Details

sample109.0ms

Algorithm

intervals

Results

37.0ms	245×	body	80	nan
36.0ms	256×	body	80	valid

simplify188.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	18	28
1	31	22
2	52	22
3	68	22
4	88	22
5	102	22
6	106	22
done	106	22

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`log-prod`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `hypot-udef` `flip3--` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

0.0ms	(hypot re im)
24.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
17.0ms	(* (atan2 im re) (log base))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series731.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(hypot re im)
104.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
35.0ms	(* (atan2 im re) (log base))
514.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify926.0ms

Counts

91 → 91

Iterations

Useful iterations: done (922.0ms)

Iter	Nodes	Cost
0	153	1628
1	329	1592
2	1301	1404
done	5001	1348

prune545.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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:

6.0ms

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

series44.0ms

Counts

1 → 3

Calls

1 calls:

44.0ms

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

simplify1.3s

Counts

36 → 36

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	64	394
1	110	375
2	305	353
3	1463	348
done	5000	346

prune193.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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:

17.0ms	(* (atan2 im re) (/ 1 (log base)))
10.0ms	(/ 1 (log base))

series292.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(* (atan2 im re) (/ 1 (log base)))
234.0ms	(/ 1 (log base))

simplify3.1s

Counts

84 → 84

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	104	789
1	225	651
2	1946	548
done	5001	540

prune191.0ms

Pruning

13 alts after pruning (11 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)))
0.3b	(* (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.4b	(* (atan2 im re) (log base))
0.5b	(pow (log base) 2)

rewrite69.0ms

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×	`add-cbrt-cube`
12×	`pow1`
6×	`log-prod` `associate-l`
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` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `flip--` `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 → 123

Calls

4 calls:

5.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
36.0ms	(* (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
20.0ms	(* (atan2 im re) (log base))
4.0ms	(pow (log base) 2)

series673.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
95.0ms	(* (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
45.0ms	(* (atan2 im re) (log base))
226.0ms	(pow (log base) 2)

simplify2.5s

Counts

135 → 135

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	207	2291
1	521	2127
2	2985	1812
done	5002	1802

prune634.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0b

regimes305.0ms

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

sample3.5s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.3s	7978×	body	80	nan