Details

sample83.0ms

Algorithm

intervals

Results

18.0ms	184×	body	80	valid
16.0ms	28×	body	2560	valid
12.0ms	10×	body	640	valid
11.0ms	19×	body	1280	valid
5.0ms	7×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 39.7b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.6b	(- (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

16.0ms	(+ (* re re) (* im im))
46.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (+ (* re re) (* im im)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* re re) (* im im))
45.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
17.0ms	(- (sqrt (+ (* re re) (* im im))) re)
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify175.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (165.0ms)

Iter	Nodes	Cost
0	260	458
1	982	428
2	3667	421
3	5001	420

prune225.0ms

Filtered

66 candidates to 52 candidates (21.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Merged error: 22.2b

Counts

67 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.3b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
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×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

45.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
50.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
11.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (+ (* re re) (* im im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune555.0ms

Filtered

138 candidates to 72 candidates (47.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	138	8	146

Merged error: 22.2b

Counts

146 → 8

localize76.0ms

Local error

Found 4 expressions with local error:

14.9b	(- (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im))))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

70.0ms	(- (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im))))))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))
20.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im))))))) re)
11.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (+ (* re re) (* im im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	158	715
1	473	608
2	1783	574
3	5001	571

prune232.0ms

Filtered

69 candidates to 56 candidates (18.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	69	8	77

Merged error: 22.2b

Counts

77 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

4.5b	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
9.3b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

26.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
23.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
12.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
9.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))

simplify190.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (177.0ms)

Iter	Nodes	Cost
0	191	746
1	442	597
2	1109	556
3	3525	548
4	5002	542

prune194.0ms

Filtered

73 candidates to 58 candidates (20.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	71	10	81

Merged error: 22.2b

Counts

81 → 10

regimes848.0ms

Accuracy

43.7% (12.2b remaining)

Error of 29.3b against oracle of 17.2b and baseline of 38.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	36
1	48	36

end0.0ms

sample2.0s

Algorithm

intervals

Results

629.0ms	6068×	body	80	valid
391.0ms	676×	body	2560	valid
245.0ms	464×	body	1280	valid
189.0ms	294×	body	5120	valid
86.0ms	261×	body	640	valid
47.0ms	159×	body	320	valid
13.0ms	78×	body	160	valid

Details

sample83.0ms

simplify11.0ms

prune7.0ms

localize20.0ms

rewrite103.0ms

series118.0ms

simplify175.0ms

prune225.0ms

localize29.0ms

rewrite118.0ms

series49.0ms

simplify100.0ms

prune555.0ms

localize76.0ms

rewrite124.0ms

series52.0ms

simplify96.0ms

prune232.0ms

localize28.0ms

rewrite65.0ms

series43.0ms

simplify190.0ms

prune194.0ms

regimes848.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling