Details

sample52.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
16.0ms	238×	body	80	nan

simplify59.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

0.0ms	(hypot re im)
5.0ms	(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series418.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
69.0ms	(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
30.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
268.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: 3 (196.0ms)

Iter	Nodes	Cost
0	105	1432
1	189	1415
2	504	1233
3	1974	1176
done	5000	1176

prune329.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

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:

2.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify1.9s

Counts

36 → 36

Iterations

Useful iterations: 4 (425.0ms)

Iter	Nodes	Cost
0	64	394
1	108	375
2	273	351
3	726	348
4	1830	344
done	5000	344

prune114.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

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:

2.0ms	(/ 1 (log base))
9.0ms	(* (atan2 im re) (/ 1 (log base)))

series186.0ms

Counts

2 → 6

Calls

2 calls:

150.0ms	(/ 1 (log base))
36.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify7.8s

Counts

84 → 84

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	104	789
1	217	650
2	645	546
3	1368	540
4	4336	533
done	5001	533

prune157.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.5b	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
0.6b	(pow (log base) 2)
0.7b	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`unpow-prod-down`
7×	`pow1`
6×	`add-exp-log` `pow-unpow` `cube-prod`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp`
1×	`pow1/3` `log-pow` `rem-cbrt-cube` `fma-udef` `unpow2` `rem-cube-cbrt`

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
1.0ms	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
1.0ms	(pow (log base) 2)
1.0ms	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

series579.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
166.0ms	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
148.0ms	(pow (log base) 2)
229.0ms	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

simplify629.0ms

Counts

91 → 91

Iterations

Useful iterations: done (627.0ms)

Iter	Nodes	Cost
0	121	1178
1	258	999
2	881	841
done	5000	829

prune304.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes222.0ms

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	6	6
done	6	6

end0.0ms

sample1.5s

Algorithm

intervals

Results

562.0ms	7982×	body	80	nan
549.0ms	8000×	body	80	valid