Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	195×	body	80	valid
4.0ms	23×	body	2560	valid
3.0ms	12×	body	5120	valid
2.0ms	12×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	4×	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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

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:

2.0ms	(+ (* re re) (* im im))
12.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
18.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
168.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	258	459
1	938	422
2	3098	412
3	5001	410

prune177.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.4b	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
18×	`sqrt-prod`
13×	`*-un-lft-identity`
9×	`pow1` `add-cube-cbrt` `associate-r`
8×	`add-log-exp`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`sqrt-div` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`flip3--` `flip3-+` `associate-*r/` `flip--` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-unprod` `diff-log` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

2.0ms	(+ (* re re) (* im im))
42.0ms	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
20.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* re re) (* im im))
168.0ms	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify134.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	314	691
1	1267	648
2	4889	633
3	5001	633

prune210.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (sqrt (+ (* re re) (* im im))) re)
5.6b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
20.3b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
13.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
191.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
62.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune278.0ms

Filtered

111 candidates to 78 candidates (70.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))
0.1b	(+ (sqrt (+ (* re re) (* im im))) re)
5.6b	(sqrt (* 2.0 (* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`associate-r`
14×	`add-cube-cbrt`
13×	`pow1` `times-frac`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`sqrt-pow1` `pow-prod-down` `sqrt-prod` `distribute-lft-out`
3×	`flip3-+` `sqrt-div` `associate-r/` `associate-l*` `flip-+`
2×	`pow1/2` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `div-exp` `sum-log` `*-commutative` `div-inv`

Counts

4 → 77

Calls

4 calls:

45.0ms	(* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))
14.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (* 2.0 (* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
192.0ms	(sqrt (* 2.0 (* im (/ im (+ (sqrt (+ (* re re) (* im im))) re)))))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	428	701
1	1831	618
2	5002	614

prune211.0ms

Filtered

89 candidates to 66 candidates (74.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

regimes257.0ms

Accuracy

44.8% (18.2b remaining)

Error of 24.1b against oracle of 5.8b and baseline of 38.8b

bsearch299.0ms

Steps

Iters	Range		Point
8	7.123313112193616e+69	1.9477646189705448e+74	1.2256843292073932e+73
8	6.621149997396504e-158	8.617823638084847e-155	7.282899940538032e-158
10	8.658111435367597e-305	1.828871157960009e-292	1.4576614458613933e-304
8	-4.975022232779082e-229	-4.501245741150392e-232	-1.8443361170365075e-231
6	-4.033472907955283e-182	-9.183397464113432e-183	-2.0514133168585066e-182
9	-2.57686138200627e-111	-4.6087528996132826e-120	-1.651091264846107e-119
7	-8.786369008283137e+83	-5.731627655371417e+81	-1.2671946284215746e+83

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	49
1	81	49
2	82	49
3	82	49

end0.0ms

sample662.0ms

Algorithm

intervals

Results

202.0ms	6025×	body	80	valid
129.0ms	684×	body	2560	valid
77.0ms	492×	body	1280	valid
69.0ms	303×	body	5120	valid
34.0ms	283×	body	640	valid
13.0ms	142×	body	320	valid
4.0ms	71×	body	160	valid