Details

sample32.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	8	9
done	8	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (sqrt (+ (* re re) (* im im))))
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

20.0ms	(log (sqrt (+ (* re re) (* im im))))
16.0ms	(sqrt (+ (* re re) (* im im)))

series145.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(log (sqrt (+ (* re re) (* im im))))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.0s

Counts

40 → 40

Iterations

Useful iterations: 3 (152.0ms)

Iter	Nodes	Cost
0	64	536
1	124	490
2	245	436
3	504	424
4	1201	424
5	3316	424
done	5000	424

prune165.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (* re re) (* im im))))
0.3b	(+ (log (fabs (cbrt (+ (* re re) (* im im))))) (log (sqrt (cbrt (+ (* re re) (* im im))))))
32.6b	(cbrt (+ (* re re) (* im im)))
32.6b	(cbrt (+ (* re re) (* im im)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

18.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
32.0ms	(+ (log (fabs (cbrt (+ (* re re) (* im im))))) (log (sqrt (cbrt (+ (* re re) (* im im))))))
5.0ms	(cbrt (+ (* re re) (* im im)))
8.0ms	(cbrt (+ (* re re) (* im im)))

series587.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
219.0ms	(+ (log (fabs (cbrt (+ (* re re) (* im im))))) (log (sqrt (cbrt (+ (* re re) (* im im))))))
112.0ms	(cbrt (+ (* re re) (* im im)))
116.0ms	(cbrt (+ (* re re) (* im im)))

simplify3.5s

Counts

87 → 87

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	140	1635
1	302	1542
2	646	1366
3	1516	1360
4	4594	1359
done	5000	1359

prune510.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.3b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(log (/ -1 re))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`log-prod`
9×	`times-frac`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log`
2×	`pow1` `rem-log-exp`
1×	`log-div` `div-exp` `log-pow` `add-cbrt-cube` `div-inv` `add-log-exp`

Counts

1 → 24

Calls

1 calls:

6.0ms

(log (/ -1 re))

series199.0ms

Counts

1 → 3

Calls

1 calls:

199.0ms

(log (/ -1 re))

simplify8.5s

Counts

27 → 27

Iterations

Useful iterations: 4 (394.0ms)

Iter	Nodes	Cost
0	63	225
1	107	208
2	215	197
3	461	191
4	1046	190
5	2313	190
6	4947	190
done	5000	190

prune75.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 9.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (cbrt (/ -1 re)))
0.2b	(+ (* 2 (log (cbrt (/ -1 re)))) (log (cbrt (/ -1 re))))
0.6b	(cbrt (/ -1 re))
0.6b	(cbrt (/ -1 re))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

78×	`cbrt-prod`
64×	`log-prod`
54×	`times-frac`
51×	`*-un-lft-identity`
50×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`associate-+l+`
16×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
6×	`pow1` `div-inv`
5×	`add-exp-log` `add-log-exp`
4×	`cbrt-div` `add-cbrt-cube`
3×	`pow1/3` `log-pow`
2×	`log-div` `distribute-rgt-out`
1×	`+-commutative` `associate-+r-` `distribute-lft1-in` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(log (cbrt (/ -1 re)))
40.0ms	(+ (* 2 (log (cbrt (/ -1 re)))) (log (cbrt (/ -1 re))))
5.0ms	(cbrt (/ -1 re))
5.0ms	(cbrt (/ -1 re))

series1.4s

Counts

4 → 12

Calls

4 calls:

374.0ms	(log (cbrt (/ -1 re)))
416.0ms	(+ (* 2 (log (cbrt (/ -1 re)))) (log (cbrt (/ -1 re))))
294.0ms	(cbrt (/ -1 re))
304.0ms	(cbrt (/ -1 re))

simplify2.4s

Counts

146 → 146

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	187	1760
1	311	1577
2	618	1464
3	2173	1386
done	5000	1384

prune647.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 9.3b

regimes506.0ms

Accuracy

58.5% (10.2b remaining)

Error of 17.5b against oracle of 7.3b and baseline of 31.9b

bsearch120.0ms

Steps

Iters	Range		Point
8	1.0656776998337841e+73	2.1069570435261278e+76	4.4335689001713803e+74
8	-8.88757827843957e-288	-5.138571342544288e-291	-1.3500686547790216e-288
9	-8.553073611070034e-194	-1.0428205539953484e-198	-1.082781542809915e-198
11	-2.9940927381484837e+161	-7.137879564257508e+129	-1.2571127341226854e+130

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	43
1	26	43
done	26	43

end0.0ms

sample552.0ms

Algorithm

intervals

Results

306.0ms

8000×

body

valid