Details

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 72.674561%

Results

10.0ms	200×	body	80	valid
8.0ms	18×	body	1280	valid
5.0ms	16×	body	2560	valid
3.0ms	8×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	5×	body	160	valid
0.0ms	3×	body	320	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

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: 39.4b

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)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
26.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	277	428
1	1024	399
2	3458	393
3	5002	391

prune124.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 15.1b

Counts

64 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
31.9b	(sqrt (+ (* re re) (* im im)))
31.9b	(sqrt (+ (* re re) (* im im)))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `sqrt-prod`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+ (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)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	141	392
1	358	380
2	866	376
3	2557	375
4	5001	375

prune115.0ms

Filtered

61 candidates to 69 candidates (-13.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	69	8	77

Merged error: 15.1b

Counts

77 → 8

localize15.0ms

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)
31.9b	(sqrt (+ (* re re) (* im im)))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
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×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

14.0ms	(* (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)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune134.0ms

Filtered

74 candidates to 136 candidates (-83.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	135	9	144

Merged error: 15.1b

Counts

144 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

31.9b	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
33.0b	(cbrt (+ (* re re) (* im im)))
33.0b	(cbrt (+ (* re re) (* im im)))
33.0b	(cbrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

17.0ms	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
4.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
22.0ms	(cbrt (+ (* re re) (* im im)))
22.0ms	(cbrt (+ (* re re) (* im im)))
25.0ms	(cbrt (+ (* re re) (* im im)))

simplify174.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (158.0ms)

Iter	Nodes	Cost
0	315	1558
1	727	1517
2	3200	1488
3	5001	1400

prune119.0ms

Filtered

64 candidates to 101 candidates (-57.8%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	101	9	110

Merged error: 15.1b

Counts

110 → 9

regimes739.0ms

Accuracy

54.7% (9.4b remaining)

Error of 27.0b against oracle of 17.6b and baseline of 38.4b

bsearch53.0ms

Steps

Iters	Range	Point
6	5.968187267600891e+131	3.2652973689964837e+132	2.477348669605469e+132
8	2.0466545128858883e-221	9.836257265161428e-218	3.512382318750746e-220
2	-1.5100189378640938e-291	-1.3911766401046742e-291	-1.4357425017644567e-291

Iters

Range

Point

5.968187267600891e+131

3.2652973689964837e+132

2.477348669605469e+132

2.0466545128858883e-221

9.836257265161428e-218

3.512382318750746e-220

-1.5100189378640938e-291

-1.3911766401046742e-291

-1.4357425017644567e-291

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample2.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 72.674561%

Results

293.0ms	6009×	body	80	valid
189.0ms	678×	body	2560	valid
121.0ms	499×	body	1280	valid
96.0ms	284×	body	5120	valid
55.0ms	300×	body	640	valid
21.0ms	153×	body	320	valid
7.0ms	77×	body	160	valid

Details

sample1.4s

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series44.0ms

simplify100.0ms

prune124.0ms

localize15.0ms

rewrite20.0ms

series25.0ms

simplify91.0ms

prune115.0ms

localize15.0ms

rewrite40.0ms

series25.0ms

simplify55.0ms

prune134.0ms

localize15.0ms

rewrite32.0ms

series75.0ms

simplify174.0ms

prune119.0ms

regimes739.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling