* (cos (+ x x)) (cos (+ x x))) (cos (+ x x)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1`
10×	`add-log-exp`
9×	`*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`sqr-cos` `swap-sqr` `associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `associate--r-`
1×	`pow2` `+-commutative` `associate-+l+` `cos-sum` `sum-log` `flip3-+` `pow-plus` `distribute-rgt-out` `distribute-rgt-out--` `count-2` `pow-prod-down` `prod-exp` `associate--l+` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `cos-2` `difference-of-squares` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

8.0ms	(* (cos x) (cos x))
11.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
74.0ms	(- (* 1.0 (* 1.0 1.0)) (* (/ (+ (* (* (cos (+ x x)) (* (cos (+ x x)) (cos (+ x x)))) 1/8) 1/8) (+ 1/4 (* 1/4 (- (* (cos (+ x x)) (cos (+ x x))) (cos (+ x x)))))) (cos x)))
40.0ms	(- (* (cos (+ x x)) (cos (+ x x))) (cos (+ x x)))

series687.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cos x) (cos x))
44.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
535.0ms	(- (* 1.0 (* 1.0 1.0)) (* (/ (+ (* (* (cos (+ x x)) (* (cos (+ x x)) (cos (+ x x)))) 1/8) 1/8) (+ 1/4 (* 1/4 (- (* (cos (+ x x)) (cos (+ x x))) (cos (+ x x)))))) (cos x)))
89.0ms	(- (* (cos (+ x x)) (cos (+ x x))) (cos (+ x x)))

simplify2.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1695
1	483
0	173

prune575.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes379.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.0b

bsearch154.0ms

Steps

Iters	Range		Point
8	0.0004390994911134099	0.778402845272117	0.020699439208913106
9	-0.1501579911863904	-8.136897775944376e-09	-0.022603209657985585

simplify22.0ms

Iterations

Iter	Nodes
done	84
1	84
0	59

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.5s	1546×	body	2560	valid
2.4s	2829×	body	1280	valid
1.3s	1797×	body	640	valid
257.0ms	958×	body	320	valid
202.0ms	495×	body	160	valid
73.0ms	370×	body	80	valid
25.0ms	5×	body	5120	valid