Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	187×	body	80	valid
4.0ms	24×	body	2560	valid
3.0ms	3×	body	320	valid
3.0ms	21×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	10×	body	640	valid
0.0ms	3×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	24	15
done	24	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize10.0ms

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)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
32.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* re re) (* im im))
183.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

63 → 63

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	108	888
1	271	774
2	755	698
3	2070	673
done	5000	668

prune187.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
16.3b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
10.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
45.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* re re) (* im im))
40.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
47.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts

72 → 72

Iterations

Useful iterations: 4 (1.0s)

Iter	Nodes	Cost
0	108	993
1	220	795
2	537	707
3	1372	699
4	3820	691
done	5001	691

prune205.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)))
6.0b	(pow E (log (sqrt (+ (* re re) (* im im)))))
16.8b	(+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite99.0ms

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` `associate-*r/` `pow-exp` `pow-sub`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `e-exp-1` `pow-pow` `pow-prod-down` `sum-log` `distribute-lft-out` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

36.0ms	(sqrt (* 2.0 (+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)))
10.0ms	(pow E (log (sqrt (+ (* re re) (* im im)))))
44.0ms	(+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(sqrt (* 2.0 (+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)))
88.0ms	(pow E (log (sqrt (+ (* re re) (* im im)))))
78.0ms	(+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

81 → 81

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	151	1392
1	359	1214
2	878	1127
3	2320	1110
done	5000	1109

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.3b

localize25.0ms

Local error

Found 4 expressions with local error:

16.8b	(+ (* (* (cbrt (pow E (log (sqrt (+ (* re re) (* im im)))))) (cbrt (pow E (log (sqrt (+ (* re re) (* im im))))))) (cbrt (pow E (log (sqrt (+ (* re re) (* im im))))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

125.0ms	(+ (* (* (cbrt (pow E (log (sqrt (+ (* re re) (* im im)))))) (cbrt (pow E (log (sqrt (+ (* re re) (* im im))))))) (cbrt (pow E (log (sqrt (+ (* re re) (* im im))))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (* (* (cbrt (pow E (log (sqrt (+ (* re re) (* im im)))))) (cbrt (pow E (log (sqrt (+ (* re re) (* im im))))))) (cbrt (pow E (log (sqrt (+ (* re re) (* im im))))))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

68 → 68

Iterations

Useful iterations: 3 (226.0ms)

Iter	Nodes	Cost
0	66	1385
1	170	1289
2	436	729
3	1156	703
4	4356	703
done	5000	703

prune306.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.3b

regimes185.0ms

Accuracy

57.7% (9.9b remaining)

Error of 27.1b against oracle of 17.2b and baseline of 40.5b

bsearch69.0ms

Steps

Iters	Range		Point
7	2396706146367806.5	3.79592842151896e+17	3.714271113375256e+17
6	1.478477427851433e-187	1.012626979561533e-186	2.0091743860303698e-187

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	81
1	45	81
2	47	81
done	47	81

end0.0ms

sample710.0ms

Algorithm

intervals

Results

190.0ms	5985×	body	80	valid
138.0ms	722×	body	2560	valid
79.0ms	478×	body	1280	valid
68.0ms	290×	body	5120	valid
34.0ms	284×	body	640	valid
13.0ms	142×	body	320	valid
6.0ms	99×	body	160	valid