Details

sample118.0ms

Algorithm

intervals

Results

15.0ms	191×	body	80	valid
10.0ms	22×	body	2560	valid
8.0ms	15×	body	5120	valid
5.0ms	15×	body	1280	valid
3.0ms	11×	body	640	valid
0.0ms	2×	body	320	valid

simplify99.0ms

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

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

series421.0ms

Counts

2 → 6

Calls

2 calls:

299.0ms	(sqrt (* (- (hypot re im) re) 2.0))
122.0ms	(- (hypot re im) re)

simplify2.1s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
3	3975
2	747
1	236
0	107

prune274.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.2b	(- (hypot re im) re)
0.3b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`sqrt-prod`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1` `associate-l`
6×	`associate-r`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `pow1/2` `fma-neg` `pow-prod-down` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 83

Calls

3 calls:

15.0ms	(sqrt (- (hypot re im) re))
5.0ms	(- (hypot re im) re)
21.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

series633.0ms

Counts

3 → 9

Calls

3 calls:

227.0ms	(sqrt (- (hypot re im) re))
105.0ms	(- (hypot re im) re)
301.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1394
1	362
0	159

prune502.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
16.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 53

Calls

4 calls:

2.0ms	(sqrt (hypot re im))
2.0ms	(sqrt (hypot re im))
6.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series1.2s

Counts

4 → 12

Calls

4 calls:

149.0ms	(sqrt (hypot re im))
139.0ms	(sqrt (hypot re im))
753.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
206.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.7s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	4704
2	756
1	204
0	94

prune440.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt (hypot re im)))
0.2b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
15.9b	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

rewrite30.0ms

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` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 129

Calls

4 calls:

2.0ms	(sqrt (sqrt (hypot re im)))
2.0ms	(sqrt (sqrt (hypot re im)))
22.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

series650.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(sqrt (sqrt (hypot re im)))
193.0ms	(sqrt (sqrt (hypot re im)))
105.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
154.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

simplify1.6s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	1203
1	287
0	133

prune588.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.8b

regimes309.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

627.0ms	6038×	body	80	valid
557.0ms	298×	body	640	valid
279.0ms	611×	body	2560	valid
250.0ms	531×	body	1280	valid
153.0ms	293×	body	5120	valid
31.0ms	140×	body	320	valid
12.0ms	89×	body	160	valid