Details

sample15.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify2.0ms

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: 30.8b

localize5.0ms

Local error

Found 1 expressions with local error:

29.0b

(sqrt (+ (* re re) (* im im)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

8.0ms

(sqrt (+ (* re re) (* im im)))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

18 → 18

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	38	213
1	91	186
2	205	170
3	444	164
4	1114	164
5	3182	164
done	5001	164

prune47.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.3b

localize10.0ms

Local error

Found 2 expressions with local error:

5.9b	(exp (log (sqrt (+ (* re re) (* im im)))))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

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

series75.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

43 → 43

Iterations

Useful iterations: 4 (280.0ms)

Iter	Nodes	Cost
0	77	573
1	136	465
2	260	415
3	511	403
4	1213	397
5	3423	397
done	5001	397

prune92.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b	(pow (exp (* (cbrt (log (sqrt (+ (* re re) (* im im))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))
29.0b	(sqrt (+ (* re re) (* im im)))
29.0b	(sqrt (+ (* re re) (* im im)))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

9.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* re re) (* im im))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))
7.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* re re) (* im im))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))
39.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

82 → 82

Iterations

Useful iterations: 3 (204.0ms)

Iter	Nodes	Cost
0	86	1674
1	190	1532
2	421	1390
3	1005	1363
4	2728	1363
done	5000	1363

prune264.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.3b

localize33.0ms

Local error

Found 4 expressions with local error:

29.0b	(sqrt (+ (* re re) (* im im)))
29.0b	(sqrt (+ (* re re) (* im im)))
29.0b	(sqrt (+ (* re re) (* im im)))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	205	680
3	444	656
4	1114	656
5	3182	656
done	5001	656

prune321.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.3b

regimes319.0ms

Accuracy

57.1% (10.1b remaining)

Error of 18.1b against oracle of 8.0b and baseline of 31.4b

bsearch44.0ms

Steps

Iters	Range		Point
10	9.511609313434486e+66	1.6770313419776726e+82	1.9498916237070175e+80
8	-3.265571337685236e+43	-5.264462161218697e+40	-3.2252572021582465e+43

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample536.0ms

Algorithm

intervals

Results

367.0ms

8000×

body

valid