Details

sample37.0ms

Algorithm

intervals

Results

9.0ms	184×	body	80	valid
8.0ms	28×	body	2560	valid
5.0ms	22×	body	1280	valid
3.0ms	9×	body	5120	valid
1.0ms	6×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	3×	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

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: 40.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:

11.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series258.0ms

Counts

3 → 9

Calls

3 calls:

172.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (71.0ms)

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

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	45	7	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	7	53

Merged error: 18.1b

Counts

53 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (+ (* re re) (* im im))) re)
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

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

series167.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 4 (78.0ms)

Iter	Nodes	Cost
0	135	456
1	332	432
2	839	424
3	2503	422
4	5002	420

prune228.0ms

Filtered

72 candidates to 56 candidates (77.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	72	7	79

Merged error: 18.1b

Counts

79 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (sqrt (+ (* re re) (* im im))) re)
5.5b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
19.1b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

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:

6.0ms	(+ (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)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
196.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
67.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (41.0ms)

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

prune263.0ms

Filtered

111 candidates to 78 candidates (70.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	2	3	5
Picked	1	0	1
Done	1	0	1
Total	110	8	118

Merged error: 5.4b

Counts

118 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))
1.4b	(+ (sqrt (+ (* re re) (* im im))) re)
5.5b	(sqrt (* 2.0 (* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

13.0ms	(* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
10.0ms	(sqrt (* 2.0 (* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
195.0ms	(sqrt (* 2.0 (* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	428	701
1	1831	618
2	5002	614

prune188.0ms

Filtered

89 candidates to 67 candidates (75.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	88	9	97

Merged error: 4.8b

Counts

97 → 9

regimes218.0ms

Accuracy

51.2% (17.5b remaining)

Error of 22.8b against oracle of 5.3b and baseline of 41.2b

bsearch265.0ms

Steps

Iters	Range		Point
8	1.4836651054597001e+114	2.4529958308920781e+117	2.4265458997480397e+117
8	5.612942259261838e-23	1.6297369194368678e-18	2.1169694866595254e-22
10	1.4968484379679263e-193	4.990939095712827e-179	2.2522826674058156e-185
7	2.646374358239448e-251	8.73209441103882e-250	7.96106282919079e-250
7	-3.5395546360482146e+146	-2.1109830459205943e+145	-1.797304937847029e+146

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	74
1	90	74
2	91	74
3	91	74

end0.0ms

sample950.0ms

Algorithm

intervals

Results

308.0ms	6061×	body	80	valid
205.0ms	703×	body	2560	valid
119.0ms	487×	body	1280	valid
95.0ms	261×	body	5120	valid
48.0ms	259×	body	640	valid
20.0ms	146×	body	320	valid
8.0ms	83×	body	160	valid

Details

sample37.0ms

simplify8.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series258.0ms

simplify77.0ms

prune141.0ms

localize13.0ms

rewrite23.0ms

series167.0ms

simplify85.0ms

prune228.0ms

localize13.0ms

rewrite35.0ms

series347.0ms

simplify56.0ms

prune263.0ms

localize12.0ms

rewrite37.0ms

series347.0ms

simplify58.0ms

prune188.0ms

regimes218.0ms

bsearch265.0ms

simplify3.0ms

end0.0ms

sample950.0ms

Profiling