Details

sample177.0ms

Algorithm

intervals

Results

17.0ms	177×	body	80	valid
16.0ms	32×	body	2560	valid
7.0ms	11×	body	5120	valid
6.0ms	15×	body	1280	valid
4.0ms	12×	body	640	valid
2.0ms	8×	body	320	valid
0.0ms	1×	body	160	valid

simplify111.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (12.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

20.0ms	(sqrt (* (- (hypot re im) re) 2.0))
17.0ms	(- (hypot re im) re)

series411.0ms

Counts

2 → 6

Calls

2 calls:

288.0ms	(sqrt (* (- (hypot re im) re) 2.0))
122.0ms	(- (hypot re im) re)

simplify2.8s

Counts

49 → 49

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	107	626
1	235	523
2	751	446
3	4110	402
done	5000	402

prune193.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* (- (hypot re im) re) 2.0)))
0.4b	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-pow1`
65×	`pow1`
44×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `sqrt-prod`
28×	`sqrt-div`
27×	`add-cube-cbrt`
23×	`pow-prod-down`
20×	`pow1/2`
18×	`prod-diff`
16×	`associate-*l/`
14×	`pow-prod-up`
9×	`flip3--` `swap-sqr` `flip--`
8×	`pow-sqr` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
2×	`sub-neg` `diff-log` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

20.0ms	(sqrt (sqrt (* (- (hypot re im) re) 2.0)))
101.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
7.0ms	(- (hypot re im) re)
7.0ms	(- (hypot re im) re)

series705.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(sqrt (sqrt (* (- (hypot re im) re) 2.0)))
272.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
89.0ms	(- (hypot re im) re)
73.0ms	(- (hypot re im) re)

simplify1.4s

Counts

170 → 170

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	217	2938
1	486	1993
2	1769	1777
done	5001	1689

prune636.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 16.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ (- (pow (cbrt (hypot re im)) 3) re) (* 0 re)) 2.0))
0.6b	(cbrt (hypot re im))
0.7b	(pow (cbrt (hypot re im)) 3)
14.1b	(- (pow (cbrt (hypot re im)) 3) re)

rewrite238.0ms

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`
8×	`pow1`
6×	`add-log-exp` `difference-of-squares` `sqr-pow`
5×	`add-exp-log` `cube-mult` `unpow3`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow`
2×	`pow-pow` `sqrt-pow1` `pow1/3` `sqrt-div` `associate-*l/`
1×	`pow-to-exp` `sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `pow-exp` `sqrt-prod` `flip--` `flip-+` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 153

Calls

4 calls:

141.0ms	(sqrt (* (+ (- (pow (cbrt (hypot re im)) 3) re) (* 0 re)) 2.0))
2.0ms	(cbrt (hypot re im))
7.0ms	(pow (cbrt (hypot re im)) 3)
80.0ms	(- (pow (cbrt (hypot re im)) 3) re)

series658.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(sqrt (* (+ (- (pow (cbrt (hypot re im)) 3) re) (* 0 re)) 2.0))
164.0ms	(cbrt (hypot re im))
142.0ms	(pow (cbrt (hypot re im)) 3)
77.0ms	(- (pow (cbrt (hypot re im)) 3) re)

simplify2.1s

Counts

165 → 165

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	206	2974
1	541	1728
2	2276	1221
done	5001	1219

prune552.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 16.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) (* 0 re)) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.0b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

86.0ms	(sqrt (* (+ (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) (* 0 re)) 2.0))
34.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
27.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series441.0ms

Counts

3 → 9

Calls

3 calls:

272.0ms	(sqrt (* (+ (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) (* 0 re)) 2.0))
73.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
96.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.3s

Counts

94 → 94

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	157	1394
1	384	726
2	1508	630
done	5001	616

prune332.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 16.6b

regimes189.0ms

Accuracy

0% (0.2b remaining)

Error of 13.7b against oracle of 13.4b and baseline of 13.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	11	10
done	11	10

end0.0ms

sample2.4s

Algorithm

intervals

Results

940.0ms	5967×	body	80	valid
365.0ms	687×	body	2560	valid
271.0ms	516×	body	1280	valid
266.0ms	304×	body	5120	valid
118.0ms	282×	body	640	valid
38.0ms	164×	body	320	valid
10.0ms	80×	body	160	valid