Details

sample109.0ms

Algorithm

intervals

Results

36.0ms	241×	body	80	nan
34.0ms	256×	body	80	valid

simplify274.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	78
5	78
4	74
3	56
2	44
1	27
0	18

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `div-sub` `div-exp` `pow-sqr` `pow-prod-up` `div-inv` `flip--`

Counts

4 → 112

Calls

4 calls:

74.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
12.0ms	(* (atan2 im re) (log base))
17.0ms	(* (log base) (log base))
20.0ms	(sqrt (+ (* re re) (* im im)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
76.0ms	(* (atan2 im re) (log base))
259.0ms	(* (log base) (log base))
75.0ms	(sqrt (+ (* re re) (* im im)))

simplify5.1s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1954
1	511
0	198

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (log base))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

14.0ms

(/ (atan2 im re) (log base))

series104.0ms

Counts

1 → 3

Calls

1 calls:

104.0ms

(/ (atan2 im re) (log base))

simplify5.4s

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
4	1849
3	649
2	272
1	109
0	63

prune491.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ 1 (log base))
0.3b	(* (atan2 im re) (/ 1 (log base)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`associate-r`
15×	`add-exp-log`
12×	`pow1`
9×	`add-cbrt-cube`
7×	`log-pow`
4×	`associate-/r*` `div-exp` `prod-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `insert-posit16` `div-inv` `add-log-exp`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

2 → 76

Calls

2 calls:

13.0ms	(/ 1 (log base))
21.0ms	(* (atan2 im re) (/ 1 (log base)))

series415.0ms

Counts

2 → 6

Calls

2 calls:

312.0ms	(/ 1 (log base))
103.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify5.6s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
4	2315
3	1479
2	769
1	220
0	102

prune737.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 im re) (cbrt (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base)))))
0.3b	(* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base)))
0.5b	(* (/ 1 (log base)) (/ 1 (log base)))
0.6b	(cbrt (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base))))

rewrite386.0ms

Algorithm

rewrite-expression-head

Rules

295×	`add-exp-log`
149×	`prod-exp`
114×	`div-exp`
86×	`times-frac`
82×	`pow1`
80×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
58×	`add-cbrt-cube`
57×	`rec-exp` `1-exp`
50×	`add-cube-cbrt`
36×	`associate-r`
31×	`pow-prod-up`
29×	`pow-flip` `inv-pow`
24×	`swap-sqr`
23×	`cbrt-unprod`
21×	`log-pow`
20×	`cbrt-div` `associate-l` `associate-*r/`
19×	`frac-times` `associate-*l/`
17×	`cbrt-undiv`
13×	`unswap-sqr`
11×	`pow-prod-down`
10×	`un-div-inv`
9×	`pow-sqr`
7×	`pow-plus` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`pow2` `*-commutative`
2×	`cbrt-prod` `pow3`
1×	`pow1/3` `rem-cbrt-cube`

Counts

4 → 304

Calls

4 calls:

28.0ms	(* (atan2 im re) (cbrt (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base)))))
128.0ms	(* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base)))
68.0ms	(* (/ 1 (log base)) (/ 1 (log base)))
112.0ms	(cbrt (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base))))

series1.2s

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (atan2 im re) (cbrt (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base)))))
351.0ms	(* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base)))
407.0ms	(* (/ 1 (log base)) (/ 1 (log base)))
295.0ms	(cbrt (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base))))

simplify8.3s

Counts

316 → 316

Iterations

Iter	Nodes
done	5114
3	3964
2	1655
1	783
0	319

prune2.0s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.0b

regimes1.3s

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	6
0	6

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.5s	7906×	body	80	nan