Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	187×	body	80	valid
7.0ms	26×	body	2560	valid
6.0ms	12×	body	640	valid
3.0ms	14×	body	1280	valid
3.0ms	8×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 39.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.6b	(+ (sqrt (+ (* re re) (* im im))) re)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
24.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5282	690

prune132.0ms

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 18.1b

Counts

64 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ re (sqrt (+ (* re re) (* im im))))
1.6b	(+ re (sqrt (+ (* re re) (* im im))))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`

Counts

4 → 54

Calls

4 calls:

5.0ms	(+ re (sqrt (+ (* re re) (* im im))))
5.0ms	(+ re (sqrt (+ (* re re) (* im im))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

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

66 → 66

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5373	656

prune109.0ms

Filtered

52 candidates to 66 candidates (-26.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	66	10	76

Merged error: 18.1b

Counts

76 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.7b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
30.1b	(cbrt (+ (* re re) (* im im)))
30.1b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

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

series103.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
30.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
20.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4983	1384
1	4983	1384

prune131.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	77	10	87

Merged error: 18.1b

Counts

87 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

5.0b	(exp (log (cbrt (+ (* re re) (* im im)))))
16.2b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
30.1b	(cbrt (+ (* re re) (* im im)))
30.1b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

5.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
11.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
30.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
20.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4908	962
1	4908	962

prune105.0ms

Filtered

54 candidates to 70 candidates (-29.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	69	11	80

Merged error: 18.1b

Counts

80 → 11

regimes355.0ms

Accuracy

58.7% (9.0b remaining)

Error of 26.2b against oracle of 17.2b and baseline of 38.9b

bsearch45.0ms

Steps

Iters	Range	Point
5	4.9831912547538184e+91	1.3655005271697367e+92	1.334568807248231e+92
9	-7.676761036242019e-305	3.3654627424431923e-307	1.220048955493332e-308
8	-9.68551370084772e-266	-3.1195446902457074e-268	-7.213823237359036e-267

Iters

Range

Point

4.9831912547538184e+91

1.3655005271697367e+92

1.334568807248231e+92

-7.676761036242019e-305

3.3654627424431923e-307

1.220048955493332e-308

-9.68551370084772e-266

-3.1195446902457074e-268

-7.213823237359036e-267

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	76
1	48	76

end0.0ms

sample995.0ms

Algorithm

intervals

Results

290.0ms	6022×	body	80	valid
192.0ms	666×	body	2560	valid
111.0ms	487×	body	1280	valid
94.0ms	283×	body	5120	valid
52.0ms	293×	body	640	valid
23.0ms	169×	body	320	valid
7.0ms	80×	body	160	valid

Details

sample41.0ms

simplify3.0ms

prune6.0ms

localize10.0ms

rewrite22.0ms

series41.0ms

simplify40.0ms

prune132.0ms

localize12.0ms

rewrite19.0ms

series26.0ms

simplify63.0ms

prune109.0ms

localize16.0ms

rewrite25.0ms

series103.0ms

simplify61.0ms

prune131.0ms

localize21.0ms

rewrite25.0ms

series90.0ms

simplify68.0ms

prune105.0ms

regimes355.0ms

bsearch45.0ms

simplify1.0ms

end0.0ms

sample995.0ms

Profiling