Details

sample122.0ms

Algorithm

intervals

Results

47.0ms	245×	body	80	nan
36.0ms	256×	body	80	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (9.0ms)

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize41.0ms

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))
0.4b	(/ (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))

rewrite39.0ms

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:

1.0ms	(hypot re im)
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
35.0ms	(/ (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))

series960.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(hypot re im)
143.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
244.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
509.0ms	(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	197	1361
2	492	1185
3	1860	1140
done	5000	1135

prune537.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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:

10.0ms	(/ 1 (hypot (log base) 0.0))
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)) (hypot (log base) 0.0))
39.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

series2.0s

Counts

4 → 12

Calls

4 calls:

1.0s	(/ 1 (hypot (log base) 0.0))
156.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
241.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
562.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

simplify2.6s

Counts

142 → 142

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	185	3303
1	473	3179
2	3051	2737
done	5000	2735

prune812.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize46.0ms

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))
0.4b	(/ (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)) (hypot (log base) 0.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

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)) (hypot (log base) 0.0))
18.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (hypot (log base) 0.0))

series676.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(hypot re im)
121.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
248.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
248.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (hypot (log base) 0.0))

simplify973.0ms

Counts

133 → 133

Iterations

Useful iterations: done (966.0ms)

Iter	Nodes	Cost
0	194	3869
1	399	3796
2	1601	3522
done	5000	3455

prune795.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
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)) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.5b	(pow (log base) 2)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`times-frac`
18×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
9×	`pow1`
4×	`expm1-log1p-u` `unpow-prod-down` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `un-div-inv` `-commutative` `fma-udef` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

6.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
22.0ms	(* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
4.0ms	(pow (log base) 2)

series834.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
152.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
228.0ms	(* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
202.0ms	(pow (log base) 2)

simplify2.3s

Counts

114 → 114

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	163	1963
1	389	1831
2	2174	1524
done	5002	1515

prune526.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0b

regimes294.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	15	24
1	19	22
2	20	22
done	20	22

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.2s	7966×	body	80	nan