Details

sample59.0ms

Algorithm

intervals

Results

19.0ms	270×	body	80	nan
17.0ms	256×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	16
1	52	16
2	68	16
3	88	16
4	102	16
5	106	16
6	106	16
done	106	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.3b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `hypot-def` `div-inv`

Counts

4 → 117

Calls

4 calls:

30.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
8.0ms	(* (atan2 im re) (log base))
9.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
29.0ms	(* (atan2 im re) (log base))
155.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	466	1254
1	1924	1122
2	5001	1083
done	5001	1083

prune425.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:

5.0ms

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

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

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

simplify53.0ms

Counts

36 → 36

Iterations

Useful iterations: 4 (50.0ms)

Iter	Nodes	Cost
0	105	215
1	272	201
2	673	200
3	1915	198
4	5002	196
done	5002	196

prune104.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

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:

5.0ms	(/ 1 (log base))
15.0ms	(* (atan2 im re) (/ 1 (log base)))

series199.0ms

Counts

2 → 6

Calls

2 calls:

160.0ms	(/ 1 (log base))
39.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify47.0ms

Counts

84 → 84

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	210	419
1	833	361
2	2681	319
3	5001	312
done	5001	312

prune176.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (/ 1 (log base)))
0.3b	(log1p (expm1 (/ 1 (log base))))
0.3b	(/ 1 (log base))
0.3b	(* (atan2 im re) (log1p (expm1 (/ 1 (log base)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
10×	`add-exp-log`
8×	`add-cbrt-cube`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-/r*` `log-pow` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`div-exp`
1×	`cbrt-undiv` `rec-exp` `log1p-udef` `expm1-log1p` `pow-flip` `frac-2neg` `1-exp` `log1p-expm1` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow` `expm1-udef` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

0.0ms	(expm1 (/ 1 (log base)))
0.0ms	(log1p (expm1 (/ 1 (log base))))
5.0ms	(/ 1 (log base))
7.0ms	(* (atan2 im re) (log1p (expm1 (/ 1 (log base)))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(expm1 (/ 1 (log base)))
293.0ms	(log1p (expm1 (/ 1 (log base))))
159.0ms	(/ 1 (log base))
64.0ms	(* (atan2 im re) (log1p (expm1 (/ 1 (log base)))))

simplify45.0ms

Counts

91 → 91

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	184	449
1	633	379
2	1485	352
3	5001	337
done	5001	337

prune174.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes219.0ms

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	3
1	6	3
done	6	3

end0.0ms

sample1.6s

Algorithm

intervals

Results

543.0ms	7931×	body	80	nan
538.0ms	8000×	body	80	valid