Details

sample60.0ms

Algorithm

intervals

Results

20.0ms	241×	body	80	nan
18.0ms	256×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

13.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
37.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
12.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
104.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
157.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

122 → 122

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	200	2451
1	442	2259
2	1344	2035
3	4400	1998
done	5000	1992

prune472.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.6b

localize248.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-pow` `pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

9.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
38.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

79 → 79

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	87	1040
1	220	921
2	657	827
3	3383	806
done	5001	804

prune513.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`add-cube-cbrt` `associate-r`
16×	`add-exp-log`
14×	`pow1`
11×	`times-frac` `add-cbrt-cube`
9×	`associate-l`
6×	`log-prod`
5×	`prod-exp` `log-pow`
4×	`unpow-prod-down` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod` `cbrt-unprod`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-pow` `1-exp` `associate-*r/` `pow-exp` `un-div-inv` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

71.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
13.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
3.0ms	(pow (log base) 2)
8.0ms	(sqrt (+ (* re re) (* im im)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
98.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
158.0ms	(pow (log base) 2)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.0s

Counts

116 → 116

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	225	2560
1	551	2351
2	1704	2090
done	5001	2065

prune490.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 7.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im)))))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
20×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `sqrt-prod`
14×	`log-pow`
12×	`log-prod`
8×	`swap-sqr`
7×	`sqrt-pow1` `pow1/2`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `sqrt-div` `associate-r` `associate-l` `add-cbrt-cube`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

22.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im)))))
8.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im)))))
37.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

105 → 105

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	100	1938
1	199	1717
2	493	1501
3	1022	1327
4	2594	1302
done	5000	1272

prune430.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.5b

regimes432.0ms

Accuracy

58.2% (10.5b remaining)

Error of 17.9b against oracle of 7.4b and baseline of 32.4b

bsearch141.0ms

Steps

Iters	Range		Point
7	8.138852437921889e+30	4.775882038212059e+32	4.701514344081404e+32
9	-7.63162467251627e+82	-8.28327475749274e+76	-7.514082888019677e+82

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	38	54
1	50	52
2	53	52
done	53	52

end0.0ms

sample1.6s

Algorithm

intervals

Results

550.0ms	8038×	body	80	nan
547.0ms	8000×	body	80	valid