Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	31×	body	2560	valid
9.0ms	184×	body	80	valid
4.0ms	12×	body	5120	valid
3.0ms	13×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	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

prune4.0ms

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: 40.9b

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)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

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))
7.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
233.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify109.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (100.0ms)

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

prune246.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	5	67

Merged error: 17.9b

Counts

67 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
8.0b	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))))
19.6b	(/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))))
12.0ms	(/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
228.0ms	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))))
66.0ms	(/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	397	881
1	1554	792
2	5001	781

prune363.0ms

Filtered

91 candidates to 71 candidates (78.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	89	7	96

Merged error: 9.2b

Counts

96 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
8.0b	(sqrt (* 2.0 (* 1 (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im)))))
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

12.0ms	(/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (* 1 (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im))
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
229.0ms	(sqrt (* 2.0 (* 1 (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im)))))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	577	1488
1	2806	1389
2	5001	1380

prune451.0ms

Filtered

134 candidates to 95 candidates (70.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	134	7	141

Merged error: 7.1b

Counts

141 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
8.0b	(sqrt (* 2.0 (* (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
31.1b	(sqrt (+ (* re re) (* im im)))
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
19.0ms	(sqrt (* 2.0 (* (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
203.0ms	(sqrt (* 2.0 (* (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
34.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	324	604
1	1188	571
2	5001	571

prune317.0ms

Filtered

69 candidates to 59 candidates (85.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Merged error: 3.9b

Counts

76 → 7

regimes161.0ms

Accuracy

38.4% (21.1b remaining)

Error of 24.0b against oracle of 2.8b and baseline of 37.1b

bsearch225.0ms

Steps

Iters	Range		Point
6	6.568970859414265e+96	5.17516796102767e+97	3.382417484031491e+97
8	8.62956116525734e-281	4.2885099102982085e-277	1.4514782576781544e-277
10	-4.977893346275263e-227	-2.460166924350784e-238	-2.799196132549358e-233
9	-6.142498275642612e+24	-7.189087651488887e+18	-6.049414038268037e+24

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	37
1	64	37
2	65	37
3	65	37

end0.0ms

sample985.0ms

Algorithm

intervals

Results

281.0ms	5981×	body	80	valid
193.0ms	720×	body	2560	valid
107.0ms	471×	body	1280	valid
106.0ms	317×	body	5120	valid
50.0ms	275×	body	640	valid
20.0ms	153×	body	320	valid
10.0ms	83×	body	160	valid

Details

sample43.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite22.0ms

series343.0ms

simplify109.0ms

prune246.0ms

localize15.0ms

rewrite37.0ms

series378.0ms

simplify55.0ms

prune363.0ms

localize14.0ms

rewrite39.0ms

series373.0ms

simplify80.0ms

prune451.0ms

localize15.0ms

rewrite35.0ms

series322.0ms

simplify38.0ms

prune317.0ms

regimes161.0ms

bsearch225.0ms

simplify2.0ms

end0.0ms

sample985.0ms

Profiling