Details

sample56.0ms

Algorithm

intervals

Results

20.0ms	283×	body	80	nan
18.0ms	256×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

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

rewrite4.0ms

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)
2.0ms	(/ (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 (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series583.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot re im)
148.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
114.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
270.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify834.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (191.0ms)

Iter	Nodes	Cost
0	111	1384
1	199	1361
2	528	1185
3	2003	1140
done	5000	1140

prune350.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

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:

2.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
10.0ms	(/ (/ (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 (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series816.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
249.0ms	(/ (/ (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))))
126.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
276.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.1s

Counts

175 → 175

Iterations

Useful iterations: 2 (173.0ms)

Iter	Nodes	Cost
0	259	6925
1	542	6658
2	1893	5576
done	5000	5576

prune665.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize18.0ms

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log`
6×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `hypot-udef` `pow-pow` `frac-2neg` `flip3-+` `div-exp` `pow-exp` `clear-num` `log-pow` `flip-+` `fma-udef` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

0.0ms	(hypot re im)
11.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (+ (pow (log base) 2) (* 0.0 0.0)))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
2.0ms	(pow (log base) 2)

series456.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
139.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (+ (pow (log base) 2) (* 0.0 0.0)))
118.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
153.0ms	(pow (log base) 2)

simplify2.0s

Counts

84 → 84

Iterations

Useful iterations: 3 (506.0ms)

Iter	Nodes	Cost
0	137	1454
1	280	1401
2	873	1202
3	3571	1190
done	5000	1190

prune350.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (pow 0.0 4))) (- (pow (log base) 2) (* 0.0 0.0)))
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.5b	(pow (log base) 2)
0.9b	(pow (log base) 4)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
51×	`associate-l`
47×	`unpow-prod-down` `*-un-lft-identity`
46×	`times-frac`
32×	`add-cube-cbrt`
31×	`difference-of-squares`
23×	`sqr-pow`
18×	`prod-diff`
15×	`pow1`
11×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in`
9×	`add-cbrt-cube` `distribute-lft-out--`
7×	`associate-r` `log-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `pow-to-exp` `sub-neg` `pow-pow` `associate-*r/` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 153

Calls

4 calls:

75.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (pow 0.0 4))) (- (pow (log base) 2) (* 0.0 0.0)))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
1.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 4)

series568.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (pow 0.0 4))) (- (pow (log base) 2) (* 0.0 0.0)))
108.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
150.0ms	(pow (log base) 2)
168.0ms	(pow (log base) 4)

simplify1.1s

Counts

165 → 165

Iterations

Useful iterations: 2 (225.0ms)

Iter	Nodes	Cost
0	293	4738
1	707	4575
2	2606	4261
done	5000	4261

prune681.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes251.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	17	27
done	17	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

582.0ms	8095×	body	80	nan
561.0ms	8000×	body	80	valid