Details

sample116.0ms

Algorithm

intervals

Results

18.0ms	186×	body	80	valid
13.0ms	26×	body	2560	valid
13.0ms	18×	body	5120	valid
6.0ms	15×	body	1280	valid
3.0ms	7×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify112.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (64.0ms)

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

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:

15.0ms	(sqrt (* (- (hypot re im) re) 2.0))
0.0ms	(hypot re im)
15.0ms	(- (hypot re im) re)

series360.0ms

Counts

3 → 9

Calls

3 calls:

199.0ms	(sqrt (* (- (hypot re im) re) 2.0))
56.0ms	(hypot re im)
104.0ms	(- (hypot re im) re)

simplify2.2s

Counts

62 → 62

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	115	686
1	245	575
2	770	498
3	4031	454
done	5000	453

prune392.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(log1p (sqrt (* (- (hypot re im) re) 2.0)))
0.2b	(- (hypot re im) re)
2.7b	(expm1 (log1p (sqrt (* (- (hypot re im) re) 2.0))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

0.0ms	(hypot re im)
1.0ms	(log1p (sqrt (* (- (hypot re im) re) 2.0)))
10.0ms	(- (hypot re im) re)
0.0ms	(expm1 (log1p (sqrt (* (- (hypot re im) re) 2.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

77.0ms	(hypot re im)
638.0ms	(log1p (sqrt (* (- (hypot re im) re) 2.0)))
82.0ms	(- (hypot re im) re)
696.0ms	(expm1 (log1p (sqrt (* (- (hypot re im) re) 2.0))))

simplify1.0s

Counts

72 → 72

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	156	961
1	375	832
2	1493	710
done	5001	680

prune424.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.5b	(cbrt (hypot re im))
0.7b	(pow (cbrt (hypot re im)) 3)
11.8b	(- (pow (cbrt (hypot re im)) 3) re)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
54×	`prod-diff`
50×	`*-un-lft-identity`
48×	`add-cube-cbrt`
35×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
18×	`fma-neg`
6×	`add-log-exp` `difference-of-squares` `sqr-pow`
5×	`cube-mult` `pow1` `unpow3` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow`
2×	`pow-pow` `pow1/3`
1×	`pow-to-exp` `hypot-udef` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 148

Calls

4 calls:

0.0ms	(hypot re im)
1.0ms	(cbrt (hypot re im))
3.0ms	(pow (cbrt (hypot re im)) 3)
47.0ms	(- (pow (cbrt (hypot re im)) 3) re)

series401.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(hypot re im)
150.0ms	(cbrt (hypot re im))
121.0ms	(pow (cbrt (hypot re im)) 3)
73.0ms	(- (pow (cbrt (hypot re im)) 3) re)

simplify1.3s

Counts

160 → 160

Iterations

Useful iterations: 2 (306.0ms)

Iter	Nodes	Cost
0	158	2671
1	397	1554
2	1780	1086
done	5001	1086

prune616.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cbrt (hypot re im)) 2)
0.6b	(cbrt (cbrt (hypot re im)))
0.7b	(pow (* (cbrt (pow (cbrt (hypot re im)) 2)) (cbrt (cbrt (hypot re im)))) 3)
14.2b	(- (pow (* (cbrt (pow (cbrt (hypot re im)) 2)) (cbrt (cbrt (hypot re im)))) 3) re)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `prod-diff`
22×	`add-cube-cbrt`
13×	`cbrt-prod`
11×	`unpow-prod-down`
8×	`pow1` `fma-neg` `add-exp-log`
7×	`sqr-pow`
6×	`pow-unpow` `pow-pow` `add-log-exp`
5×	`cube-mult` `add-cbrt-cube` `unpow3` `cube-prod`
4×	`expm1-log1p-u` `pow1/3` `log1p-expm1-u`
3×	`pow-exp`
2×	`pow-to-exp` `pow-prod-down` `unpow2` `rem-cube-cbrt` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `pow3` `prod-exp` `cbrt-unprod` `flip--` `distribute-lft-out--`

Counts

4 → 115

Calls

4 calls:

5.0ms	(pow (cbrt (hypot re im)) 2)
2.0ms	(cbrt (cbrt (hypot re im)))
20.0ms	(pow (* (cbrt (pow (cbrt (hypot re im)) 2)) (cbrt (cbrt (hypot re im)))) 3)
27.0ms	(- (pow (* (cbrt (pow (cbrt (hypot re im)) 2)) (cbrt (cbrt (hypot re im)))) 3) re)

series471.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(pow (cbrt (hypot re im)) 2)
132.0ms	(cbrt (cbrt (hypot re im)))
96.0ms	(pow (* (cbrt (pow (cbrt (hypot re im)) 2)) (cbrt (cbrt (hypot re im)))) 3)
75.0ms	(- (pow (* (cbrt (pow (cbrt (hypot re im)) 2)) (cbrt (cbrt (hypot re im)))) 3) re)

simplify1.7s

Counts

127 → 127

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	181	2525
1	450	1703
2	1844	1044
done	5002	852

prune654.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.9b

regimes260.0ms

Accuracy

0% (0.2b remaining)

Error of 12.7b against oracle of 12.5b and baseline of 12.7b

bsearch0.0ms

simplify3.0ms

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

611.0ms	290×	body	640	valid
508.0ms	6092×	body	80	valid
403.0ms	601×	body	2560	valid
222.0ms	495×	body	1280	valid
204.0ms	299×	body	5120	valid
27.0ms	142×	body	320	valid
15.0ms	81×	body	160	valid