Details

sample45.0ms

Algorithm

intervals

Results

15.0ms	192×	body	80	valid
8.0ms	24×	body	2560	valid
5.0ms	12×	body	5120	valid
4.0ms	15×	body	1280	valid
2.0ms	8×	body	640	valid
1.0ms	5×	body	320	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: 36.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(- (sqrt (+ (* re re) (* im im))) re)
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
27.5b	(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:

3.0ms	(+ (* re re) (* im im))
21.0ms	(- (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
167.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (86.0ms)

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

prune182.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
15.6b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

19.0ms	(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
29.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
36.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
44.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	283	630
1	843	573
2	2616	551
3	5001	542

prune208.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 17.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* 2.0 (- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)))
6.2b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
15.4b	(- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
28.7b	(log (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`pow1`
9×	`add-cube-cbrt`
7×	`log-prod`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`unpow-prod-up` `unpow-prod-down` `log-div` `pow-unpow` `pow-pow` `add-cbrt-cube` `difference-of-squares`
3×	`exp-prod`
2×	`flip3--` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `log-pow` `flip--` `flip-+` `pow-sub` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow1/2` `diff-log` `rem-log-exp` `pow-prod-down` `pow-exp` `sqrt-prod` `distribute-lft-out--`

Counts

4 → 70

Calls

4 calls:

18.0ms	(sqrt (* 2.0 (- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)))
4.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
31.0ms	(- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
3.0ms	(log (+ (* re re) (* im im)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(sqrt (* 2.0 (- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)))
90.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
83.0ms	(- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
50.0ms	(log (+ (* re re) (* im im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	357	777
1	1044	725
2	3608	711
3	5001	711

prune252.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 17.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
5.7b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
18.8b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite56.0ms

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:

16.0ms	(+ (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)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
190.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
66.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

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

prune269.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.4b

regimes261.0ms

Accuracy

49.8% (16.9b remaining)

Error of 23.5b against oracle of 6.6b and baseline of 40.3b

bsearch273.0ms

Steps

Iters	Range		Point
9	9.50952901782843e-47	6.779405834972355e-42	1.9398757964769447e-46
4	7.098467696212769e-70	1.1045196728765084e-69	1.0921861446497823e-69
9	5.747594650239893e-182	8.817810593434959e-176	8.691413232173067e-176
10	-3.26871225291865e-154	-1.5627956907882408e-164	-1.4954106951247716e-157
8	-9.72357179598616e+41	-2.255398393290054e+38	-6.949865884075484e+41

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	41
1	87	41
2	88	41
3	88	41

end0.0ms

sample1.2s

Algorithm

intervals

Results

492.0ms	6072×	body	80	valid
238.0ms	677×	body	2560	valid
140.0ms	474×	body	1280	valid
118.0ms	282×	body	5120	valid
67.0ms	281×	body	640	valid
30.0ms	154×	body	320	valid
8.0ms	60×	body	160	valid