Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	180×	body	80	valid
5.0ms	26×	body	2560	valid
4.0ms	15×	body	5120	valid
3.0ms	18×	body	1280	valid
1.0ms	10×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

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: 38.9b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-log-exp`
6×	`*-un-lft-identity`
4×	`pow1` `add-cube-cbrt` `sqrt-prod`
3×	`add-exp-log` `add-cbrt-cube`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `sum-log` `flip--` `distribute-lft-out--`

Counts

3 → 41

Calls

3 calls:

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

series114.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	172	305
1	661	282
2	1936	278
3	5002	276

prune131.0ms

Filtered

50 candidates to 38 candidates (76.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	6	51

Merged error: 18.3b

Counts

51 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
18.3b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt` `log-prod` `exp-sum` `add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`exp-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3-+` `log-pow` `flip-+` `difference-of-squares`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `diff-log` `sum-log` `flip--` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
10.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
38.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
46.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	223	519
1	737	467
2	2078	451
3	5001	442

prune194.0ms

Filtered

76 candidates to 53 candidates (69.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	73	9	82

Merged error: 18.2b

Counts

82 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
6.3b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
17.8b	(- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
29.9b	(log (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`pow1` `log-prod`
5×	`add-exp-log`
4×	`unpow-prod-up` `unpow-prod-down` `log-div` `pow-unpow` `pow-pow` `add-cbrt-cube` `difference-of-squares`
3×	`exp-prod` `flip3-+` `flip-+`
2×	`log-pow` `pow-sub` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `distribute-lft-out--`

Counts

4 → 68

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
6.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
9.0ms	(- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
4.0ms	(log (+ (* re re) (* im im)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
98.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
90.0ms	(- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
54.0ms	(log (+ (* re re) (* im im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	302	653
1	1000	609
2	3205	604
3	5001	604

prune242.0ms

Filtered

80 candidates to 59 candidates (73.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	77	12	89

Merged error: 18.1b

Counts

89 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

17.8b	(- (* (* (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
29.9b	(log (+ (* re re) (* im im)))
29.9b	(log (+ (* re re) (* im im)))
29.9b	(log (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
7×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-div` `add-log-exp`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 54

Calls

4 calls:

32.0ms	(- (* (* (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
4.0ms	(log (+ (* re re) (* im im)))
4.0ms	(log (+ (* re re) (* im im)))
4.0ms	(log (+ (* re re) (* im im)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (* (* (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
48.0ms	(log (+ (* re re) (* im im)))
53.0ms	(log (+ (* re re) (* im im)))
49.0ms	(log (+ (* re re) (* im im)))

simplify122.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 4 (114.0ms)

Iter	Nodes	Cost
0	182	818
1	426	645
2	1123	607
3	4102	607
4	5002	587

prune262.0ms

Filtered

66 candidates to 53 candidates (80.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	66	12	78

Merged error: 18.1b

Counts

78 → 12

regimes569.0ms

Accuracy

56.7% (9.3b remaining)

Error of 26.3b against oracle of 17.0b and baseline of 38.4b

bsearch105.0ms

Steps

Iters	Range	Point
7	8.554373099101626e-290	2.7552220295623955e-288	1.1868703169839283e-289
9	-2.2365661558835998e-197	-6.33701187792121e-204	-3.196517835772386e-203
5	-2.1804788916246727e+94	-8.504827414387646e+93	-2.1469124341159173e+94

Iters

Range

Point

8.554373099101626e-290

2.7552220295623955e-288

1.1868703169839283e-289

-2.2365661558835998e-197

-6.33701187792121e-204

-3.196517835772386e-203

-2.1804788916246727e+94

-8.504827414387646e+93

-2.1469124341159173e+94

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	26
1	48	26

end0.0ms

sample696.0ms

Algorithm

intervals

Results

213.0ms	6067×	body	80	valid
131.0ms	662×	body	2560	valid
81.0ms	509×	body	1280	valid
75.0ms	287×	body	5120	valid
36.0ms	252×	body	640	valid
15.0ms	163×	body	320	valid
4.0ms	60×	body	160	valid

Details

sample29.0ms

simplify8.0ms

prune3.0ms

localize15.0ms

rewrite16.0ms

series114.0ms

simplify63.0ms

prune131.0ms

localize15.0ms

rewrite25.0ms

series150.0ms

simplify66.0ms

prune194.0ms

localize22.0ms

rewrite25.0ms

series269.0ms

simplify96.0ms

prune242.0ms

localize26.0ms

rewrite45.0ms

series242.0ms

simplify122.0ms

prune262.0ms

regimes569.0ms

bsearch105.0ms

simplify2.0ms

end0.0ms

sample696.0ms

Profiling