Details

sample34.0ms

Algorithm

intervals

Results

9.0ms	196×	body	80	valid
6.0ms	24×	body	2560	valid
3.0ms	9×	body	5120	valid
3.0ms	12×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	4×	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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 36.3b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
26.2b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:

8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (* re re) (* im im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(+ (* re re) (* im im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify103.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (97.0ms)

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

prune106.0ms

Filtered

66 candidates to 52 candidates (21.2%)

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: 19.0b

Counts

67 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
7.3b	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))))
20.3b	(/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))
26.2b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

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)
14.0ms	(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)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
22.0ms	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (44.0ms)

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

prune152.0ms

Filtered

91 candidates to 71 candidates (22.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	90	6	96

Merged error: 7.9b

Counts

96 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* 2.0 (+ 0 (pow im 2)))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
26.2b	(sqrt (+ (* re re) (* im im)))
29.0b	(sqrt (* 2.0 (+ 0 (pow im 2))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

16.0ms	(/ (sqrt (* 2.0 (+ 0 (pow im 2)))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (* 2.0 (+ 0 (pow im 2))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (sqrt (* 2.0 (+ 0 (pow im 2)))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (* 2.0 (+ 0 (pow im 2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	441	1342
1	1671	1268
2	5001	1234

prune193.0ms

Filtered

108 candidates to 80 candidates (25.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	105	9	114

Merged error: 2.2b

Counts

114 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (fabs im))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
26.2b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

11.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(* (sqrt 2.0) (fabs im))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(* (sqrt 2.0) (fabs im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	437	805
1	2002	734
2	5001	725

prune235.0ms

Filtered

92 candidates to 66 candidates (28.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	89	12	101

Merged error: 0.4b

Counts

101 → 12

regimes209.0ms

Accuracy

44.3% (20.9b remaining)

Error of 21.3b against oracle of 0.4b and baseline of 37.9b

bsearch67.0ms

Steps

Iters	Range		Point
9	1.4084025144316139e+88	1.3907891785976965e+93	1.294245882346397e+91
9	-2.173433833306078e-131	-1.2323979110488597e-139	-7.46472792011177e-134
4	-3299728841212.5835	-1664988039241.9263	-1969972166812.6543

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	31
1	64	31
2	65	31
3	65	31

end0.0ms

sample964.0ms

Algorithm

intervals

Results

284.0ms	6051×	body	80	valid
182.0ms	667×	body	2560	valid
104.0ms	466×	body	1280	valid
95.0ms	282×	body	5120	valid
55.0ms	294×	body	640	valid
24.0ms	167×	body	320	valid
6.0ms	73×	body	160	valid

Details

sample34.0ms

simplify6.0ms

prune3.0ms

localize9.0ms

rewrite26.0ms

series41.0ms

simplify103.0ms

prune106.0ms

localize14.0ms

rewrite39.0ms

series45.0ms

simplify53.0ms

prune152.0ms

localize16.0ms

rewrite35.0ms

series38.0ms

simplify60.0ms

prune193.0ms

localize13.0ms

rewrite27.0ms

series44.0ms

simplify52.0ms

prune235.0ms

regimes209.0ms

bsearch67.0ms

simplify2.0ms

end0.0ms

sample964.0ms

Profiling