Details

sample221.0ms

Algorithm

intervals

Results

122.0ms	194×	body	1280	valid
52.0ms	108×	body	640	valid
10.0ms	39×	body	320	valid
10.0ms	125×	body	80	valid
4.0ms	23×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4672
5	686
4	186
3	99
2	44
1	21
0	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.2b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- (exp (- 0.0 im)) (exp im)) (cos re))
6.3b	(- (exp (- 0.0 im)) (exp im))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
5×	`associate-l`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
3×	`associate-r`
2×	`flip3--` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 36

Calls

2 calls:

189.0ms	(* (- (exp (- 0.0 im)) (exp im)) (cos re))
57.0ms	(- (exp (- 0.0 im)) (exp im))

series186.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(* (- (exp (- 0.0 im)) (exp im)) (cos re))
69.0ms	(- (exp (- 0.0 im)) (exp im))

simplify570.0ms

Counts

42 → 42

Iterations

Iter	Nodes
done	5000
2	647
1	191
0	85

prune231.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (pow im 3) -1/3) (+ (+ im im) (* (pow im 5) 1/60)))
0.0b	(* (pow im 5) 1/60)
0.1b	(* (- (* (pow im 3) -1/3) (+ (+ im im) (* (pow im 5) 1/60))) (cos re))
0.1b	(* (pow im 3) -1/3)

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`associate-l`
16×	`add-exp-log`
13×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
10×	`add-cbrt-cube`
9×	`associate-r`
8×	`unpow-prod-down` `unswap-sqr`
7×	`prod-exp`
6×	`pow1`
4×	`cube-prod` `sqr-pow`
3×	`sum-log` `diff-log` `*-commutative` `cbrt-unprod`
2×	`pow-to-exp` `flip3--` `associate-*l/` `pow-exp` `flip--`
1×	`cube-mult` `sub-neg` `unpow3` `pow-prod-down` `associate--r+`

Counts

4 → 91

Calls

4 calls:

67.0ms	(- (* (pow im 3) -1/3) (+ (+ im im) (* (pow im 5) 1/60)))
9.0ms	(* (pow im 5) 1/60)
201.0ms	(* (- (* (pow im 3) -1/3) (+ (+ im im) (* (pow im 5) 1/60))) (cos re))
19.0ms	(* (pow im 3) -1/3)

series386.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (pow im 3) -1/3) (+ (+ im im) (* (pow im 5) 1/60)))
97.0ms	(* (pow im 5) 1/60)
135.0ms	(* (- (* (pow im 3) -1/3) (+ (+ im im) (* (pow im 5) 1/60))) (cos re))
73.0ms	(* (pow im 3) -1/3)

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5002
2	1941
1	409
0	165

prune604.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos re)) (cbrt (cos re)))
0.3b	(cbrt (cos re))
0.3b	(cbrt (cos re))
0.3b	(cbrt (cos re))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

19.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
2.0ms	(cbrt (cos re))
2.0ms	(cbrt (cos re))
2.0ms	(cbrt (cos re))

series605.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
140.0ms	(cbrt (cos re))
127.0ms	(cbrt (cos re))
128.0ms	(cbrt (cos re))

simplify690.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	623
1	146
0	64

prune555.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (pow (cos re) 2) 1/3)
0.1b	(* (* (pow (pow (cos re) 2) 1/3) (- (- (- (* (pow im 3) -1/3) im) im) (* 1/60 (pow im 5)))) (cbrt (cos re)))
0.2b	(pow (cos re) 2)
0.3b	(cbrt (cos re))

rewrite654.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
14×	`unpow-prod-down`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`prod-exp`
9×	`pow-exp`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`cbrt-prod` `pow-unpow` `associate-r`
5×	`pow-to-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`sqr-pow`
2×	`pow-pow` `unpow1/3` `associate-l/` `associate-r/` `unpow2`
1×	`flip3--` `pow1/3` `associate-l` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 81

Calls

4 calls:

8.0ms	(pow (pow (cos re) 2) 1/3)
636.0ms	(* (* (pow (pow (cos re) 2) 1/3) (- (- (- (* (pow im 3) -1/3) im) im) (* 1/60 (pow im 5)))) (cbrt (cos re)))
5.0ms	(pow (cos re) 2)
2.0ms	(cbrt (cos re))

series696.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(pow (pow (cos re) 2) 1/3)
251.0ms	(* (* (pow (pow (cos re) 2) 1/3) (- (- (- (* (pow im 3) -1/3) im) im) (* 1/60 (pow im 5)))) (cbrt (cos re)))
32.0ms	(pow (cos re) 2)
132.0ms	(cbrt (cos re))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	2244
1	465
0	158

prune501.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample10.1s

Algorithm

intervals

Results

5.7s	5706×	body	1280	valid
2.5s	3622×	body	640	valid
509.0ms	4375×	body	80	valid
508.0ms	1417×	body	320	valid
128.0ms	697×	body	160	valid