Details

sample133.0ms

Algorithm

intervals

Results

17.0ms	196×	body	80	valid
11.0ms	21×	body	2560	valid
6.0ms	14×	body	1280	valid
6.0ms	9×	body	5120	valid
4.0ms	7×	body	320	valid
3.0ms	8×	body	640	valid
0.0ms	1×	body	160	valid

simplify74.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	36	10
4	43	10
5	45	10
done	45	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)
0.1b	(- (hypot re im) re)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`add-exp-log` `expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-*l/` `flip--`
1×	`sub-neg` `hypot-udef` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 53

Calls

3 calls:

18.0ms	(sqrt (* (- (hypot re im) re) 2.0))
1.0ms	(hypot re im)
19.0ms	(- (hypot re im) re)

series478.0ms

Counts

3 → 9

Calls

3 calls:

291.0ms	(sqrt (* (- (hypot re im) re) 2.0))
71.0ms	(hypot re im)
116.0ms	(- (hypot re im) re)

simplify2.4s

Counts

62 → 62

Iterations

Useful iterations: 3 (933.0ms)

Iter	Nodes	Cost
0	115	686
1	244	575
2	772	498
3	4052	454
done	5000	454

prune304.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
0.4b	(cbrt (- (hypot re im) re))
0.4b	(cbrt (- (hypot re im) re))
0.4b	(cbrt (- (hypot re im) re))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

62.0ms	(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
4.0ms	(cbrt (- (hypot re im) re))
4.0ms	(cbrt (- (hypot re im) re))
4.0ms	(cbrt (- (hypot re im) re))

series982.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
226.0ms	(cbrt (- (hypot re im) re))
253.0ms	(cbrt (- (hypot re im) re))
269.0ms	(cbrt (- (hypot re im) re))

simplify1.0s

Counts

121 → 121

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	149	1928
1	330	1783
2	1238	1691
done	5001	1586

prune593.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.8b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

26×	`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×	`prod-diff` `pow-sqr`
2×	`flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`pow2` `sub-neg` `hypot-udef` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

1.0ms	(hypot re im)
38.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
26.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
28.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series515.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(hypot re im)
277.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
64.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
90.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.3s

Counts

107 → 107

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	152	1374
1	339	755
2	1349	687
done	5001	670

prune373.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
5.2b	(- (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

11.0ms	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
52.0ms	(- (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

series597.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
145.0ms	(cbrt (hypot re im))
174.0ms	(cbrt (hypot re im))
150.0ms	(- (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

simplify1.1s

Counts

80 → 80

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	147	1230
1	368	1160
2	1491	1016
done	5001	990

prune486.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.7b

regimes175.0ms

Accuracy

0% (0.2b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	11	10
done	11	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

662.0ms	6009×	body	80	valid
496.0ms	276×	body	640	valid
334.0ms	681×	body	2560	valid
261.0ms	486×	body	1280	valid
167.0ms	306×	body	5120	valid
34.0ms	166×	body	320	valid
10.0ms	76×	body	160	valid