Details

sample92.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
29.0ms	245×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize84.0ms

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))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite158.0ms

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:

28.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
87.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
21.0ms	(* (log base) (log base))
15.0ms	(sqrt (+ (* re re) (* im im)))

series592.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
152.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
269.0ms	(* (log base) (log base))
61.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

122 → 122

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	200	2451
1	508	2278
2	2908	2038
done	5002	2023

prune764.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.7b

localize42.0ms

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)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
0.5b	(pow (log base) 2)
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite511.0ms

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:

28.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
457.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
3.0ms	(pow (log base) 2)
16.0ms	(sqrt (+ (* re re) (* im im)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
130.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
206.0ms	(pow (log base) 2)
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify6.5s

Counts

116 → 116

Iterations

Useful iterations: 2 (1.7s)

Iter	Nodes	Cost
0	225	2560
1	631	2395
2	4128	2097
done	5000	2097

prune635.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (* 0.0 (pow 0.0 3)))) (- (pow (log base) 2) (* 0.0 0.0)))
0.5b	(pow (log base) 2)
0.9b	(pow (log base) 4)
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-l`
11×	`pow1` `add-exp-log`
10×	`times-frac`
9×	`unpow-prod-down` `add-cbrt-cube`
7×	`associate-r`
6×	`pow-unpow`
4×	`add-log-exp` `difference-of-squares`
3×	`flip3--` `sqrt-prod` `flip--` `sqr-pow`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `sqrt-div` `associate-*r/` `pow-exp` `prod-exp` `associate-/r/` `log-pow` `cbrt-unprod` `unpow2` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

141.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (* 0.0 (pow 0.0 3)))) (- (pow (log base) 2) (* 0.0 0.0)))
3.0ms	(pow (log base) 2)
4.0ms	(pow (log base) 4)
11.0ms	(sqrt (+ (* re re) (* im im)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (* 0.0 (pow 0.0 3)))) (- (pow (log base) 2) (* 0.0 0.0)))
202.0ms	(pow (log base) 2)
279.0ms	(pow (log base) 4)
66.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

110 → 110

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	214	2769
1	625	2646
2	3130	2265
done	5000	2110

prune854.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 7.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
0.7b	(pow (pow (log base) 2) 3)
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`unpow-prod-down`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow-unpow` `cube-prod`
8×	`add-exp-log`
6×	`pow-exp`
5×	`add-cbrt-cube` `sqr-pow`
4×	`pow-to-exp` `log-pow` `unpow2` `add-log-exp`
3×	`pow-pow` `sqrt-prod`
2×	`sqrt-div`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `flip-+` `rem-cube-cbrt`

Counts

4 → 90

Calls

4 calls:

3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
7.0ms	(pow (pow (log base) 2) 3)
16.0ms	(sqrt (+ (* re re) (* im im)))

series859.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(pow (log base) 2)
245.0ms	(pow (log base) 2)
306.0ms	(pow (pow (log base) 2) 3)
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	107	930
1	325	741
2	1452	640
done	5002	616

prune592.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 7.7b

regimes611.0ms

Accuracy

57.6% (10.1b remaining)

Error of 17.4b against oracle of 7.3b and baseline of 31.1b

bsearch268.0ms

Steps

Iters	Range		Point
9	3.3798017511670253e+59	1.829741004869073e+67	4.036687402249309e+65
10	-2.0012938897636947e+86	-6.8211334069886725e+75	-1.0214999287375747e+86

simplify962.0ms

Iterations

Useful iterations: 3 (13.0ms)

Iter	Nodes	Cost
0	42	70
1	60	68
2	81	68
3	128	66
4	260	66
5	379	66
6	519	66
7	708	66
8	958	66
9	1195	66
10	1466	66
11	1747	66
12	2043	66
13	2354	66
14	2675	66
15	3006	66
16	3347	66
17	3713	66
18	4105	66
19	4513	66
20	4948	66
done	5000	66

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.4s	7966×	body	80	nan
1.3s	8000×	body	80	valid