Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	185×	body	80	valid
6.0ms	29×	body	2560	valid
4.0ms	14×	body	5120	valid
3.0ms	17×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (sqrt (+ (* re re) (* im im))) re)
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

2 → 30

Calls

2 calls:

22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series84.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 4 (75.0ms)

Iter	Nodes	Cost
0	135	228
1	332	216
2	839	212
3	2503	211
4	5002	210

prune114.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.2b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

27.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
17.0ms	(- (* (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)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
49.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune299.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.2b

localize19.0ms

Local error

Found 4 expressions with local error:

32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

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

series143.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify138.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (133.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune309.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.2b

localize16.0ms

Local error

Found 4 expressions with local error:

4.8b	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
9.2b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-prod` `add-log-exp`
4×	`add-exp-log` `log-prod` `exp-prod` `sqrt-div` `exp-sum` `add-cbrt-cube`
2×	`rem-sqrt-square` `log-div` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `exp-diff` `flip--` `flip-+` `difference-of-squares`
1×	`sub-neg` `diff-log` `log-pow` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

26.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
20.0ms	(- (* (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)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
47.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify111.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (104.0ms)

Iter	Nodes	Cost
0	191	746
1	442	597
2	1109	556
3	3525	548
4	5002	542

prune259.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.2b

regimes222.0ms

Accuracy

52.8% (10.3b remaining)

Error of 27.9b against oracle of 17.6b and baseline of 39.4b

bsearch209.0ms

Steps

Iters	Range		Point
9	168.70424079671096	30809428.134158503	170.89403868901658
5	7.481821374969571e-94	2.990939763206502e-93	2.9310422556598998e-93
11	-1.697635983764772e-254	-9.078934504337964e-275	-3.29470748031614e-260
6	-9.994260456895444e-161	-1.1592916664118923e-161	-1.180833083521909e-161
7	-2.6889041873995e+131	-4.523388921878605e+129	-8.727030045062286e+129

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	63
1	75	63
2	78	63
3	78	63

end0.0ms

sample686.0ms

Algorithm

intervals

Results

203.0ms	6004×	body	80	valid
146.0ms	741×	body	2560	valid
76.0ms	480×	body	1280	valid
71.0ms	296×	body	5120	valid
34.0ms	257×	body	640	valid
13.0ms	142×	body	320	valid
5.0ms	80×	body	160	valid