Details

sample12.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	7	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.4b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite7.0ms

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:

3.0ms	(+ (* re re) (* im im))
3.0ms	(sqrt (+ (* re re) (* im im)))

series64.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* re re) (* im im))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	125	177
1	530	163
2	1540	163
3	5001	162

prune68.0ms

Filtered

32 candidates to 25 candidates (78.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Merged error: 6.0b

Counts

33 → 5

localize11.0ms

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)))))
32.3b	(cbrt (+ (* re re) (* im im)))
32.3b	(cbrt (+ (* re re) (* im im)))

rewrite20.0ms

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:

4.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
111.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
97.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify125.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	277	853
1	1072	799
2	4426	786
3	5002	779

prune235.0ms

Filtered

86 candidates to 72 candidates (83.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	86	5	91

Merged error: 6.0b

Counts

91 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

32.3b	(cbrt (+ (* re re) (* im im)))
32.3b	(cbrt (+ (* re re) (* im im)))
32.3b	(cbrt (+ (* re re) (* im im)))
32.3b	(cbrt (+ (* re re) (* im im)))

rewrite15.0ms

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:

3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (+ (* re re) (* im im)))
98.0ms	(cbrt (+ (* re re) (* im im)))
96.0ms	(cbrt (+ (* re re) (* im im)))
90.0ms	(cbrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	123	488
1	408	452
2	1386	444
3	5001	444

prune261.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	64	5	69

Merged error: 6.0b

Counts

69 → 5

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Merged error: 6.0b

Counts

5 → 5

regimes255.0ms

Accuracy

57.4% (10.2b remaining)

Error of 18.2b against oracle of 8.1b and baseline of 32.0b

bsearch149.0ms

Steps

Iters	Range		Point
7	1.1965702813225714e+120	7.306927196198172e+121	9.233782125719961e+120
7	1.979179890411355e-260	2.941604502943217e-258	5.55126095100351e-260
7	2.363660519479911e-304	1.3429956514040144e-302	6.334115908524809e-304
10	-2.5170109662579546e-211	-5.785550335923721e-221	-1.4034448373480268e-212
10	-2.368742889503448e-151	-4.8620484299604695e-170	-1.1813831187355925e-160
11	-1.2994787762702041e+157	-5.181389473418066e+135	-3.083108636099379e+138

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	13
1	29	13

end0.0ms

sample291.0ms

Algorithm

intervals

Results

170.0ms

8000×

body

valid