Details

sample17.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
done	7	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

8.0ms	(+ (* re re) (* im im))
10.0ms	(sqrt (+ (* re re) (* im im)))

series87.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(+ (* re re) (* im im))
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

32 → 32

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	48	379
1	124	347
2	343	295
3	968	295
4	2668	295
done	5000	295

prune105.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (* re re) (* im im))))
0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
29.4b	(cbrt (+ (* re re) (* im im)))
29.4b	(cbrt (+ (* re re) (* im im)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

19.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
40.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
7.0ms	(cbrt (+ (* re re) (* im im)))
7.0ms	(cbrt (+ (* re re) (* im im)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
159.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
125.0ms	(cbrt (+ (* re re) (* im im)))
114.0ms	(cbrt (+ (* re re) (* im im)))

simplify1.9s

Counts

86 → 86

Iterations

Useful iterations: 3 (595.0ms)

Iter	Nodes	Cost
0	126	1572
1	277	1459
2	737	1290
3	1780	1274
done	5000	1274

prune347.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (exp (log (cbrt (+ (* re re) (* im im)))))) (sqrt (cbrt (+ (* re re) (* im im)))))
5.0b	(exp (log (cbrt (+ (* re re) (* im im)))))
29.4b	(cbrt (+ (* re re) (* im im)))
29.4b	(cbrt (+ (* re re) (* im im)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
13×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div` `sqrt-prod`
7×	`pow1`
6×	`add-exp-log` `log-prod` `exp-sum` `add-cbrt-cube`
5×	`exp-prod`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`log-div` `exp-diff` `sqrt-div` `associate-*r/` `log-pow`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 75

Calls

4 calls:

33.0ms	(* (fabs (exp (log (cbrt (+ (* re re) (* im im)))))) (sqrt (cbrt (+ (* re re) (* im im)))))
10.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
5.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (fabs (exp (log (cbrt (+ (* re re) (* im im)))))) (sqrt (cbrt (+ (* re re) (* im im)))))
129.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
129.0ms	(cbrt (+ (* re re) (* im im)))
110.0ms	(cbrt (+ (* re re) (* im im)))

simplify1.5s

Counts

87 → 87

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	150	1701
1	298	1492
2	749	1290
3	1772	1271
done	5001	1263

prune445.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.6b

localize27.0ms

Local error

Found 4 expressions with local error:

29.4b	(cbrt (+ (* re re) (* im im)))
29.4b	(cbrt (+ (* re re) (* im im)))
29.4b	(cbrt (+ (* re re) (* im im)))
29.4b	(cbrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

6.0ms	(cbrt (+ (* re re) (* im im)))
12.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (+ (* re re) (* im im)))
102.0ms	(cbrt (+ (* re re) (* im im)))
111.0ms	(cbrt (+ (* re re) (* im im)))
115.0ms	(cbrt (+ (* re re) (* im im)))

simplify1.5s

Counts

64 → 64

Iterations

Useful iterations: 3 (178.0ms)

Iter	Nodes	Cost
0	51	928
1	125	904
2	286	776
3	612	764
4	1581	764
done	5001	764

prune429.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.6b

regimes370.0ms

Accuracy

56.8% (10.2b remaining)

Error of 18.0b against oracle of 7.8b and baseline of 31.3b

bsearch70.0ms

Steps

Iters	Range		Point
9	3.1969220264351404e+107	2.622192972460871e+114	2.566938280750768e+114
6	-1.932089816811951e+60	-2.426943492373032e+59	-6.38087000272631e+59

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	19
1	14	19
done	14	19

end0.0ms

sample893.0ms

Algorithm

intervals

Results

708.0ms

8000×

body

valid