Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	189×	body	80	valid
6.0ms	21×	body	2560	valid
5.0ms	23×	body	1280	valid
4.0ms	12×	body	5120	valid
1.0ms	7×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	320	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: 38.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

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)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	232	382
1	768	356
2	2506	346
3	5001	344

prune141.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	6	53

Merged error: 17.9b

Counts

53 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.9b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(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)))))
14.0ms	(- (* (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)))

series155.0ms

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)
34.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (34.0ms)

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

prune259.0ms

Filtered

138 candidates to 74 candidates (53.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

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

Merged error: 17.9b

Counts

144 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

9.6b	(- (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(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:

17.0ms	(- (* (* (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)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (79.0ms)

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

prune275.0ms

Filtered

69 candidates to 57 candidates (82.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 17.9b

Counts

75 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
6.0b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
20.7b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
193.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
67.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune249.0ms

Filtered

111 candidates to 78 candidates (70.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	3	2	5
Picked	1	0	1
Done	1	0	1
Total	110	8	118

Merged error: 6.3b

Counts

118 → 8

regimes129.0ms

Accuracy

51.1% (16.5b remaining)

Error of 23.3b against oracle of 6.9b and baseline of 40.5b

bsearch325.0ms

Steps

Iters	Range		Point
11	1.9245887430533797e+94	5.58893751983651e+113	1.523986902974247e+108
9	1.3365158712397386e-160	4.579929683924865e-155	6.609119448413203e-159
8	-1.1988158349702404e-300	-2.5281410119806125e-304	-1.1809982177552133e-300
8	-7.945090232726338e-274	-1.6635196992340694e-277	-6.370511219197754e-277
8	-9.509273333275887e-116	-1.9559932207109768e-119	-6.361555833725335e-119
5	-3.8757153595728125e+31	-1.3413705027017693e+31	-2.2147762130159914e+31

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	48
1	78	48
2	79	48
3	79	48

end0.0ms

sample959.0ms

Algorithm

intervals

Results

309.0ms	6008×	body	80	valid
204.0ms	712×	body	2560	valid
113.0ms	493×	body	1280	valid
105.0ms	295×	body	5120	valid
51.0ms	269×	body	640	valid
20.0ms	147×	body	320	valid
7.0ms	76×	body	160	valid