Details

sample118.0ms

Algorithm

intervals

Results

45.0ms	256×	body	80	valid
38.0ms	305×	body	80	nan

simplify95.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	18	28
1	31	22
2	52	22
3	68	22
4	88	22
5	100	22
6	104	22
done	104	22

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(* (atan2 im re) (log base))
0.4b	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

0.0ms	(hypot re im)
10.0ms	(* (atan2 im re) (log base))
48.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series614.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(hypot re im)
44.0ms	(* (atan2 im re) (log base))
115.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
380.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.3s

Counts

91 → 91

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	153	1628
1	308	1592
2	926	1401
3	3228	1342
done	5000	1341

prune536.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

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` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `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))

simplify2.8s

Counts

36 → 36

Iterations

Useful iterations: 4 (299.0ms)

Iter	Nodes	Cost
0	64	394
1	105	375
2	207	351
3	385	348
4	680	344
5	2117	344
done	5000	344

prune169.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b	(expm1 (/ (atan2 im re) (log base)))
0.2b	(log1p (expm1 (/ (atan2 im re) (log base))))
0.3b	(/ (atan2 im re) (log base))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`associate-/r*` `log-pow` `log1p-expm1-u`
3×	`expm1-log1p-u` `associate-/l*` `add-log-exp`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `div-inv` `expm1-udef`

Counts

3 → 55

Calls

3 calls:

0.0ms	(expm1 (/ (atan2 im re) (log base)))
0.0ms	(log1p (expm1 (/ (atan2 im re) (log base))))
6.0ms	(/ (atan2 im re) (log base))

series215.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(expm1 (/ (atan2 im re) (log base)))
102.0ms	(log1p (expm1 (/ (atan2 im re) (log base))))
44.0ms	(/ (atan2 im re) (log base))

simplify2.1s

Counts

64 → 64

Iterations

Useful iterations: 4 (461.0ms)

Iter	Nodes	Cost
0	88	677
1	139	622
2	277	572
3	538	561
4	1203	549
done	5000	549

prune254.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

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×	`div-exp` `prod-exp` `associate-/r*`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 78

Calls

2 calls:

30.0ms	(* (atan2 im re) (/ 1 (log base)))
9.0ms	(/ 1 (log base))

series247.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(* (atan2 im re) (/ 1 (log base)))
211.0ms	(/ 1 (log base))

simplify3.9s

Counts

84 → 84

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	104	789
1	201	614
2	435	546
3	866	540
4	1647	534
done	5001	534

prune177.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

regimes381.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
done	8	8

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
1.4s	8062×	body	80	nan