Details

sample37.0ms

Algorithm

intervals

Results

9.0ms	197×	body	80	valid
5.0ms	19×	body	2560	valid
3.0ms	11×	body	5120	valid
2.0ms	9×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

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

prune8.0ms

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: 34.7b

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)))
1.4b	(- (sqrt (+ (* re re) (* im im))) re)
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* re re) (* im im))
285.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
58.0ms	(- (sqrt (+ (* re re) (* im im))) re)
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify109.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (102.0ms)

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

prune568.0ms

Filtered

66 candidates to 52 candidates (21.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	6	67

Merged error: 16.7b

Counts

67 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

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:

15.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
17.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
57.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
45.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (33.0ms)

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

prune791.0ms

Filtered

138 candidates to 75 candidates (45.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	138	6	144

Merged error: 16.7b

Counts

144 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

4.7b	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
8.0b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

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:

16.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
18.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
58.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
45.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify116.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (106.0ms)

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

prune660.0ms

Filtered

73 candidates to 58 candidates (20.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	72	7	79

Merged error: 16.7b

Counts

79 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ re (sqrt (+ (* re re) (* im im))))
5.2b	(sqrt (* 2.0 (/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))))
20.2b	(/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`times-frac` `associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
2×	`cbrt-undiv` `pow1/2` `div-exp` `associate-/r/`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l`

Counts

4 → 64

Calls

4 calls:

8.0ms	(+ re (sqrt (+ (* re re) (* im im))))
8.0ms	(sqrt (* 2.0 (/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))))
8.0ms	(/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ re (sqrt (+ (* re re) (* im im))))
282.0ms	(sqrt (* 2.0 (/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))))
80.0ms	(/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	360	615
1	1446	549
2	5001	544

prune529.0ms

Filtered

76 candidates to 61 candidates (19.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	3	2	5
Picked	1	0	1
Done	1	0	1
Total	75	8	83

Merged error: 5.9b

Counts

83 → 8

regimes278.0ms

Accuracy

51.1% (16.9b remaining)

Error of 23.6b against oracle of 6.7b and baseline of 41.2b

bsearch225.0ms

Steps

Iters	Range		Point
7	4.8914605440667675e-73	6.934968998500573e-71	6.833290088645846e-71
7	2.258437560461299e-144	5.301064092581315e-143	2.5078630276629363e-144
8	-9.016048349064981e-116	-1.611851990013556e-120	-1.5117392918292036e-117
8	-4.6951025956694755e+83	-2.6917416856478413e+79	-2.1221575183959992e+83

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	34
1	69	34
2	70	34
3	70	34

end0.0ms

sample971.0ms

Algorithm

intervals

Results

286.0ms	6060×	body	80	valid
178.0ms	662×	body	2560	valid
108.0ms	503×	body	1280	valid
100.0ms	300×	body	5120	valid
44.0ms	257×	body	640	valid
19.0ms	151×	body	320	valid
6.0ms	67×	body	160	valid

Details

sample37.0ms

simplify6.0ms

prune8.0ms

localize10.0ms

rewrite23.0ms

series418.0ms

simplify109.0ms

prune568.0ms

localize12.0ms

rewrite44.0ms

series187.0ms

simplify46.0ms

prune791.0ms

localize16.0ms

rewrite42.0ms

series201.0ms

simplify116.0ms

prune660.0ms

localize12.0ms

rewrite29.0ms

series460.0ms

simplify41.0ms

prune529.0ms

regimes278.0ms

bsearch225.0ms

simplify2.0ms

end0.0ms

sample971.0ms

Profiling