Details

sample174.0ms

Algorithm

intervals

Results

22.0ms	186×	body	80	valid
20.0ms	30×	body	2560	valid
10.0ms	17×	body	1280	valid
9.0ms	12×	body	5120	valid
2.0ms	5×	body	320	valid
2.0ms	6×	body	640	valid

simplify68.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	44
5	44
4	42
3	35
2	27
1	19
0	12

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.9b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (hypot re im) re)
0.0b	(hypot re im)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`hypot-udef` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

11.0ms	(- (hypot re im) re)
2.0ms	(hypot re im)

series207.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(- (hypot re im) re)
99.0ms	(hypot re im)

simplify912.0ms

Counts

46 → 46

Iterations

Iter	Nodes
4	2090
3	705
2	233
1	127
0	71

prune375.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(hypot re im)
0.0b	(hypot re im)
17.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`hypot-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
0.0ms	(hypot re im)
0.0ms	(hypot re im)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series468.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt (hypot re im))
63.0ms	(hypot re im)
74.0ms	(hypot re im)
218.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify1.3s

Counts

61 → 61

Iterations

Iter	Nodes
4	2514
3	819
2	300
1	137
0	73

prune729.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
0.4b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
17.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
17.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

2.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
24.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series928.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
232.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
235.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
222.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify4.0s

Counts

102 → 102

Iterations

Iter	Nodes
4	7512
3	1418
2	453
1	185
0	96

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt (hypot re im)))
0.2b	(sqrt (sqrt (hypot re im)))
0.6b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
17.1b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

86×	`sqrt-prod`
54×	`add-sqr-sqrt`
40×	`sqrt-pow1`
31×	`pow1`
20×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 133

Calls

4 calls:

2.0ms	(sqrt (sqrt (hypot re im)))
2.0ms	(sqrt (sqrt (hypot re im)))
13.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

series654.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(sqrt (sqrt (hypot re im)))
161.0ms	(sqrt (sqrt (hypot re im)))
133.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
190.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

simplify2.2s

Counts

145 → 145

Iterations

Iter	Nodes
4	3875
3	1424
2	579
1	275
0	136

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 14.7b

regimes238.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	11
1	11
0	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	6030×	body	80	valid
622.0ms	673×	body	2560	valid
316.0ms	291×	body	5120	valid
290.0ms	458×	body	1280	valid
171.0ms	284×	body	640	valid
64.0ms	187×	body	320	valid
18.0ms	77×	body	160	valid