Details

sample227.0ms

Algorithm

intervals

Results

103.0ms	190×	body	80	valid
9.0ms	19×	body	2560	valid
8.0ms	13×	body	5120	valid
7.0ms	16×	body	1280	valid
4.0ms	8×	body	320	valid
2.0ms	8×	body	640	valid
0.0ms	2×	body	160	valid

simplify74.0ms

Counts

1 → 1

Iterations

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

prune59.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))
1.2b	(- (hypot re im) re)

rewrite96.0ms

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

Counts

3 → 53

Calls

3 calls:

0.0ms	(hypot re im)
17.0ms	(sqrt (* (- (hypot re im) re) 2.0))
17.0ms	(- (hypot re im) re)

series604.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(hypot re im)
321.0ms	(sqrt (* (- (hypot re im) re) 2.0))
223.0ms	(- (hypot re im) re)

simplify1.9s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	4021
2	770
1	245
0	115

prune396.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (* (- (hypot re im) re) 2.0)))
1.2b	(- (hypot re im) re)
1.2b	(- (hypot re im) re)
1.2b	(- (hypot re im) re)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

14.0ms	(cbrt (sqrt (* (- (hypot re im) re) 2.0)))
10.0ms	(- (hypot re im) re)
10.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)

series718.0ms

Counts

4 → 12

Calls

4 calls:

478.0ms	(cbrt (sqrt (* (- (hypot re im) re) 2.0)))
76.0ms	(- (hypot re im) re)
75.0ms	(- (hypot re im) re)
88.0ms	(- (hypot re im) re)

simplify1.7s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	3866
2	827
1	275
0	135

prune652.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.6b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.2b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
15×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
10.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
14.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series460.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(sqrt (hypot re im))
155.0ms	(sqrt (hypot re im))
67.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
87.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.0s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	1140
1	290
0	124

prune506.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.3b	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
0.8b	(pow (sqrt (sqrt (hypot re im))) 3)
13.6b	(- (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

97×	`sqrt-prod`
71×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`-un-lft-identity` `associate-l*` `add-cube-cbrt` `unswap-sqr`
10×	`pow1` `add-exp-log`
9×	`associate-r`
8×	`sqrt-pow1`
7×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u`
3×	`pow-unpow` `prod-diff` `prod-exp`
2×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `unpow3` `pow-exp`
1×	`sub-neg` `pow-plus` `flip3--` `fma-neg` `diff-log` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqrt-pow2` `flip--` `rem-cube-cbrt`

Counts

4 → 154

Calls

4 calls:

4.0ms	(sqrt (sqrt (hypot re im)))
45.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
4.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
19.0ms	(- (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

series516.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(sqrt (sqrt (hypot re im)))
71.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
178.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
93.0ms	(- (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

simplify2.0s

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
2	2106
1	462
0	172

prune612.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 12.9b

regimes192.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

606.0ms	5986×	body	80	valid
475.0ms	303×	body	640	valid
473.0ms	707×	body	2560	valid
176.0ms	509×	body	1280	valid
152.0ms	290×	body	5120	valid
68.0ms	139×	body	320	valid
8.0ms	66×	body	160	valid