Details

sample112.0ms

Algorithm

intervals

Results

48.0ms	256×	body	80	valid
32.0ms	248×	body	80	nan

simplify91.0ms

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	102	22
6	106	22
done	106	22

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

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)
46.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
14.0ms	(* (atan2 im re) (log base))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series566.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(hypot re im)
73.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
42.0ms	(* (atan2 im re) (log base))
392.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify829.0ms

Counts

91 → 91

Iterations

Useful iterations: done (826.0ms)

Iter	Nodes	Cost
0	153	1628
1	329	1592
2	1301	1404
done	5001	1348

prune536.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 184

Calls

4 calls:

33.0ms	(/ (/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
13.0ms	(* (atan2 im re) (log base))
33.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (hypot (log base) 0.0))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series790.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
40.0ms	(* (atan2 im re) (log base))
114.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (hypot (log base) 0.0))
417.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.4s

Counts

196 → 196

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	301	7380
1	685	7075
2	3051	6003
done	5001	5809

prune973.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite16.0ms

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

Counts

1 → 65

Calls

1 calls:

12.0ms

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

series80.0ms

Counts

1 → 3

Calls

1 calls:

80.0ms

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

simplify1.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (622.0ms)

Iter	Nodes	Cost
0	108	903
1	201	857
2	688	833
3	3734	828
done	5000	828

prune225.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite70.0ms

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` `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 → 134

Calls

2 calls:

11.0ms	(/ 1 (- (log base)))
49.0ms	(* (atan2 im re) (/ 1 (- (log base))))

series304.0ms

Counts

2 → 6

Calls

2 calls:

233.0ms	(/ 1 (- (log base)))
70.0ms	(* (atan2 im re) (/ 1 (- (log base))))

simplify7.9s

Counts

140 → 140

Iterations

Useful iterations: done (7.9s)

Iter	Nodes	Cost
0	160	1500
1	378	1189
2	2974	1045
done	5000	1041

prune274.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes252.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	28
1	19	28
done	19	28

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.2s	7721×	body	80	nan