Details

sample62.0ms

Algorithm

intervals

Results

20.0ms	207×	body	80	valid
13.0ms	19×	body	2560	valid
9.0ms	15×	body	1280	valid
6.0ms	8×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	640	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	24
2	24
1	22
0	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `sqrt-prod` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `sum-log` `pow1/2` `associate-*r/`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

14.0ms	(+ (* re re) (* im im))
31.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
28.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* re re) (* im im))
277.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
71.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

63 → 63

Iterations

Iter	Nodes
3	3034
2	862
1	275
0	108

prune675.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (sqrt (+ (* im im) (* re re))) re)
17.9b	(cbrt (* (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2.0)) (* (+ (sqrt (+ (* im im) (* re re))) re) 2.0)))
31.8b	(sqrt (+ (* im im) (* re re)))
31.8b	(sqrt (+ (* im im) (* re re)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

14×	`associate-*l/`
10×	`sqrt-div`
9×	`flip3-+` `flip-+`
8×	`add-sqr-sqrt` `cbrt-div` `*-un-lft-identity`
6×	`pow1` `add-cube-cbrt` `sqrt-prod` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `add-exp-log`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `+-commutative` `sum-log` `pow1/3` `distribute-lft-out`

Counts

4 → 59

Calls

4 calls:

18.0ms	(+ (sqrt (+ (* im im) (* re re))) re)
112.0ms	(cbrt (* (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2.0)) (* (+ (sqrt (+ (* im im) (* re re))) re) 2.0)))
10.0ms	(sqrt (+ (* im im) (* re re)))
10.0ms	(sqrt (+ (* im im) (* re re)))

series927.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (sqrt (+ (* im im) (* re re))) re)
748.0ms	(cbrt (* (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2.0)) (* (+ (sqrt (+ (* im im) (* re re))) re) 2.0)))
43.0ms	(sqrt (+ (* im im) (* re re)))
53.0ms	(sqrt (+ (* im im) (* re re)))

simplify1.9s

Counts

71 → 71

Iterations

Iter	Nodes
3	5135
2	1250
1	383
0	157

prune879.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
6.1b	(exp (log (sqrt (+ (* re re) (* im im)))))
11.8b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`sqrt-prod`
6×	`log-prod` `exp-prod` `sqrt-div` `exp-sum` `add-log-exp`
4×	`sqrt-pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
3×	`pow1/2` `log-pow`
2×	`log-div` `exp-diff` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `pow-prod-down` `distribute-lft-out` `rem-exp-log`

Counts

4 → 62

Calls

4 calls:

45.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
14.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
26.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
56.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
81.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify756.0ms

Counts

74 → 74

Iterations

Iter	Nodes
3	2145
2	750
1	292
0	138

prune808.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)))
6.3b	(pow E (log (sqrt (+ (* re re) (* im im)))))
11.6b	(+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
7×	`sqrt-prod`
6×	`unpow-prod-up` `pow-unpow` `log-prod` `sqrt-div` `add-log-exp`
5×	`add-exp-log`
4×	`sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`unpow-prod-down` `pow1/2` `log-pow`
2×	`log-div` `pow-exp` `associate-*r/` `pow-sub`
1×	`pow-to-exp` `+-commutative` `rem-sqrt-square` `e-exp-1` `sum-log` `pow-pow` `pow-prod-down` `distribute-lft-out` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

37.0ms	(sqrt (* 2.0 (+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)))
13.0ms	(pow E (log (sqrt (+ (* re re) (* im im)))))
47.0ms	(+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(sqrt (* 2.0 (+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)))
100.0ms	(pow E (log (sqrt (+ (* re re) (* im im)))))
104.0ms	(+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

81 → 81

Iterations

Iter	Nodes
3	2971
2	953
1	369
0	151

prune929.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.7b

regimes944.0ms

Accuracy

57.8% (8.7b remaining)

Error of 26.3b against oracle of 17.6b and baseline of 38.2b

bsearch501.0ms

Steps

Iters	Range		Point
10	1.5347927881719531e+137	1.0303134579162717e+148	4.4479284942813524e+142
9	8.078157939339514e-228	5.9061123396576155e-223	1.4105722211090752e-227
10	-7.074938547279042e-300	4.152164446645693e-307	1.1909114483375085e-307
9	-5.217970362381025e-156	-3.024207974548735e-165	-2.563508143180615e-158
9	-1.2268005148271795e-109	-1.0428395993042302e-117	-3.896078043343783e-117

simplify13.0ms

Iterations

Iter	Nodes
2	67
1	67
0	51

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	5984×	body	80	valid
500.0ms	678×	body	2560	valid
363.0ms	519×	body	1280	valid
312.0ms	305×	body	5120	valid
137.0ms	276×	body	640	valid
52.0ms	163×	body	320	valid
38.0ms	75×	body	160	valid