Details

sample121.0ms

Algorithm

intervals

Results

45.0ms	273×	body	80	nan
35.0ms	256×	body	80	valid

simplify97.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.6b	(fma (log base) (log base) (* 0.0 0.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

31.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
7.0ms	(* (atan2 im re) (log base))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series541.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
52.0ms	(* (atan2 im re) (log base))
416.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify765.0ms

Counts

78 → 78

Iterations

Useful iterations: done (761.0ms)

Iter	Nodes	Cost
0	141	1568
1	312	1534
2	1287	1350
done	5000	1294

prune574.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (+ 0 (log base)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
15×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`distribute-lft-out`
5×	`pow1` `associate-/r*`
4×	`log-pow`
3×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
2×	`associate-/r/`
1×	`expm1-log1p-u` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

13.0ms

(/ (atan2 im re) (+ 0 (log base)))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(/ (atan2 im re) (+ 0 (log base)))

simplify517.0ms

Counts

42 → 42

Iterations

Useful iterations: done (516.0ms)

Iter	Nodes	Cost
0	76	562
1	161	429
2	678	408
done	5001	403

prune217.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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×	`associate-/r*` `div-exp` `prod-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

2 → 78

Calls

2 calls:

13.0ms	(* (atan2 im re) (/ 1 (log base)))
5.0ms	(/ 1 (log base))

series284.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(* (atan2 im re) (/ 1 (log base)))
226.0ms	(/ 1 (log base))

simplify3.2s

Counts

84 → 84

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	104	789
1	225	657
2	1838	548
done	5001	540

prune301.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.3b	(* (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.4b	(* (atan2 im re) (log base))
0.6b	(pow (log base) 2)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac` `add-exp-log`
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` `associate-/r` `distribute-lft-in` `cbrt-unprod` `associate-/l`
2×	`frac-times` `cbrt-undiv` `rec-exp` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `div-inv` `flip--`
1×	`pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `pow-exp` `associate-*r/` `un-div-inv` `pow-flip` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

9.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
52.0ms	(* (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
13.0ms	(* (atan2 im re) (log base))
5.0ms	(pow (log base) 2)

series661.0ms

Counts

4 → 12

Calls

4 calls:

307.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
90.0ms	(* (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
39.0ms	(* (atan2 im re) (log base))
224.0ms	(pow (log base) 2)

simplify1.8s

Counts

135 → 135

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	207	2291
1	521	2127
2	2534	1810
done	5000	1789

prune877.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes391.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	9	6
2	10	6
done	10	6

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.0s	8160×	body	80	nan
1.4s	8000×	body	80	valid