Details

sample249.0ms

Algorithm

intervals

Results

125.0ms	53×	body	2560	valid
65.0ms	79×	body	1280	valid
29.0ms	65×	body	640	valid
9.0ms	27×	body	320	valid
5.0ms	20×	body	160	valid
2.0ms	12×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 1.0 (cos x))

rewrite67.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

53.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(- 1.0 (cos x))

series70.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify3.1s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	106	665
1	235	645
2	531	609
3	1194	609
4	3136	608
done	5000	608

prune271.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`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×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

27.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
23.0ms	(* 1/240 (pow x 5))
17.0ms	(* 1/24 (pow x 3))

series169.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
55.0ms	(* 1/240 (pow x 5))
52.0ms	(* 1/24 (pow x 3))

simplify4.3s

Counts

78 → 78

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	123	847
1	305	750
2	952	704
3	4946	704
done	5000	704

prune282.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.8b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

117.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
6.0ms	(pow (cos x) 3)
13.0ms	(+ (cos x) 1.0)
31.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series348.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
59.0ms	(pow (cos x) 3)
19.0ms	(+ (cos x) 1.0)
72.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.5s

Counts

201 → 201

Iterations

Useful iterations: 2 (474.0ms)

Iter	Nodes	Cost
0	264	5407
1	611	5084
2	2038	4978
done	5000	4978

prune701.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.8b	(- (pow 1.0 3) (pow (cos x) 3))
1.9b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
32×	`difference-of-squares`
31×	`*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
26×	`log-pow`
25×	`exp-prod`
17×	`sqr-pow`
10×	`distribute-lft-out--`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `log-prod` `add-cbrt-cube`
3×	`pow-unpow`
2×	`difference-cubes` `sub-neg` `exp-sum`
1×	`+-commutative` `cube-mult` `pow-to-exp` `log-div` `flip3--` `pow-pow` `flip3-+` `exp-diff` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 109

Calls

4 calls:

4.0ms	(pow (cos x) 3)
7.0ms	(+ (cos x) 1.0)
39.0ms	(- (pow 1.0 3) (pow (cos x) 3))
98.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series181.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow (cos x) 3)
11.0ms	(+ (cos x) 1.0)
65.0ms	(- (pow 1.0 3) (pow (cos x) 3))
60.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify979.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (213.0ms)

Iter	Nodes	Cost
0	169	1422
1	347	1208
2	959	1152
done	5000	1152

prune490.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes218.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.6b

bsearch113.0ms

Steps

Iters	Range		Point
9	0.0030847216915828425	5729.342694487068	0.021960105445277742
11	-30636816361710.875	-9.292394687435822e-10	-0.021208012362493478

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	30	85
1	42	55
done	42	55

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.5s	1572×	body	2560	valid
2.4s	2712×	body	1280	valid
2.0s	1918×	body	640	valid
422.0ms	940×	body	320	valid
99.0ms	484×	body	160	valid
44.0ms	369×	body	80	valid
23.0ms	5×	body	5120	valid