Details

sample61.0ms

Algorithm

intervals

Results

22.0ms	270×	body	80	nan
17.0ms	256×	body	80	valid

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: 30.8b

localize19.0ms

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))
28.6b	(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)))
9.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
103.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
152.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune449.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(* (log base) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
146.0ms	(* (log base) (log base))
153.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify155.0ms

Counts

127 → 127

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	262	719
1	966	639
2	4681	599
3	5001	592
done	5001	592

prune594.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(* (log base) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(* (log base) (log base))
147.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify142.0ms

Counts

127 → 127

Iterations

Useful iterations: 3 (135.0ms)

Iter	Nodes	Cost
0	262	719
1	966	639
2	4681	599
3	5001	592
done	5001	592

prune417.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

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:

9.0ms	(* (log base) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
8.0ms	(sqrt (+ (* re re) (* im im)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (log base) (log base))
183.0ms	(cbrt base)
184.0ms	(cbrt base)
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Counts

85 → 85

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	212	330
1	679	298
2	2893	277
3	5002	269
done	5002	269

prune422.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

regimes619.0ms

Accuracy

57.3% (10.3b remaining)

Error of 17.6b against oracle of 7.2b and baseline of 31.4b

bsearch72.0ms

Steps

Iters	Range		Point
1	3.035498575876273e+124	3.192300066163628e+124	3.0746989484481115e+124
5	-3.9748410989376374e+83	-1.447130845847479e+83	-2.296946323958964e+83

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	59
1	74	59
2	77	59
3	77	59
done	77	59

end0.0ms

sample1.6s

Algorithm

intervals

Results

550.0ms	8000×	body	80	valid
549.0ms	7931×	body	80	nan