Details

sample81.0ms

Algorithm

intervals

Results

27.0ms	251×	body	80	nan
27.0ms	256×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

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))
6.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series896.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(hypot re im)
187.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
177.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
454.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: done (1.3s)

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

prune397.0ms

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))
0.3b	(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))
23.0ms	(/ (/ (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))))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
117.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
374.0ms	(/ (/ (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))))
422.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.2s

Counts

175 → 175

Iterations

Useful iterations: done (2.2s)

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

prune957.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (hypot (log base) 0.0))
0.3b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
0.3b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.4b	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

5.0ms	(/ 1 (hypot (log base) 0.0))
5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
25.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base))))

series1.7s

Counts

4 → 12

Calls

4 calls:

500.0ms	(/ 1 (hypot (log base) 0.0))
493.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
131.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
612.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base))))

simplify2.8s

Counts

142 → 142

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	197	3303
1	437	3105
2	1252	2729
3	4166	2723
done	5000	2721

prune811.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0))
0.3b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
0.3b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.4b	(* (/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`add-exp-log`
28×	`times-frac`
26×	`add-cbrt-cube`
23×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 112

Calls

4 calls:

29.0ms	(/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0))
8.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
52.0ms	(* (/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base))))

series1.4s

Counts

4 → 12

Calls

4 calls:

486.0ms	(/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0))
208.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
131.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
596.0ms	(* (/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base))))

simplify2.8s

Counts

124 → 124

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	186	3345
1	444	2937
2	1189	2408
3	3992	2402
done	5000	2400

prune774.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes379.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	16	24
1	20	22
done	20	22

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.4s	8157×	body	80	nan