Details

sample37.0ms

Algorithm

intervals

Results

10.0ms	197×	body	80	valid
7.0ms	24×	body	2560	valid
4.0ms	15×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	8×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 38.9b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.5b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

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)))

series40.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify30.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5508	551

prune110.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 18.0b

Counts

50 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
6.4b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.8b	(sqrt (+ (* re re) (* im im)))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

19.0ms	(sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
15.0ms	(+ (* (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)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
8.0ms	(+ (* (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)))

simplify34.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5664	705

prune116.0ms

Filtered

53 candidates to 66 candidates (-24.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	66	7	73

Merged error: 18.0b

Counts

73 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
14.0b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
29.8b	(sqrt (+ (* re re) (* im im)))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
8×	`pow1`
6×	`log-prod` `exp-prod` `sqrt-div` `exp-sum` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1` `pow1/2` `log-pow`
2×	`rem-sqrt-square` `log-div` `exp-diff`
1×	`+-commutative` `sum-log` `rem-exp-log`

Counts

4 → 63

Calls

4 calls:

7.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
19.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
11.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4955	706
1	4955	706

prune139.0ms

Filtered

58 candidates to 75 candidates (-29.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Merged error: 18.0b

Counts

82 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

6.2b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
14.2b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
29.8b	(sqrt (+ (* re re) (* im im)))
31.0b	(log (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`log-prod` `add-log-exp`
5×	`add-exp-log`
4×	`log-div` `pow-unpow` `pow-pow` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`unpow-prod-up` `unpow-prod-down` `exp-prod` `sqrt-prod`
2×	`sqrt-div` `log-pow` `pow-sub`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-exp` `sum-log` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

7.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
16.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(log (+ (* re re) (* im im)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
50.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(log (+ (* re re) (* im im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4929	866
1	4929	866

prune139.0ms

Filtered

58 candidates to 78 candidates (-34.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	78	8	86

Merged error: 18.0b

Counts

86 → 8

regimes277.0ms

Accuracy

59% (9.6b remaining)

Error of 26.9b against oracle of 17.3b and baseline of 40.6b

bsearch56.0ms

Steps

Iters	Range	Point
9	3.43401543638109e+114	5.025550553073085e+120	1.4458217502685124e+120
10	1.3994626587696508e-214	2.9831774035161146e-199	4.1753668252846765e-213
6	-3.9639939611996993e-296	-2.6703687768748694e-297	-1.613340222761899e-296

Iters

Range

Point

3.43401543638109e+114

5.025550553073085e+120

1.4458217502685124e+120

1.3994626587696508e-214

2.9831774035161146e-199

4.1753668252846765e-213

-3.9639939611996993e-296

-2.6703687768748694e-297

-1.613340222761899e-296

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	98
1	58	98

end0.0ms

sample1.1s

Algorithm

intervals

Results

313.0ms	6013×	body	80	valid
221.0ms	717×	body	2560	valid
123.0ms	493×	body	1280	valid
105.0ms	296×	body	5120	valid
53.0ms	274×	body	640	valid
18.0ms	125×	body	320	valid
8.0ms	82×	body	160	valid

Details

sample37.0ms

simplify2.0ms

prune10.0ms

localize11.0ms

rewrite21.0ms

series40.0ms

simplify30.0ms

prune110.0ms

localize14.0ms

rewrite45.0ms

series47.0ms

simplify34.0ms

prune116.0ms

localize18.0ms

rewrite36.0ms

series30.0ms

simplify47.0ms

prune139.0ms

localize21.0ms

rewrite34.0ms

series93.0ms

simplify105.0ms

prune139.0ms

regimes277.0ms

bsearch56.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling