Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	187×	body	80	valid
5.0ms	24×	body	2560	valid
3.0ms	9×	body	640	valid
3.0ms	22×	body	1280	valid
2.0ms	7×	body	5120	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

prune2.0ms

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: 39.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.4b	(- (sqrt (+ (* re re) (* im im))) re)
29.3b	(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)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* re re) (* im im))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (56.0ms)

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

prune132.0ms

Filtered

50 candidates to 38 candidates (76.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Merged error: 18.1b

Counts

51 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.4b	(- (* (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)))

rewrite42.0ms

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)))))
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)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
48.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (34.0ms)

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

prune253.0ms

Filtered

138 candidates to 72 candidates (52.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	138	7	145

Merged error: 18.1b

Counts

145 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

6.4b	(- (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (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)))

rewrite30.0ms

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:

15.0ms	(- (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	211	717
1	760	652
2	2681	633
3	5001	618

prune280.0ms

Filtered

69 candidates to 57 candidates (82.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	67	9	76

Merged error: 18.1b

Counts

76 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))
30.2b	(cbrt (+ (* re re) (* im im)))
30.2b	(cbrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

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

series260.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))
92.0ms	(cbrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	141	444
1	440	420
2	1469	416
3	5002	414

prune339.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	68	9	77

Merged error: 18.1b

Counts

77 → 9

regimes217.0ms

Accuracy

55.6% (9.7b remaining)

Error of 27.2b against oracle of 17.6b and baseline of 39.3b

bsearch133.0ms

Steps

Iters	Range	Point
8	1.1972840764496082e-119	4.95419650764683e-115	1.3403485374210323e-119
9	-2.280053641928557e-301	-1.6123238595482796e-307	-8.038653233652543e-303
10	-1.7033952878190482e+127	-1.5035025016881667e+117	-2.88499570758548e+124

Iters

Range

Point

1.1972840764496082e-119

4.95419650764683e-115

1.3403485374210323e-119

-2.280053641928557e-301

-1.6123238595482796e-307

-8.038653233652543e-303

-1.7033952878190482e+127

-1.5035025016881667e+117

-2.88499570758548e+124

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	33
1	50	33

end0.0ms

sample673.0ms

Algorithm

intervals

Results

199.0ms	6060×	body	80	valid
138.0ms	665×	body	2560	valid
78.0ms	500×	body	1280	valid
72.0ms	290×	body	5120	valid
36.0ms	274×	body	640	valid
12.0ms	134×	body	320	valid
5.0ms	77×	body	160	valid