Details

sample56.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
19.0ms	260×	body	80	nan

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 31.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

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:

17.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
3.0ms	(sqrt (+ (* re re) (* im im)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
87.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
144.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify731.0ms

Counts

122 → 122

Iterations

Useful iterations: done (727.0ms)

Iter	Nodes	Cost
0	200	2451
1	441	2259
2	1349	2035
done	5000	2023

prune487.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.0ms	(cbrt base)
0.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
179.0ms	(cbrt base)
182.0ms	(cbrt base)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

77 → 77

Iterations

Useful iterations: 4 (757.0ms)

Iter	Nodes	Cost
0	116	875
1	229	828
2	555	728
3	1255	707
4	2981	705
done	5000	705

prune398.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
30.2b	(log (+ (* re re) (* im im)))
30.2b	(log (+ (* re re) (* im im)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-prod` `log-prod`
4×	`log-div` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `pow1/3` `rem-log-exp` `log-pow` `flip-+`

Counts

4 → 50

Calls

4 calls:

0.0ms	(cbrt base)
0.0ms	(cbrt base)
2.0ms	(log (+ (* re re) (* im im)))
3.0ms	(log (+ (* re re) (* im im)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt base)
180.0ms	(cbrt base)
53.0ms	(log (+ (* re re) (* im im)))
47.0ms	(log (+ (* re re) (* im im)))

simplify1.7s

Counts

62 → 62

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	70	592
1	151	564
2	312	484
3	648	466
4	1362	466
5	3467	466
done	5000	466

prune396.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
5.1b	(pow (/ 1 base) -1/3)
30.2b	(log (+ (* re re) (* im im)))
30.2b	(log (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`unpow-prod-down`
11×	`add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`log-prod`
4×	`log-div` `pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `pow-pow`
2×	`flip3-+` `div-exp` `rem-log-exp` `log-pow` `flip-+`
1×	`pow-to-exp` `rec-exp` `pow-flip` `pow1/3` `1-exp` `div-inv` `inv-pow` `sqr-pow`

Counts

4 → 71

Calls

4 calls:

0.0ms	(cbrt base)
4.0ms	(pow (/ 1 base) -1/3)
3.0ms	(log (+ (* re re) (* im im)))
3.0ms	(log (+ (* re re) (* im im)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt base)
177.0ms	(pow (/ 1 base) -1/3)
52.0ms	(log (+ (* re re) (* im im)))
46.0ms	(log (+ (* re re) (* im im)))

simplify1.5s

Counts

83 → 83

Iterations

Useful iterations: 4 (677.0ms)

Iter	Nodes	Cost
0	144	856
1	311	769
2	575	679
3	1178	657
4	2951	653
done	5001	653

prune424.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.5b

regimes373.0ms

Accuracy

59.3% (10.0b remaining)

Error of 17.2b against oracle of 7.3b and baseline of 31.8b

bsearch132.0ms

Steps

Iters	Range		Point
9	1.8684288122828866e+141	1.3023166688765237e+147	1.978996135853368e+145
6	-7.134127296663583e+142	-6.065115406379256e+141	-9.507267753592183e+141

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	66
1	50	66
done	50	66

end0.0ms

sample1.6s

Algorithm

intervals

Results

595.0ms	8174×	body	80	nan
591.0ms	8000×	body	80	valid