Details

sample40.0ms

Algorithm

intervals

Results

10.0ms	184×	body	80	valid
9.0ms	31×	body	2560	valid
4.0ms	17×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

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: 41.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.1b	(- (sqrt (+ (* re re) (* im im))) re)
32.8b	(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:

4.0ms	(+ (* re re) (* im im))
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)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5269	741

prune118.0ms

Filtered

52 candidates to 66 candidates (-26.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	5	67

Merged error: 18.1b

Counts

67 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (* (* im im) 2.0)) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
1.0b	(+ re (sqrt (+ (* re re) (* im im))))
27.7b	(sqrt (* (* im im) 2.0))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

13.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
8.0ms	(+ re (sqrt (+ (* re re) (* im im))))
4.0ms	(sqrt (* (* im im) 2.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify60.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4945	1904
1	4945	1904

prune162.0ms

Filtered

77 candidates to 105 candidates (-36.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	5	105
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	102	8	110

Merged error: 8.4b

Counts

110 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs im) (/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* re re) (* im im)))))))
0.3b	(/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
1.0b	(+ re (sqrt (+ (* re re) (* im im))))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 167

Calls

4 calls:

18.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* re re) (* im im)))))))
11.0ms	(/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
5.0ms	(+ re (sqrt (+ (* re re) (* im im))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* re re) (* im im)))))))
23.0ms	(/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
7.0ms	(+ re (sqrt (+ (* re re) (* im im))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5156	3251

prune211.0ms

Filtered

102 candidates to 179 candidates (-75.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	178	9	187

Merged error: 6.7b

Counts

187 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 2.0 (+ re (sqrt (+ (* re re) (* im im))))))
0.2b	(* (fabs im) (sqrt (/ 2.0 (+ re (sqrt (+ (* re re) (* im im)))))))
1.0b	(+ re (sqrt (+ (* re re) (* im im))))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

41×	`sqrt-prod`
37×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
8×	`pow1`
7×	`distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+`
3×	`rem-sqrt-square` `associate-l` `unswap-sqr`
2×	`sqrt-pow1` `pow1/2` `div-inv`
1×	`+-commutative` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `-commutative` `cbrt-unprod`

Counts

4 → 96

Calls

4 calls:

8.0ms	(sqrt (/ 2.0 (+ re (sqrt (+ (* re re) (* im im))))))
13.0ms	(* (fabs im) (sqrt (/ 2.0 (+ re (sqrt (+ (* re re) (* im im)))))))
5.0ms	(+ re (sqrt (+ (* re re) (* im im))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (/ 2.0 (+ re (sqrt (+ (* re re) (* im im))))))
28.0ms	(* (fabs im) (sqrt (/ 2.0 (+ re (sqrt (+ (* re re) (* im im)))))))
7.0ms	(+ re (sqrt (+ (* re re) (* im im))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify28.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5215	1705

prune138.0ms

Filtered

83 candidates to 108 candidates (-30.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 6.7b

Counts

117 → 8

regimes318.0ms

Accuracy

57.7% (12.6b remaining)

Error of 20.3b against oracle of 7.7b and baseline of 37.6b

bsearch47.0ms

Steps

Iters	Range		Point
9	2.14645613255865e+90	2.4314027802128217e+95	2.618001455490907e+93
2	-1.6548579541458244e-52	-1.509006250309409e-52	-1.527237713288961e-52

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	50
1	43	50

end0.0ms

sample1.1s

Algorithm

intervals

Results

321.0ms	6024×	body	80	valid
227.0ms	721×	body	2560	valid
119.0ms	451×	body	1280	valid
110.0ms	300×	body	5120	valid
55.0ms	281×	body	640	valid
20.0ms	139×	body	320	valid
9.0ms	84×	body	160	valid

Details

sample40.0ms

simplify3.0ms

prune3.0ms

localize10.0ms

rewrite26.0ms

series42.0ms

simplify40.0ms

prune118.0ms

localize13.0ms

rewrite32.0ms

series39.0ms

simplify60.0ms

prune162.0ms

localize14.0ms

rewrite45.0ms

series65.0ms

simplify63.0ms

prune211.0ms

localize12.0ms

rewrite32.0ms

series64.0ms

simplify28.0ms

prune138.0ms

regimes318.0ms

bsearch47.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling