Details

sample43.0ms

Algorithm

intervals

Results

13.0ms	202×	body	80	valid
7.0ms	19×	body	2560	valid
3.0ms	12×	body	1280	valid
3.0ms	11×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	24	15
done	24	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 38

Calls

3 calls:

8.0ms	(+ (* re re) (* im im))
59.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (+ (* re re) (* im im)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* re re) (* im im))
67.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify673.0ms

Counts

47 → 47

Iterations

Useful iterations: done (671.0ms)

Iter	Nodes	Cost
0	69	595
1	196	534
2	1003	468
done	5000	460

prune175.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
13.2b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

17.0ms	(+ (* re re) (* im im))
22.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
73.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
17.0ms	(sqrt (+ (* re re) (* im im)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* re re) (* im im))
48.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
67.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify734.0ms

Counts

72 → 72

Iterations

Useful iterations: done (730.0ms)

Iter	Nodes	Cost
0	108	993
1	247	807
2	1124	707
done	5000	699

prune262.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (+ (* re re) (* im im))) re)
5.2b	(sqrt (* 2.0 (/ (+ (* im im) 0) (- (sqrt (+ (* re re) (* im im))) re))))
22.4b	(/ (+ (* im im) 0) (- (sqrt (+ (* re re) (* im im))) re))
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
9×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out--`
3×	`sqrt-pow1` `sqrt-div` `associate-/l*`
2×	`flip3--` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `frac-2neg` `diff-log` `associate-*r/` `div-exp` `pow-prod-down` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
53.0ms	(sqrt (* 2.0 (/ (+ (* im im) 0) (- (sqrt (+ (* re re) (* im im))) re))))
67.0ms	(/ (+ (* im im) 0) (- (sqrt (+ (* re re) (* im im))) re))
8.0ms	(sqrt (+ (* re re) (* im im)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (sqrt (+ (* re re) (* im im))) re)
324.0ms	(sqrt (* 2.0 (/ (+ (* im im) 0) (- (sqrt (+ (* re re) (* im im))) re))))
90.0ms	(/ (+ (* im im) 0) (- (sqrt (+ (* re re) (* im im))) re))
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

97 → 97

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	174	1974
1	429	1702
2	2204	1554
done	5000	1538

prune482.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fabs im) (/ (fabs im) (- (sqrt (+ (* re re) (* im im))) re)))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
5.2b	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (- (sqrt (+ (* re re) (* im im))) re)))))
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite744.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

110.0ms	(* (fabs im) (/ (fabs im) (- (sqrt (+ (* re re) (* im im))) re)))
63.0ms	(- (sqrt (+ (* re re) (* im im))) re)
556.0ms	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (- (sqrt (+ (* re re) (* im im))) re)))))
9.0ms	(sqrt (+ (* re re) (* im im)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (fabs im) (/ (fabs im) (- (sqrt (+ (* re re) (* im im))) re)))
81.0ms	(- (sqrt (+ (* re re) (* im im))) re)
216.0ms	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (- (sqrt (+ (* re re) (* im im))) re)))))
54.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

98 → 98

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	193	1756
1	520	1630
2	3091	1444
done	5001	1428

prune515.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.1b

regimes137.0ms

Accuracy

51.1% (13.7b remaining)

Error of 26.3b against oracle of 12.6b and baseline of 40.7b

bsearch322.0ms

Steps

Iters	Range		Point
10	3.702960000671357e-60	1.0190280957314654e-48	1.1534517708784038e-53
10	8.626847762404864e-188	5.329946125936946e-176	8.736784500225598e-188
9	2.725864644827383e-286	3.074726605702059e-281	3.787000431377414e-283
7	-7.442420077395135e+150	-3.1912007869219815e+148	-7.240673218843522e+150

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	94
1	67	94
done	67	94

end0.0ms

sample2.1s

Algorithm

intervals

Results

968.0ms	6025×	body	80	valid
417.0ms	696×	body	2560	valid
182.0ms	290×	body	5120	valid
144.0ms	466×	body	1280	valid
75.0ms	296×	body	640	valid
27.0ms	150×	body	320	valid
9.0ms	77×	body	160	valid