Details

sample36.0ms

Algorithm

intervals

Results

11.0ms	192×	body	80	valid
6.0ms	21×	body	2560	valid
3.0ms	10×	body	5120	valid
3.0ms	13×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	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

localize10.0ms

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)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

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))
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)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
176.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	274	428
1	986	391
2	3089	381
3	5002	379

prune177.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 17.2b

Counts

64 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.5b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
29.6b	(cbrt (+ (* re re) (* im im)))
29.6b	(cbrt (+ (* re re) (* im im)))

rewrite31.0ms

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:

13.0ms	(* (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)
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
77.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
93.0ms	(cbrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	323	928
1	1214	868
2	5002	841

prune274.0ms

Filtered

77 candidates to 66 candidates (85.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	77	8	85

Merged error: 17.2b

Counts

85 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.8b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.6b	(sqrt (+ (* re re) (* im im)))
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

16.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(+ (* (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)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (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)
34.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune281.0ms

Filtered

136 candidates to 75 candidates (55.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	134	10	144

Merged error: 17.2b

Counts

144 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (pow (sqrt (sqrt (+ (* re re) (* im im)))) 2) re)))
0.5b	(pow (sqrt (sqrt (+ (* re re) (* im im)))) 2)
6.8b	(+ (pow (sqrt (sqrt (+ (* re re) (* im im)))) 2) re)
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

13×	`sqrt-prod`
11×	`pow1` `*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `unpow-prod-down`
7×	`sqrt-pow1`
6×	`add-log-exp`
5×	`add-exp-log` `pow-pow`
4×	`pow1/2` `sqrt-div` `add-cbrt-cube`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`associate-*r/`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow-prod-down` `pow-exp` `sum-log` `sqrt-pow2` `distribute-lft-out` `unpow2` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

12.0ms	(sqrt (* 2.0 (+ (pow (sqrt (sqrt (+ (* re re) (* im im)))) 2) re)))
6.0ms	(pow (sqrt (sqrt (+ (* re re) (* im im)))) 2)
10.0ms	(+ (pow (sqrt (sqrt (+ (* re re) (* im im)))) 2) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(sqrt (* 2.0 (+ (pow (sqrt (sqrt (+ (* re re) (* im im)))) 2) re)))
63.0ms	(pow (sqrt (sqrt (+ (* re re) (* im im)))) 2)
45.0ms	(+ (pow (sqrt (sqrt (+ (* re re) (* im im)))) 2) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify135.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	346	652
1	1078	537
2	3855	517
3	5001	517

prune197.0ms

Filtered

81 candidates to 57 candidates (70.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 17.1b

Counts

91 → 11

regimes257.0ms

Accuracy

57.7% (9.0b remaining)

Error of 27.1b against oracle of 18.1b and baseline of 39.5b

bsearch94.0ms

Steps

Iters	Range		Point
7	3.3840843726061656e+70	7.402926812642739e+71	4.869034385609646e+71
9	4.73015617242873e-254	5.196307842503446e-248	4.796976235399724e-254

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	37
1	45	37

end0.0ms

sample916.0ms

Algorithm

intervals

Results

293.0ms	6010×	body	80	valid
194.0ms	701×	body	2560	valid
110.0ms	490×	body	1280	valid
97.0ms	289×	body	5120	valid
48.0ms	272×	body	640	valid
20.0ms	150×	body	320	valid
8.0ms	88×	body	160	valid