Details

sample17.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	8
1	7	8

prune3.0ms

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: 31.0b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
29.2b	(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)))

series11.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ (* re re) (* im im))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify27.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5098	295

prune53.0ms

Filtered

25 candidates to 32 candidates (-28.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	6	33

Merged error: 7.3b

Counts

33 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

6.0ms	(+ (* re re) (* im im))
15.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
5.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5300	1445

prune105.0ms

Filtered

69 candidates to 136 candidates (-97.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	136	6	142

Merged error: 7.3b

Counts

142 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (sqrt (+ (* re re) (* im im)))))
1.0b	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 5)
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
18×	`cbrt-prod`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
8×	`sqrt-div`
7×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`rem-sqrt-square` `cbrt-div` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

4.0ms	(cbrt (sqrt (sqrt (+ (* re re) (* im im)))))
6.0ms	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 5)
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (sqrt (sqrt (+ (* re re) (* im im)))))
38.0ms	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 5)
6.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

simplify35.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4916	1153
1	4916	1153

prune117.0ms

Filtered

65 candidates to 88 candidates (-35.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	88	6	94

Merged error: 7.3b

Counts

94 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

5.0b	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt 5))
6.1b	(pow (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt 5)) (sqrt 5))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

40×	`unpow-prod-down`
30×	`sqrt-prod`
21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`cbrt-prod`
12×	`pow-unpow`
7×	`pow1` `add-exp-log`
5×	`pow-exp`
4×	`sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `sqr-pow`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow1/3`

Counts

4 → 95

Calls

4 calls:

7.0ms	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt 5))
9.0ms	(pow (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt 5)) (sqrt 5))
4.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt 5))
55.0ms	(pow (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt 5)) (sqrt 5))
5.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4904	1779
1	4904	1779

prune192.0ms

Filtered

77 candidates to 107 candidates (-39.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	107	6	113

Merged error: 7.3b

Counts

113 → 6

regimes493.0ms

Accuracy

58.2% (9.9b remaining)

Error of 17.9b against oracle of 8.0b and baseline of 31.6b

bsearch44.0ms

Steps

Iters	Range		Point
5	4.9831912547538184e+91	1.3655005271697367e+92	1.2882041961296455e+92
9	-7.676761036242019e-305	3.3654627424431923e-307	-2.7978321376001454e-306
8	-9.68551370084772e-266	-3.1195446902457074e-268	-4.786656859853452e-266
7	-3.8095654050866245e+140	-5.961519079968264e+138	-9.340803523077166e+139

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	36
1	20	36

end0.0ms

sample443.0ms

Algorithm

intervals

Results

233.0ms

8000×

body

valid

Details

sample17.0ms

simplify3.0ms

prune3.0ms

localize5.0ms

rewrite7.0ms

series11.0ms

simplify27.0ms

prune53.0ms

localize8.0ms

rewrite32.0ms

series22.0ms

simplify63.0ms

prune105.0ms

localize11.0ms

rewrite19.0ms

series69.0ms

simplify35.0ms

prune117.0ms

localize22.0ms

rewrite25.0ms

series103.0ms

simplify44.0ms

prune192.0ms

regimes493.0ms

bsearch44.0ms

simplify1.0ms

end0.0ms

sample443.0ms

Profiling