Details

sample86.0ms

Algorithm

intervals

Results

29.0ms	256×	body	80	valid
25.0ms	224×	body	80	nan

simplify134.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	18	28
1	31	22
2	52	22
3	68	22
4	88	22
5	100	22
6	104	22
done	104	22

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize46.0ms

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))

rewrite53.0ms

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)
31.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
18.0ms	(* (atan2 im re) (log base))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series714.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(hypot re im)
117.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
45.0ms	(* (atan2 im re) (log base))
465.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.7s

Counts

91 → 91

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	153	1628
1	308	1592
2	923	1401
3	3207	1342
done	5002	1341

prune612.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r*`
9×	`pow1`
8×	`log-pow`
4×	`neg-mul-1`
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 → 65

Calls

1 calls:

8.0ms

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

series48.0ms

Counts

1 → 3

Calls

1 calls:

48.0ms

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

simplify4.1s

Counts

68 → 68

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	108	903
1	186	857
2	396	831
3	777	823
4	1638	823
done	5000	820

prune243.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
4×	`associate-/r*`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 70

Calls

2 calls:

5.0ms	(/ -1 (log base))
16.0ms	(* (atan2 im re) (/ -1 (log base)))

series308.0ms

Counts

2 → 6

Calls

2 calls:

236.0ms	(/ -1 (log base))
71.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify5.4s

Counts

76 → 76

Iterations

Useful iterations: done (5.4s)

Iter	Nodes	Cost
0	103	741
1	205	670
2	665	612
3	1955	604
done	5000	600

prune278.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (atan2 im re) (log base))
0.5b	(pow (log base) 2)
0.6b	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
0.7b	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
10×	`pow1` `unpow-prod-down`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`pow-unpow` `log-prod` `cube-prod`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `log-pow`
1×	`pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `unpow2` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

15.0ms	(* (atan2 im re) (log base))
3.0ms	(pow (log base) 2)
3.0ms	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
4.0ms	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

series793.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (atan2 im re) (log base))
209.0ms	(pow (log base) 2)
256.0ms	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
292.0ms	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

simplify3.7s

Counts

108 → 108

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	147	1272
1	286	1082
2	788	914
3	4493	803
done	5000	801

prune401.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes316.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 2 (2.0ms)

Iter	Nodes	Cost
0	9	9
1	14	9
2	19	8
3	21	8
done	21	8

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.8s	7907×	body	80	nan
1.2s	8000×	body	80	valid