Details

sample66.0ms

Algorithm

intervals

Results

17.0ms	198×	body	80	valid
7.0ms	11×	body	5120	valid
7.0ms	17×	body	1280	valid
7.0ms	13×	body	2560	valid
3.0ms	8×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	30	10
3	32	10
done	32	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (+ re (hypot re im)) 2.0))
1.1b	(+ re (hypot re im))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`add-exp-log` `expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `hypot-udef` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

3 → 42

Calls

3 calls:

0.0ms	(hypot re im)
24.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
10.0ms	(+ re (hypot re im))

series440.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(hypot re im)
284.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
84.0ms	(+ re (hypot re im))

simplify5.0s

Counts

51 → 51

Iterations

Useful iterations: 4 (2.4s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	459	354
3	1219	345
4	3260	344
done	5001	344

prune214.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.7b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`pow1`
19×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1`
9×	`pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-sqr`
2×	`flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `pow2` `hypot-udef` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 92

Calls

4 calls:

1.0ms	(hypot re im)
16.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
22.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
6.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(hypot re im)
263.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
60.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
97.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify2.7s

Counts

104 → 104

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	129	1271
1	260	679
2	684	634
3	2064	608
done	5000	597

prune356.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
6.5b	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-prod` `associate-r` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `associate-l`
2×	`pow1/3` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 66

Calls

4 calls:

10.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
7.0ms	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
177.0ms	(cbrt (hypot re im))
161.0ms	(cbrt (hypot re im))
193.0ms	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

simplify3.4s

Counts

78 → 78

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	132	1125
1	321	1047
2	1025	910
3	3860	865
done	5000	861

prune484.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
7.7b	(+ re (* (* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (hypot re im)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `associate-r` `sqrt-prod` `add-cbrt-cube`
6×	`cbrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `associate-l` `sum-log` `*-commutative` `flip-+`

Counts

4 → 68

Calls

4 calls:

43.0ms	(* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
7.0ms	(+ re (* (* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (hypot re im)))))

series675.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
180.0ms	(cbrt (hypot re im))
175.0ms	(cbrt (hypot re im))
152.0ms	(+ re (* (* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (hypot re im)))))

simplify3.6s

Counts

80 → 80

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	143	1503
1	369	1144
2	1191	969
3	4569	916
done	5000	912

prune482.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.9b

regimes151.0ms

Accuracy

43.3% (0.8b remaining)

Error of 13.7b against oracle of 12.9b and baseline of 14.3b

bsearch113.0ms

Steps

Iters	Range		Point
8	-2.9045277458302067e+170	-1.141419347192945e+166	-1.7266820139992573e+170

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	32
1	26	32
done	26	32

end0.0ms

sample2.2s

Algorithm

intervals

Results

821.0ms	698×	body	2560	valid
549.0ms	6055×	body	80	valid
179.0ms	280×	body	5120	valid
155.0ms	495×	body	1280	valid
102.0ms	255×	body	640	valid
60.0ms	137×	body	320	valid
9.0ms	80×	body	160	valid