Details

sample220.0ms

Algorithm

intervals

Results

101.0ms	178×	body	1280	valid
75.0ms	128×	body	640	valid
16.0ms	56×	body	320	valid
10.0ms	147×	body	80	valid
2.0ms	15×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.8b

localize39.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))
3.5b	(- (exp (- 0 im)) (exp im))

rewrite370.0ms

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:

243.0ms	(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))
115.0ms	(- (exp (- 0 im)) (exp im))

series198.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))
74.0ms	(- (exp (- 0 im)) (exp im))

simplify3.2s

Counts

192 → 192

Iterations

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

prune446.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (pow im 5) -1/60) (+ im im))
0.0b	(* (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))))

rewrite107.0ms

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:

31.0ms	(- (* (pow im 5) -1/60) (+ im im))
14.0ms	(* (pow im 5) -1/60)
35.0ms	(* (* im im) im)
22.0ms	(* (* 0.5 (cos re)) (fma -1/3 (* (* im im) im) (- (* (pow im 5) -1/60) (+ im im))))

series638.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(- (* (pow im 5) -1/60) (+ im im))
83.0ms	(* (pow im 5) -1/60)
62.0ms	(* (* im im) im)
272.0ms	(* (* 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

prune716.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -1/3 (* (* im im) im)) (* 0.5 (cos re)))
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))))

rewrite786.0ms

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:

276.0ms	(* (* -1/3 (* (* im im) im)) (* 0.5 (cos re)))
392.0ms	(* (* im im) im)
89.0ms	(* -1/3 (* (* im im) im))
26.0ms	(* (* 0.5 (cos re)) (fma -2 im (* -1/60 (pow im 5))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (* -1/3 (* (* im im) im)) (* 0.5 (cos re)))
65.0ms	(* (* im im) im)
41.0ms	(* -1/3 (* (* im im) im))
364.0ms	(* (* 0.5 (cos re)) (fma -2 im (* -1/60 (pow im 5))))

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	5003
2	1622
1	434
0	163

prune740.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize117.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt im)
0.6b	(cbrt im)
0.6b	(cbrt im)
59.1b	(fma (- (+ (cbrt im) (cbrt im))) (* (cbrt im) (cbrt im)) (* (+ (cbrt im) (cbrt im)) (* (cbrt im) (cbrt im))))

rewrite4.0ms

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)
0.0ms	(fma (- (+ (cbrt im) (cbrt im))) (* (cbrt im) (cbrt im)) (* (+ (cbrt im) (cbrt im)) (* (cbrt im) (cbrt im))))

series1.9s

Counts

4 → 12

Calls

4 calls:

341.0ms	(cbrt im)
299.0ms	(cbrt im)
360.0ms	(cbrt im)
889.0ms	(fma (- (+ (cbrt im) (cbrt im))) (* (cbrt im) (cbrt im)) (* (+ (cbrt im) (cbrt im)) (* (cbrt im) (cbrt im))))

simplify7.7s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
4	4173
3	693
2	192
1	76
0	43

prune572.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes547.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample9.9s

Algorithm

intervals

Results

5.1s	5666×	body	1280	valid
2.3s	3485×	body	640	valid
1.3s	4287×	body	80	valid
610.0ms	1494×	body	320	valid
191.0ms	714×	body	160	valid