Details

sample100.0ms

Algorithm

intervals

Results

32.0ms	254×	body	80	nan
31.0ms	256×	body	80	valid

simplify109.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	106
6	106
5	102
4	88
3	68
2	52
1	31
0	18

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize44.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.4b	(* (log base) (atan2 im re))
0.6b	(fma (log base) (log base) (* 0.0 0.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
4×	`associate-l`
3×	`expm1-log1p-u` `associate-/r` `associate-r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `flip--` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

24.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
10.0ms	(* (log base) (atan2 im re))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series612.0ms

Counts

3 → 9

Calls

3 calls:

198.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
44.0ms	(* (log base) (atan2 im re))
368.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1131
1	290
0	125

prune664.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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×	`expm1-log1p-u` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

5.0ms

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

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify1.1s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
3	1366
2	302
1	110
0	64

prune322.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r*`
9×	`pow1`
8×	`log-pow`
4×	`neg-mul-1`
3×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
1×	`expm1-log1p-u` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 65

Calls

1 calls:

7.0ms

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

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

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

simplify2.0s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	3854
2	697
1	201
0	108

prune443.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0)))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
0.4b	(* (log base) (atan2 im re))
0.6b	(fma (log base) (log base) (* 0.0 0.0))
0.6b	(fma (log base) (log base) (* 0.0 0.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
145×	`add-sqr-sqrt`
143×	`*-un-lft-identity` `add-cube-cbrt`
132×	`sqrt-prod`
22×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
8×	`div-inv`
7×	`pow1`
6×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r`
2×	`div-sub` `fma-udef`
1×	`clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`

Counts

4 → 219

Calls

4 calls:

38.0ms	(/ (/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0)))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
11.0ms	(* (log base) (atan2 im re))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0)))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
55.0ms	(* (log base) (atan2 im re))
383.0ms	(fma (log base) (log base) (* 0.0 0.0))
368.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.3s

Counts

231 → 231

Iterations

Iter	Nodes
done	5001
2	3931
1	740
0	309

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes615.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
1.7s	7946×	body	80	nan