Details

sample299.0ms

Algorithm

intervals

Results

181.0ms	208×	body	1280	valid
52.0ms	109×	body	640	valid
16.0ms	50×	body	320	valid
13.0ms	133×	body	80	valid
5.0ms	23×	body	160	valid

simplify8.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	12
1	21	12
2	44	12
3	104	12
4	209	12
5	305	12
6	451	12
7	524	12
8	785	12
9	1485	12
10	1940	12
11	1978	12
12	2019	12
done	2019	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.4b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
5.4b	(- (exp (- 0.0 im)) (exp im))

rewrite407.0ms

Algorithm

rewrite-expression-head

Rules

216×	`prod-diff`
119×	`add-sqr-sqrt` `*-un-lft-identity`
115×	`add-cube-cbrt`
110×	`exp-sum`
44×	`distribute-rgt-in` `distribute-lft-in`
14×	`fma-neg`
13×	`sub-neg`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-r`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `associate-l` `*-commutative`

Counts

2 → 184

Calls

2 calls:

235.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
142.0ms	(- (exp (- 0.0 im)) (exp im))

series172.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
54.0ms	(- (exp (- 0.0 im)) (exp im))

simplify1.7s

Counts

190 → 190

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	284	7174
1	631	4912
2	1555	3505
done	5000	2656

prune413.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))
0.1b	(* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-r`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef`
2×	`expm1-log1p-u` `distribute-neg-in` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `neg-mul-1` `distribute-lft-in` `associate-l` `*-commutative` `distribute-rgt-neg-out`

Counts

2 → 40

Calls

2 calls:

0.0ms	(fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))
40.0ms	(* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))

series323.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))
243.0ms	(* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))

simplify1.2s

Counts

46 → 46

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	101	998
1	273	969
2	1082	835
done	5001	828

prune284.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b

(fma (* 0.008333333333333333 (pow im 5)) (cos re) (* (cos re) (fma 0.16666666666666666 (pow im 3) (* 1.0 im))))

0.1b

(* 0.008333333333333333 (pow im 5))

0.1b

(* (cos re) (fma 0.16666666666666666 (pow im 3) (* 1.0 im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `associate-r`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
6×	`associate-l`
5×	`pow1`
4×	`unpow-prod-down` `prod-exp` `unswap-sqr`
3×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `cbrt-unprod` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-prod-down` `pow-exp`

Counts

3 → 59

Calls

3 calls:

1.0ms

(fma (* 0.008333333333333333 (pow im 5)) (cos re) (* (cos re) (fma 0.16666666666666666 (pow im 3) (* 1.0 im))))

29.0ms

(* 0.008333333333333333 (pow im 5))

16.0ms

(* (cos re) (fma 0.16666666666666666 (pow im 3) (* 1.0 im)))

series421.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms

(fma (* 0.008333333333333333 (pow im 5)) (cos re) (* (cos re) (fma 0.16666666666666666 (pow im 3) (* 1.0 im))))

79.0ms

(* 0.008333333333333333 (pow im 5))

220.0ms

(* (cos re) (fma 0.16666666666666666 (pow im 3) (* 1.0 im)))

simplify2.4s

Counts

68 → 68

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	119	909
1	244	877
2	722	769
3	2560	747
done	5002	737

prune334.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))) (cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))
0.7b	(cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))
0.7b	(cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))
0.7b	(cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

78×	`cbrt-prod`
37×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
29×	`add-cube-cbrt`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
15×	`swap-sqr`
13×	`associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3`
7×	`neg-mul-1`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 125

Calls

4 calls:

25.0ms	(* (cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))) (cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))
4.0ms	(cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))
14.0ms	(cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))
4.0ms	(cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

293.0ms	(* (cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))) (cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))
291.0ms	(cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))
300.0ms	(cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))
262.0ms	(cbrt (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))

simplify2.8s

Counts

137 → 137

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	186	4656
1	401	4439
2	1174	4218
3	4395	3624
done	5000	3623

prune864.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes405.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	20
1	19	20
done	19	20

end0.0ms

sample10.3s

Algorithm

intervals

Results

5.8s	5696×	body	1280	valid
2.7s	3615×	body	640	valid
496.0ms	4293×	body	80	valid
456.0ms	1524×	body	320	valid
165.0ms	694×	body	160	valid