Details

sample265.0ms

Algorithm

intervals

Results

142.0ms	203×	body	1280	valid
78.0ms	108×	body	640	valid
12.0ms	145×	body	80	valid
10.0ms	42×	body	320	valid
4.0ms	21×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	2308
6	1015
5	490
4	246
3	106
2	46
1	22
0	11

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.0b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))
5.1b	(- (exp (- 0 im)) (exp im))

rewrite232.0ms

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-cbrt-cube` `add-exp-log`
5×	`associate-r`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `associate-*r/` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `associate-l` `*-commutative`

Counts

2 → 186

Calls

2 calls:

133.0ms	(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))
94.0ms	(- (exp (- 0 im)) (exp im))

series180.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))
63.0ms	(- (exp (- 0 im)) (exp im))

simplify3.1s

Counts

192 → 192

Iterations

Iter	Nodes
done	5000
3	4958
2	1647
1	763
0	286

prune449.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1`
20×	`add-sqr-sqrt`
19×	`add-exp-log`
16×	`*-un-lft-identity` `add-cbrt-cube`
14×	`add-cube-cbrt`
12×	`prod-diff`
9×	`associate-r` `associate-l` `prod-exp` `add-log-exp`
7×	`cbrt-unprod`
6×	`pow-plus` `pow-prod-down` `pow-prod-up`
4×	`expm1-log1p-u` `unpow-prod-down` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`distribute-rgt-out` `*-commutative` `distribute-lft-out`
2×	`pow2` `diff-log` `pow-sqr` `fma-udef` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `sum-log` `sub-neg` `distribute-lft-in` `distribute-lft1-in` `flip3--` `count-2` `fma-neg` `pow3` `distribute-rgt1-in` `pow-exp` `flip--` `associate--r+`

Counts

4 → 112

Calls

4 calls:

32.0ms	(- (* (pow im 5) -1/60) (+ im im))
18.0ms	(* (pow im 5) -1/60)
33.0ms	(* (* im im) im)
19.0ms	(* (* 0.5 (cos re)) (fma -1/3 (* (* im im) im) (- (* (pow im 5) -1/60) (+ im im))))

series570.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(- (* (pow im 5) -1/60) (+ im im))
74.0ms	(* (pow im 5) -1/60)
59.0ms	(* (* im im) im)
247.0ms	(* (* 0.5 (cos re)) (fma -1/3 (* (* im im) im) (- (* (pow im 5) -1/60) (+ im im))))

simplify1.8s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1738
1	578
0	230

prune678.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

69×	`pow1`
55×	`add-cbrt-cube` `add-exp-log`
36×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `associate-r`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus` `associate-l` `pow-prod-up`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `pow3` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

158.0ms	(* (* 0.5 (cos re)) (* -1/3 (* (* im im) im)))
33.0ms	(* (* im im) im)
72.0ms	(* -1/3 (* (* im im) im))
39.0ms	(* (* 0.5 (cos re)) (fma -2 im (* -1/60 (pow im 5))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (* 0.5 (cos re)) (* -1/3 (* (* im im) im)))
38.0ms	(* (* im im) im)
59.0ms	(* -1/3 (* (* im im) im))
388.0ms	(* (* 0.5 (cos re)) (fma -2 im (* -1/60 (pow im 5))))

simplify1.6s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1598
1	423
0	163

prune662.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt im)
0.7b	(cbrt im)
0.7b	(cbrt im)
58.2b	(fma (- (+ (* (cbrt im) (cbrt im)) (* (cbrt im) (cbrt im)))) (cbrt im) (* (+ (* (cbrt im) (cbrt im)) (* (cbrt im) (cbrt im))) (cbrt im)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt im)
1.0ms	(cbrt im)
1.0ms	(cbrt im)
1.0ms	(fma (- (+ (* (cbrt im) (cbrt im)) (* (cbrt im) (cbrt im)))) (cbrt im) (* (+ (* (cbrt im) (cbrt im)) (* (cbrt im) (cbrt im))) (cbrt im)))

series1.8s

Counts

4 → 12

Calls

4 calls:

308.0ms	(cbrt im)
241.0ms	(cbrt im)
309.0ms	(cbrt im)
921.0ms	(fma (- (+ (* (cbrt im) (cbrt im)) (* (cbrt im) (cbrt im)))) (cbrt im) (* (+ (* (cbrt im) (cbrt im)) (* (cbrt im) (cbrt im))) (cbrt im)))

simplify8.9s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
4	4124
3	670
2	186
1	76
0	43

prune557.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes393.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample9.9s

Algorithm

intervals

Results

5.4s	5732×	body	1280	valid
2.2s	3579×	body	640	valid
946.0ms	4441×	body	80	valid
835.0ms	1539×	body	320	valid
206.0ms	723×	body	160	valid