Details

sample49.0ms

Algorithm

intervals

Results

11.0ms	199×	body	80	valid
9.0ms	2×	body	640	valid
7.0ms	21×	body	2560	valid
4.0ms	11×	body	5120	valid
3.0ms	14×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify33.0ms

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: 11.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.0b	(hypot re im)
0.7b	(+ re (hypot re im))

rewrite16.0ms

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:

8.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
0.0ms	(hypot re im)
6.0ms	(+ re (hypot re im))

series455.0ms

Counts

3 → 9

Calls

3 calls:

271.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
71.0ms	(hypot re im)
113.0ms	(+ re (hypot re im))

simplify5.1s

Counts

51 → 51

Iterations

Useful iterations: 4 (2.7s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	459	354
3	1221	345
4	3261	344
done	5001	344

prune251.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.3b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`pow1`
22×	`sqrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`sqrt-pow1`
10×	`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` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

3.0ms	(sqrt (hypot re im))
15.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
28.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
12.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series603.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (hypot re im))
321.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
80.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
91.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify3.2s

Counts

109 → 109

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	143	1359
1	308	755
2	807	698
3	2369	668
done	5000	658

prune344.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
6.4b	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

rewrite27.0ms

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))
13.0ms	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
157.0ms	(cbrt (hypot re im))
158.0ms	(cbrt (hypot re im))
152.0ms	(+ 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

prune421.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.6b	(cbrt (sqrt (hypot re im)))
0.6b	(cbrt (sqrt (hypot re im)))
7.3b	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `pow1/3`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (sqrt (hypot re im)))
3.0ms	(cbrt (sqrt (hypot re im)))
12.0ms	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (hypot re im))
223.0ms	(cbrt (sqrt (hypot re im)))
182.0ms	(cbrt (sqrt (hypot re im)))
161.0ms	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))))

simplify2.3s

Counts

73 → 73

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	110	1048
1	251	880
2	730	791
3	2494	765
done	5000	759

prune462.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.2b

regimes203.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.3b and baseline of 13.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	12	10
done	12	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

972.0ms	5987×	body	80	valid
487.0ms	702×	body	2560	valid
265.0ms	496×	body	1280	valid
137.0ms	288×	body	5120	valid
79.0ms	297×	body	640	valid
35.0ms	160×	body	320	valid
9.0ms	70×	body	160	valid