Details

sample114.0ms

Algorithm

intervals

Results

45.0ms	232×	body	80	nan
34.0ms	256×	body	80	valid

simplify83.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	27	28
2	44	28
3	56	28
4	74	28
5	80	28
done	80	28

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize34.0ms

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))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

63.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms	(* (atan2 im re) (log base))
15.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
39.0ms	(* (atan2 im re) (log base))
225.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

120 → 120

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	194	2236
1	508	2059
2	2935	1858
done	5000	1836

prune557.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r*`
9×	`pow1`
8×	`log-pow`
4×	`neg-mul-1`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 63

Calls

1 calls:

10.0ms

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

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

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

simplify1.8s

Counts

66 → 66

Iterations

Useful iterations: 3 (437.0ms)

Iter	Nodes	Cost
0	106	887
1	199	841
2	687	817
3	3597	812
done	5000	812

prune170.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
57×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
50×	`add-cube-cbrt`
40×	`associate-r`
28×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
19×	`pow1`
15×	`add-exp-log`
14×	`log-pow`
12×	`associate-/r*`
9×	`add-cbrt-cube`
7×	`neg-mul-1`
4×	`div-exp` `prod-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 130

Calls

2 calls:

13.0ms	(/ 1 (- (log base)))
42.0ms	(* (atan2 im re) (/ 1 (- (log base))))

series288.0ms

Counts

2 → 6

Calls

2 calls:

219.0ms	(/ 1 (- (log base)))
69.0ms	(* (atan2 im re) (/ 1 (- (log base))))

simplify9.7s

Counts

136 → 136

Iterations

Useful iterations: 2 (792.0ms)

Iter	Nodes	Cost
0	156	1468
1	373	1151
2	3142	1017
done	5000	1017

prune313.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (- (log base)) (atan2 im re))
0.6b	(/ 1 (/ (- (log base)) (atan2 im re)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

300×	`times-frac`
156×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
64×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
43×	`associate-/r*`
35×	`pow1`
32×	`log-pow`
16×	`neg-mul-1`
15×	`add-exp-log` `associate-/l*`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `associate-/r/` `inv-pow`

Counts

2 → 249

Calls

2 calls:

15.0ms	(/ (- (log base)) (atan2 im re))
17.0ms	(/ 1 (/ (- (log base)) (atan2 im re)))

series145.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (- (log base)) (atan2 im re))
80.0ms	(/ 1 (/ (- (log base)) (atan2 im re)))

simplify498.0ms

Counts

255 → 255

Iterations

Useful iterations: done (488.0ms)

Iter	Nodes	Cost
0	303	4424
1	818	3733
done	5000	3641

prune459.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes281.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	10	10
1	17	10
2	22	9
done	22	9

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.4s	8096×	body	80	nan