Details

analyze326.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample33.0ms

Algorithm

intervals

Results

10.0ms	198×	body	80	valid
7.0ms	25×	body	2560	valid
3.0ms	12×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	8×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	52	15
1	52	15

prune7.0ms

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: 35.8b

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)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
24.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify31.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4968	690
1	4968	690

prune132.0ms

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 15.4b

Counts

64 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
13.8b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
12.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
7.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4947	691
1	4947	691

prune139.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	68	11	79

Merged error: 15.3b

Counts

79 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)))
6.2b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
14.0b	(+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
28.1b	(log (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`pow1`
9×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`log-prod` `add-log-exp`
5×	`add-exp-log`
4×	`log-div` `pow-unpow` `pow-pow` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`unpow-prod-up` `unpow-prod-down` `exp-prod`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/` `log-pow` `pow-sub`
1×	`+-commutative` `pow-to-exp` `pow1/2` `rem-log-exp` `pow-prod-down` `pow-exp` `sum-log` `sqrt-prod` `distribute-lft-out` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

10.0ms	(sqrt (* 2.0 (+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)))
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)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (* 2.0 (+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)))
22.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
20.0ms	(+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
10.0ms	(log (+ (* re re) (* im im)))

simplify102.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5346	1046

prune175.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	75	13	88

Merged error: 15.3b

Counts

88 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

5.2b	(pow (exp 1/2) (log (sqrt (+ (* re re) (* im im)))))
14.0b	(+ (* (pow (exp 1/2) (log (sqrt (+ (* re re) (* im im))))) (pow (exp 1/2) (log (sqrt (+ (* re re) (* im im)))))) re)
27.0b	(sqrt (+ (* re re) (* im im)))
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

7.0ms	(pow (exp 1/2) (log (sqrt (+ (* re re) (* im im)))))
15.0ms	(+ (* (pow (exp 1/2) (log (sqrt (+ (* re re) (* im im))))) (pow (exp 1/2) (log (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (exp 1/2) (log (sqrt (+ (* re re) (* im im)))))
24.0ms	(+ (* (pow (exp 1/2) (log (sqrt (+ (* re re) (* im im))))) (pow (exp 1/2) (log (sqrt (+ (* re re) (* im im)))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4926	1103
1	4926	1103

prune187.0ms

Filtered

66 candidates to 84 candidates (-27.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	83	14	97

Merged error: 15.3b

Counts

97 → 14

regimes805.0ms

Accuracy

60.1% (8.6b remaining)

Error of 25.8b against oracle of 17.2b and baseline of 38.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	116	75
1	116	75

end0.0ms

sample950.0ms

Algorithm

intervals

Results

307.0ms	6019×	body	80	valid
199.0ms	692×	body	2560	valid
114.0ms	493×	body	1280	valid
91.0ms	264×	body	5120	valid
54.0ms	301×	body	640	valid
23.0ms	154×	body	320	valid
7.0ms	77×	body	160	valid

Details

analyze326.0ms

sample33.0ms

simplify3.0ms

prune7.0ms

localize10.0ms

rewrite23.0ms

series42.0ms

simplify31.0ms

prune132.0ms

localize14.0ms

rewrite27.0ms

series23.0ms

simplify58.0ms

prune139.0ms

localize23.0ms

rewrite31.0ms

series80.0ms

simplify102.0ms

prune175.0ms

localize23.0ms

rewrite33.0ms

series58.0ms

simplify68.0ms

prune187.0ms

regimes805.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample950.0ms

Profiling