Details

sample236.0ms

Algorithm

intervals

Results

19.0ms	189×	body	80	valid
13.0ms	21×	body	2560	valid
9.0ms	21×	body	1280	valid
6.0ms	9×	body	5120	valid
3.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify124.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

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:

1.0ms	(hypot re im)
21.0ms	(sqrt (* (- (hypot re im) re) 2.0))
18.0ms	(- (hypot re im) re)

series632.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(hypot re im)
367.0ms	(sqrt (* (- (hypot re im) re) 2.0))
161.0ms	(- (hypot re im) re)

simplify3.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
3	1705
2	559
1	243
0	115

prune487.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.5b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite84.0ms

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:

0.0ms	(hypot re im)
32.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
28.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
18.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series674.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(hypot re im)
380.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
83.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
118.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify3.7s

Counts

107 → 107

Iterations

Iter	Nodes
done	5002
3	2373
2	806
1	331
0	152

prune764.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt (hypot re im)))
0.3b	(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
0.3b	(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
12.4b	(- (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) re)

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

50×	`sqrt-pow1`
47×	`pow1`
43×	`sqrt-prod`
35×	`add-sqr-sqrt`
32×	`pow-prod-up`
28×	`pow1/2`
18×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down`
7×	`associate-l`
6×	`pow3` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sqrt-unprod` `prod-diff`
2×	`rem-sqrt-square` `pow-plus` `*-commutative`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 129

Calls

4 calls:

5.0ms	(sqrt (sqrt (hypot re im)))
83.0ms	(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
35.0ms	(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
104.0ms	(- (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) re)

series680.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(sqrt (sqrt (hypot re im)))
87.0ms	(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
252.0ms	(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
114.0ms	(- (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) re)

simplify5.5s

Counts

141 → 141

Iterations

Iter	Nodes
done	5001
3	3713
2	1089
1	412
0	174

prune983.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.3b

localize100.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (fabs (cbrt (sqrt (hypot re im)))))
0.5b	(cbrt (sqrt (hypot re im)))
0.5b	(cbrt (sqrt (hypot re im)))
11.5b	(- (* (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (fabs (cbrt (sqrt (hypot re im))))) (sqrt (cbrt (sqrt (hypot re im))))) re)

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

84.0ms	(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (fabs (cbrt (sqrt (hypot re im)))))
3.0ms	(cbrt (sqrt (hypot re im)))
3.0ms	(cbrt (sqrt (hypot re im)))
308.0ms	(- (* (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (fabs (cbrt (sqrt (hypot re im))))) (sqrt (cbrt (sqrt (hypot re im))))) re)

series1.0s

Counts

4 → 12

Calls

4 calls:

296.0ms	(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (fabs (cbrt (sqrt (hypot re im)))))
237.0ms	(cbrt (sqrt (hypot re im)))
212.0ms	(cbrt (sqrt (hypot re im)))
275.0ms	(- (* (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (fabs (cbrt (sqrt (hypot re im))))) (sqrt (cbrt (sqrt (hypot re im))))) re)

simplify5.2s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
3	3557
2	1073
1	396
0	164

prune980.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.3b

regimes345.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	5979×	body	80	valid
672.0ms	730×	body	2560	valid
325.0ms	500×	body	1280	valid
209.0ms	306×	body	5120	valid
155.0ms	279×	body	640	valid
32.0ms	133×	body	320	valid
12.0ms	73×	body	160	valid