Details

sample129.0ms

Algorithm

intervals

Results

63.0ms	307×	body	80	nan
32.0ms	256×	body	80	valid

simplify96.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (log base) (atan2 im re))
0.3b	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite42.0ms

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:

18.0ms	(* (log base) (atan2 im re))
22.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series540.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* (log base) (atan2 im re))
158.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
336.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1139
1	290
0	125

prune659.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ (atan2 im re) (log base))

rewrite9.0ms

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:

7.0ms

(/ (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

prune257.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize38.0ms

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))))
0.4b	(* (/ 1 (sqrt (fma (log base) (log base) (* 0.0 0.0)))) (/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0)))))
0.5b	(fma (log base) (log base) (* 0.0 0.0))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
76×	`times-frac`
51×	`*-un-lft-identity`
45×	`add-cube-cbrt`
41×	`sqrt-prod`
28×	`add-exp-log`
22×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `1-exp` `fma-udef` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 149

Calls

4 calls:

24.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
47.0ms	(* (/ 1 (sqrt (fma (log base) (log base) (* 0.0 0.0)))) (/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0)))))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

257.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
202.0ms	(* (/ 1 (sqrt (fma (log base) (log base) (* 0.0 0.0)))) (/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0)))))
412.0ms	(fma (log base) (log base) (* 0.0 0.0))
466.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.5s

Counts

161 → 161

Iterations

Iter	Nodes
done	5001
2	3214
1	589
0	207

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
19×	`pow1` `associate-/r*`
16×	`log-pow`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`expm1-log1p-u` `rec-exp` `clear-num` `frac-2neg` `1-exp` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

2 → 123

Calls

2 calls:

9.0ms	(/ (log base) (atan2 im re))
14.0ms	(/ 1 (/ (log base) (atan2 im re)))

series125.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (log base) (atan2 im re))
66.0ms	(/ 1 (/ (log base) (atan2 im re)))

simplify1.7s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	2215
1	389
0	166

prune428.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes540.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.6s	7995×	body	80	nan
1.2s	8000×	body	80	valid