Details

sample61.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
17.0ms	242×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16
done	23	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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)))
0.6b	(* (log base) (log base))
30.1b	(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:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
40.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
105.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
144.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5001	1205
done	5001	1205

prune466.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

41.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
10.0ms	(* (log base) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
150.0ms	(* (log base) (log base))
150.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	386	1610
1	1345	1484
2	5002	1464
done	5002	1464

prune536.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (log base) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

13.0ms	(* (log base) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
8.0ms	(sqrt (+ (* re re) (* im im)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (log base) (log base))
185.0ms	(cbrt base)
176.0ms	(cbrt base)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify101.0ms

Counts

85 → 85

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	212	331
1	679	298
2	2893	277
3	5002	269
done	5002	269

prune650.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
0.6b	(* (log base) (log base))
0.9b	(pow (log base) 4)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

56.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
10.0ms	(* (log base) (log base))
3.0ms	(pow (log base) 4)
8.0ms	(sqrt (+ (* re re) (* im im)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
155.0ms	(* (log base) (log base))
159.0ms	(pow (log base) 4)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	465	1176
1	1940	1064
2	5001	1045
done	5001	1045

prune493.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 7.7b

regimes784.0ms

Accuracy

57.1% (10.7b remaining)

Error of 17.8b against oracle of 7.0b and baseline of 32.1b

bsearch160.0ms

Steps

Iters	Range		Point
8	3.8522157627345126e+68	4.06665183914022e+71	3.0690461012884864e+71
6	-8808000.967096206	-2019765.2821828434	-6023378.701296394

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	86
1	63	86
done	63	86

end0.0ms

sample1.7s

Algorithm

intervals

Results

590.0ms	8215×	body	80	nan
562.0ms	8000×	body	80	valid