Details

sample124.0ms

Algorithm

intervals

Results

47.0ms	48×	body	2560	valid
24.0ms	52×	body	640	valid
22.0ms	42×	body	1280	valid
6.0ms	27×	body	320	valid
5.0ms	68×	body	80	valid
3.0ms	19×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize19.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

9.0ms	(- 1.0 (cos x))
29.0ms	(/ (- 1.0 (cos x)) (* x x))

series98.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
78.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify859.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1129
1	232
0	88

prune270.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.1b	(- 1.0 (cos x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 114

Calls

3 calls:

45.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
20.0ms	(/ (- 1.0 (cos x)) x)
8.0ms	(- 1.0 (cos x))

series128.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
53.0ms	(/ (- 1.0 (cos x)) x)
21.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

123 → 123

Iterations

Iter	Nodes
done	5001
2	3248
1	546
0	189

prune508.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
0.5b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 139

Calls

4 calls:

6.0ms	(pow (cos x) 3)
107.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
5.0ms	(+ 1.0 (cos x))
22.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series364.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (cos x) 3)
245.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
11.0ms	(+ 1.0 (cos x))
69.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.4s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	3398
1	634
0	219

prune733.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (cos x) (* (cos x) (cos x))) (* (* (cos x) (* (cos x) (cos x))) (* (cos x) (* (cos x) (cos x))))))
0.4b	(/ (- (pow 1.0 3) (cbrt (* (* (cos x) (* (cos x) (cos x))) (* (* (cos x) (* (cos x) (cos x))) (* (cos x) (* (cos x) (cos x))))))) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
0.5b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (cbrt (* (* (cos x) (* (cos x) (cos x))) (* (* (cos x) (* (cos x) (cos x))) (* (cos x) (* (cos x) (cos x)))))))

rewrite520.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
17×	`associate-*r/`
14×	`*-un-lft-identity`
12×	`cos-mult` `difference-of-squares`
9×	`add-cbrt-cube` `add-exp-log`
8×	`times-frac` `associate-/l*` `add-log-exp`
7×	`cbrt-div`
6×	`add-cube-cbrt`
5×	`frac-times` `associate-*l/`
4×	`pow1` `cube-unmult`
3×	`unpow-prod-down` `cube-prod` `distribute-lft-out--` `sqr-pow`
2×	`cbrt-undiv` `flip3-+` `flip3--` `div-exp` `pow-prod-down` `associate-/r/` `rem-cbrt-cube` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-prod` `+-commutative` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `pow1/3` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 83

Calls

4 calls:

432.0ms	(cbrt (* (* (cos x) (* (cos x) (cos x))) (* (* (cos x) (* (cos x) (cos x))) (* (cos x) (* (cos x) (cos x))))))
54.0ms	(/ (- (pow 1.0 3) (cbrt (* (* (cos x) (* (cos x) (cos x))) (* (* (cos x) (* (cos x) (cos x))) (* (cos x) (* (cos x) (cos x))))))) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
5.0ms	(+ 1.0 (cos x))
26.0ms	(- (pow 1.0 3) (cbrt (* (* (cos x) (* (cos x) (cos x))) (* (* (cos x) (* (cos x) (cos x))) (* (cos x) (* (cos x) (cos x)))))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(cbrt (* (* (cos x) (* (cos x) (cos x))) (* (* (cos x) (* (cos x) (cos x))) (* (cos x) (* (cos x) (cos x))))))
272.0ms	(/ (- (pow 1.0 3) (cbrt (* (* (cos x) (* (cos x) (cos x))) (* (* (cos x) (* (cos x) (cos x))) (* (cos x) (* (cos x) (cos x))))))) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
11.0ms	(+ 1.0 (cos x))
64.0ms	(- (pow 1.0 3) (cbrt (* (* (cos x) (* (cos x) (cos x))) (* (* (cos x) (* (cos x) (cos x))) (* (cos x) (* (cos x) (cos x)))))))

simplify2.5s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	3229
1	554
0	201

prune638.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes180.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch88.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.033302914266201536
8	-0.9341403346610884	-0.003292329160956242	-0.037051728393040065

simplify13.0ms

Iterations

Iter	Nodes
done	52
2	52
1	51
0	37

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	1623×	body	2560	valid
941.0ms	1237×	body	1280	valid
651.0ms	1505×	body	640	valid
182.0ms	923×	body	320	valid
134.0ms	2205×	body	80	valid
65.0ms	507×	body	160	valid