Details

sample114.0ms

Algorithm

intervals

Results

41.0ms	305×	body	80	nan
33.0ms	256×	body	80	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	18	28
1	27	21
2	33	21
done	33	21

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.5b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.5b	(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)
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series860.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(hypot re im)
162.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
221.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
419.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	111	1384
1	196	1361
2	433	1185
3	1261	1140
done	5000	1131

prune510.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
89×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`associate-/l/`

Counts

4 → 163

Calls

4 calls:

10.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
34.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
172.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
400.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
379.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.5s

Counts

175 → 175

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	259	6925
1	533	6630
2	1110	5576
3	2996	5382
done	5002	5253

prune904.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

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`
8×	`pow1`
6×	`log-prod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`frac-2neg` `clear-num` `log-pow`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 181

Calls

4 calls:

8.0ms	(/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0))
25.0ms	(* (log (hypot re im)) (log base))
24.0ms	(/ (/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0))
125.0ms	(* (log (hypot re im)) (log base))
352.0ms	(/ (/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
404.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.1s

Counts

193 → 193

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	302	7072
1	602	6770
2	1303	5702
3	3499	5505
done	5001	5378

prune980.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.3b	(* (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.4b	(* (log (hypot re im)) (log base))
0.5b	(pow (log base) 2)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`add-exp-log` `times-frac`
17×	`associate-r`
13×	`pow1` `add-cbrt-cube`
7×	`associate-l`
6×	`log-prod`
5×	`prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `associate-/r` `log-pow` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `un-div-inv` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

10.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
34.0ms	(* (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
17.0ms	(* (log (hypot re im)) (log base))
6.0ms	(pow (log base) 2)

series851.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
188.0ms	(* (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
148.0ms	(* (log (hypot re im)) (log base))
209.0ms	(pow (log base) 2)

simplify3.1s

Counts

132 → 132

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	201	2110
1	392	1926
2	996	1642
3	3542	1627
done	5000	1624

prune582.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

regimes526.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	22
1	20	22
done	20	22

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.3s	8062×	body	80	nan