Details

sample34.0ms

Algorithm

intervals

Results

9.0ms	195×	body	80	valid
5.0ms	20×	body	2560	valid
3.0ms	13×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	30	10
3	32	10
done	32	10

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
1.5b	(+ re (hypot re im))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`add-exp-log` `expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `hypot-udef` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

3 → 42

Calls

3 calls:

1.0ms	(hypot re im)
18.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
13.0ms	(+ re (hypot re im))

series470.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(hypot re im)
318.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
100.0ms	(+ re (hypot re im))

simplify4.9s

Counts

51 → 51

Iterations

Useful iterations: 4 (2.3s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	459	354
3	1219	345
4	3260	344
done	5001	344

prune200.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.6b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`pow1`
22×	`sqrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`sqrt-pow1`
10×	`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×	`fma-def` `pow-sqr`
2×	`flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

2.0ms	(sqrt (hypot re im))
19.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
27.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
13.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (hypot re im))
278.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
97.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
71.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify3.0s

Counts

109 → 109

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	143	1359
1	308	755
2	807	698
3	2369	668
done	5000	658

prune409.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.3b	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
0.8b	(pow (sqrt (sqrt (hypot re im))) 3)
11.7b	(+ re (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

97×	`sqrt-prod`
71×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `unswap-sqr`
10×	`pow1` `add-exp-log`
9×	`associate-l`
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` `fma-def` `prod-exp`
2×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `unpow3` `pow-exp`
1×	`+-commutative` `flip3-+` `sum-log` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `flip-+` `rem-cube-cbrt`

Counts

4 → 151

Calls

4 calls:

5.0ms	(sqrt (sqrt (hypot re im)))
47.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
9.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
12.0ms	(+ re (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(sqrt (sqrt (hypot re im)))
76.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
217.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
76.0ms	(+ re (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)))

simplify1.4s

Counts

163 → 163

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	155	2501
1	357	2124
2	1172	1463
done	5000	1319

prune573.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.3b	(* (sqrt (sqrt (hypot re im))) (pow (pow (hypot re im) 1/4) 3))
0.8b	(pow (pow (hypot re im) 1/4) 3)
10.3b	(+ re (* (sqrt (sqrt (hypot re im))) (pow (pow (hypot re im) 1/4) 3)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
43×	`sqrt-prod`
41×	`unpow-prod-down`
24×	`unswap-sqr`
23×	`cube-prod`
20×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
15×	`sqr-pow`
14×	`add-exp-log`
9×	`associate-l`
8×	`pow-exp`
7×	`add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `pow-to-exp` `sqrt-pow1` `log1p-expm1-u`
3×	`pow-unpow` `fma-def`
2×	`cube-mult` `rem-sqrt-square` `pow1/2` `unpow3`
1×	`+-commutative` `pow-pow` `flip3-+` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `rem-cube-cbrt`

Counts

4 → 141

Calls

4 calls:

3.0ms	(sqrt (sqrt (hypot re im)))
49.0ms	(* (sqrt (sqrt (hypot re im))) (pow (pow (hypot re im) 1/4) 3))
6.0ms	(pow (pow (hypot re im) 1/4) 3)
7.0ms	(+ re (* (sqrt (sqrt (hypot re im))) (pow (pow (hypot re im) 1/4) 3)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(sqrt (sqrt (hypot re im)))
77.0ms	(* (sqrt (sqrt (hypot re im))) (pow (pow (hypot re im) 1/4) 3))
220.0ms	(pow (pow (hypot re im) 1/4) 3)
70.0ms	(+ re (* (sqrt (sqrt (hypot re im))) (pow (pow (hypot re im) 1/4) 3)))

simplify1.5s

Counts

153 → 153

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	168	2413
1	380	2096
2	1258	2007
done	5000	1996

prune641.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.1b

regimes204.0ms

Accuracy

41.4% (1.3b remaining)

Error of 15.2b against oracle of 13.9b and baseline of 16.2b

bsearch103.0ms

Steps

Iters	Range		Point
6	-3.290796722930356e+197	-4.295207093644367e+196	-7.139122052802705e+196

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	32
1	25	32
done	25	32

end0.0ms

sample2.1s

Algorithm

intervals

Results

968.0ms	5940×	body	80	valid
352.0ms	707×	body	2560	valid
190.0ms	301×	body	640	valid
172.0ms	542×	body	1280	valid
116.0ms	255×	body	5120	valid
30.0ms	166×	body	320	valid
12.0ms	89×	body	160	valid